Implicit calculation method and device for electromagnetic scattering of dielectric-coated conductor composite targets

Abstract

This application discloses a method and device for implicitly calculating electromagnetic scattering of a dielectric-coated conductor composite target. The method comprises: obtaining target data, including a grid data file, a boundary condition file, target calculation electromagnetic parameters, and numerical calculation control parameters, and initializing the calculation space electromagnetic field; iteratively solving the dielectric Maxwell equations using an implicit dual-time-step method based on time iterative advancement of the conserved electromagnetic field in the dielectric and the spatial flux residual: a physical time-step loop is used in the outer layer of the simulation model, and a virtual time-step sub-iteration loop is used in the inner layer; during each virtual time sub-iteration, each edge grid cell in each grid block is sequentially expanded with a virtual image point of the dielectric / conductor boundary; any grid cell in each grid block is subjected to dielectric / dielectric boundary decomposition and interpolation based on discontinuous electromagnetic characteristics; spatial flux and implicit iterative solution calculations are performed; and the next level of numerical values ​​are updated. This method can improve computational efficiency while ensuring accuracy and save costs.

Description

Technical Field

[0001] The present application relates to the field of electromagnetic technology, and in particular to a method and device for implicitly calculating electromagnetic scattering of a dielectric-coated conductor composite target. Background Art

[0002] There are two main categories of numerical simulation methods for electromagnetic scattering from conductor / dielectric composite targets. One is the method of moments family of numerical algorithms for solving electromagnetic current equations. These primarily employ coupled integral equations (CIE) for analysis. Conductor surfaces are described using electric field integral equations (EFIE), magnetic field integral equations (MFIE), or combined field integral equations (CFIE), while dielectric surfaces are analyzed using EFIE or the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equations. Both the equivalent current and the equivalent magnetic flux on the dielectric surface must be calculated. For metal-dielectric composite targets, the surface integral equations require special consideration at the conductor-dielectric interface and the dielectric-dielectric interface to ensure high accuracy. While surface integral equations are generally applicable to targets with piecewise homogeneous dielectrics, as the number of inhomogeneous dielectrics increases, boundary conditions at the interfaces between different dielectrics must be considered, reducing the efficiency of the surface integral equations. For inhomogeneous media, a volume-surface mixed integral equation algorithm must be used. In summary, although the moment method has achieved great success in solving electromagnetic scattering from electrically large-scale conductive targets, for composite targets containing dielectrics / conductors, whether using surface integral equations with surface current basis functions or volume integral equations with volume current basis functions, the number of unknowns increases significantly compared to pure metal scattering problems, and the computational efficiency decreases. Another major category is to solve the electromagnetic Maxwell equations or Helmholtz wave equations to further obtain the time and space distribution of the electromagnetic field. Among the differential equation methods, the finite element method (FEM) and the finite-difference time-domain (FDTD) method are traditionally used. When analyzing scatterer targets, the FEM and FDTD methods require the use of a grid to divide the continuous three-dimensional space region. For spatial regions of finite size, these two methods can effectively solve the target analysis; for the case where the space outside the scatterer is infinite, it is necessary to artificially set boundary conditions to make the solution region have a finite size. This approach will bring truncation errors and grid dispersion errors, and also has high requirements for computer hardware resources.On the other hand, since the 1990s, the hyperbolic mathematical characteristics of the Euler equation have promoted the application of computational fluid dynamics (CFD) techniques in electromagnetic field calculations, with the Finite Difference Time Domain (FDTD) and Finite Volume Time Domain (FVTD) methods being the most prominent. In the 1960s, KSYee published the pioneering Finite Difference Time Domain algorithm, FDTD, which uses a Cartesian orthogonal grid. Simulating complex geometries can easily lead to step effects and errors. The advantage of differential electromagnetic field solutions over integral equation numerical algorithms is that the introduction of a medium does not significantly increase the number of unknowns; the medium primarily affects the eigenvalue relationships between electromagnetic field quantities.

[0003] Changes in the electromagnetic parameters of the medium, such as the dielectric constant and magnetic susceptibility, also cause corresponding changes in the electromagnetic wavelength. Traditional time-domain finite-difference and time-domain finite-volume methods use explicit time-marching formats. A major drawback of the explicit time-domain method is that it is subject to stability constraints. The entire computational space must use a unified minimum global computational step size. The body-fitting mesh generated to simulate drastic changes in geometric shape (for example, the geometric singularities of the leading and trailing edges of a wing lead to drastic changes in electromagnetic field gradients, requiring careful mesh simulation, as well as electromagnetic multi-scale problems) will result in a very small global time step. Large grid cells require more time steps to propagate information within the cell, resulting in a longer computational time for obtaining a stable time-varying electromagnetic field. This is especially true when the electromagnetic wavelength in the medium is smaller than the vacuum electromagnetic wavelength. The stability requirements of the explicit format make the physical time step smaller than that of vacuum electromagnetic scattering problems, resulting in the disadvantage of longer computational time. As a result, the small time step limited by stability leads to a significant increase in the amount of time-domain electromagnetic field calculations, consuming a large amount of computing resources. Secondly, at the dielectric / conductor interface, since the electromagnetic field quantity inside the conductor is zero everywhere, no computational grid is arranged. At the dielectric / conductor boundary, each time step must be specially processed, which brings inconvenience to the field quantity interpolation, information exchange and parallelization, and affects the computational efficiency.

[0004] In summary, how to improve the computational efficiency of electromagnetic scattering problems of dielectric-coated conductor composite targets while ensuring accuracy and saving costs is an urgent problem that needs to be solved. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a method and device for implicitly calculating electromagnetic scattering from composite targets of dielectric-coated conductors. This method can improve the computational efficiency of electromagnetic scattering from composite targets of dielectric-coated conductors while ensuring accuracy, thereby saving costs. The specific solution is as follows:

[0006] In a first aspect, the present application discloses an implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target, comprising:

[0007] Acquire target data and initialize the calculation space electromagnetic field; wherein the target data includes a grid data file, a boundary condition file, target calculation electromagnetic parameters, and numerical calculation control parameters; the grid data file is a grid data file obtained by meshing a simulation model, and the simulation model is a model obtained by simulation modeling based on the physical background and boundary condition information of the electromagnetic problem simulated by the dielectric-coated conductor composite target;

[0008] Based on the target data, and in an implicit dual-time-step method based on time iterative advancement of the conserved electromagnetic field in the medium and spatial flux residual, the time-varying electromagnetic field of the medium Maxwell equations is iteratively solved to obtain the electromagnetic field parameters of the dielectric-coated conductor composite target;

[0009] Among them, the iterative solution of the time-varying electromagnetic field of the medium Maxwell equations based on the target data and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual includes: using a physical time step loop in the outer layer of the simulation model until the calculation converges; using a virtual time step sub-iteration loop in the inner layer of the simulation model until the sub-iteration converges; in each virtual time sub-iteration process, each edge grid unit in each grid block is sequentially expanded with a virtual image point of the dielectric / conductor boundary according to the boundary conditions, any grid unit in each grid block is decomposed and interpolated according to the discontinuous electromagnetic characteristics, spatial flux calculation and implicit iterative solution calculation are performed, and the conserved electromagnetic field value of the next level virtual time sub-iteration step is updated.

[0010] Optionally, obtain the mesh data file, including:

[0011] The simulation model is meshed using a quadrilateral or hexahedron structure. The mesh is denser at the scattering wall and geometric singularities, and becomes increasingly sparse away from the scattering wall. The mesh of the corresponding area is numerically calculated to obtain a mesh data file.

[0012] Optionally, the physical time step loop and virtual time step sub-iterative loop process is:

[0013] Add virtual time derivative term The time-domain Maxwell equations of the medium to be solved are modified as follows:

[0014]

[0015]

[0016]

[0017]

[0018] Where W is the electromagnetic field conservation variable, μ r is the relative magnetic susceptibility, μ0 is the vacuum magnetic susceptibility, ε r is the relative dielectric constant, ε0 is the vacuum dielectric constant, σ m is the magnetic permeability, σ e is the conductivity. Q is the original variable of the scattered electromagnetic field, τ is the virtual time, t is the normalized physical time, F x 、F y 、F z are the x, y, and z components of the electromagnetic flux in the rectangular coordinate system, S is the external source term caused by the magnetic permeability and electrical conductivity of the medium, J is the external forced current vector, and J x 、J y 、J z are the x, y, and z components of the externally forced current in the rectangular coordinate system, and B i is the real-number incident magnetic field intensity vector, D i is the real number incident field electric displacement vector, B is the real number scattered magnetic induction intensity vector, D is the real number scattered field electric displacement vector, E i is the incident electric field intensity vector, H i is the incident field magnetic field intensity vector, E is the scattered field electric field intensity vector, H is the scattered field magnetic field intensity vector, the scalars with subscripts x, y, and z are the rectangular coordinate system x, y, and z components of the corresponding vectors, respectively, and the superscript t corresponds to the total electromagnetic field form;

[0019] when When converged, the system of equations is equivalent to the original system of equations, and the constant virtual time τ subiteration is expressed as:

[0020]

[0021]

[0022] Among them, W * is the value of the electromagnetic field conservation variable after W undergoes virtual time iteration, W * It's W n+1 The superscript * represents the value of the conserved variable corresponding to the virtual time sub-iteration, R is the flux residual, and R * is the residual of the flux residual R after adding the physical time derivative term and the source term; n is the number of physical time steps; Δt is the physical time step length, W n is the electromagnetic conservation variable at the nth physical time step, W n-1 is the electromagnetic conservation variable at the n-1th physical time step; R * (W * ) is W *The corresponding intermediate state flux residual; the physical time derivative of the backward second-order difference is the second-order time accuracy; the stationary sub-iteration part adopts the implicit algorithm:

[0023]

[0024] Among them, ξ, η, ζ represent the three different directions of the structure grid curve coordinate system; F, G, H are the electromagnetic fluxes corresponding to the ξ, η, ζ directions of the curve coordinate system respectively; is the source term of the corresponding curvilinear coordinate system; ω is the implicit control parameter, which is fully implicit when ω = 1; the subscripts i, j, and k are the grid unit numbers. is the electromagnetic conservation variable of the n+1th virtual time step of the i, j, kth grid cell, is the electromagnetic conservation variable of the nth virtual time step of the i, j, kth grid cell, W n+1 is the electromagnetic conservation variable at the n+1th physical time step, W n is the electromagnetic conservation variable at the nth physical time step, W n-1 is the electromagnetic conservation variable at the n-1th physical time step, is the spatial flux residual of the n+1th virtual time step of the i, j, kth grid cell, is the spatial flux residual of the nth virtual time step of the i, j, k-th grid cell, Δτ is the virtual time step controlled by stability, which is calculated by the CFL number and the local grid cell geometric scale and eigenvalue. Different local virtual time sub-iteration steps are used to calculate different grid cells.

[0025] Optionally, the spatial flux calculation process is as follows:

[0026] The Steger-Warming splitting method is used to calculate the interface flux of the grid cells.

[0027]

[0028]

[0029]

[0030] Where the subscript k is one of the directions of the curvilinear coordinate system ξ, η, ζ, and the corresponding F k That is, the electromagnetic flux corresponding to the directions of ξ, η, and ζ, represents the electromagnetic flux obtained by splitting the positive eigenvalue in the Steger-Warming splitting in the corresponding directions of the curvilinear coordinate system ξ, η, ζ; represents the electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding directions of the curvilinear coordinate system ξ, η, ζ; S, S - is the similarity matrix, Λ+ , Λ - are diagonal matrices composed of positive and negative eigenvalues, Q L , Q R Respectively represent the left and right state variables at the interface, using the MUSCL format:

[0031]

[0032]

[0033] Where φ=1 is the limiter, and the subscript i is the grid unit number. Corresponding to the unit interface, κ=1 / 3 is the control parameter of the third-order accuracy format, and Δ are the back-difference and front-difference operators respectively; Represented in grid cells The conserved variables of the left-state electromagnetic field at the interface are: Represented in grid cells The conservation variable of the right state electromagnetic field at the interface; Q i is the conservation variable of the scattered electromagnetic field of the i-th grid unit, Q i+1 is the conservation variable of the scattered electromagnetic field of the i+1th grid cell.

[0034] Optionally, at the medium / conductor boundary, physical and numerical boundary conditions are used to construct the electromagnetic field value of the virtual image point expansion layer;

[0035] The physical and numerical boundary conditions used are:

[0036]

[0037]

[0038]

[0039]

[0040] in, is the unit external normal vector of the conductor wall, E t is the total electric field strength vector on the conductor wall, B t is the total magnetic induction field vector of the conductor wall, E t n is the normal component of the total electric field intensity on the conductor wall, H t is the total magnetic field strength vector on the conductor wall;

[0041] The electromagnetic field value of the constructed virtual image point expansion layer is:

[0042]

[0043]

[0044] E x-2 t =E x-1 t

[0045] H x-2 t =H x-1 t

[0046] The cells in the grid block are numbered x, the two expansion layers are numbered x-1 and x-2 respectively, and the superscript t represents the total field.

[0047] Optionally, corrections can be made to adjacent cells with different wave resistances based on the following physical boundary conditions between media:

[0048]

[0049]

[0050]

[0051]

[0052] Among them, the superscripts s and t represent the scattered field and the total field respectively, and the subscripts L and R represent the left and right states of the interface with different wave resistances respectively. is the unit normal vector of the dielectric interface. The specific correction method of MUSCL interpolation for dielectric interfaces with different wave resistance is as follows: perform MUSCL interpolation on the tangential components of the adjacent electric field intensity and magnetic field intensity respectively; perform MUSCL interpolation on the normal components of the adjacent electric displacement vector and magnetic induction intensity vector respectively; finally, combine the two MUSCL interpolation results to obtain the dielectric interfaces with different wave resistance.

[0053] Optionally, the spatial flux implicit iteration and the splitting forward and backward iteration of the Jacobi coefficient matrix are used to solve the problem, and the Jacobi coefficient Steger-Warming splitting generated by the flux partial derivative conservation variable is obtained.

[0054]

[0055] Among them, A + , A - , B + , B - , C + , C - is the coefficient matrix after splitting, RHS is the spatial flux residual calculated in the previous physical time step, ΔW n is the implicit sub-iteration electromagnetic field difference;

[0056]

[0057] Expressed as LDU, the approximate factorization is:

[0058]

[0059]

[0060]

[0061]

[0062] Wherein, the subscripts i, j, and k are the grid cell numbers, β is the maximum eigenvalue splitting parameter of the Jacobian coefficient matrix, and γ A , γ B , γ C is the maximum eigenvalue of the Jacobian coefficient matrix, I is the unit diagonal matrix, D is the diagonal matrix calculated as above, D + is the upper triangular matrix formed after the negative eigenvalue split, D - is the lower triangular matrix formed after the positive eigenvalue splitting, ΔW + is the difference in electromagnetic conservation variables in the upper triangle corresponding to the split, ΔW - The difference of electromagnetic conservation variables in the lower triangle corresponding to the split; ΔW i-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i-1; ΔW j-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j-1; ΔW k-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k-1; ΔW i+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i+1; ΔW j+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j+1; ΔW k+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k+1; It refers to the coefficient matrix after the adjacent i-1 grid cells are split; It refers to the coefficient matrix after the adjacent j-1 grid cells are split; It refers to the coefficient matrix after the adjacent k-1 grid cells are split; It refers to the coefficient matrix after the adjacent i+1 grid cells are split; It refers to the coefficient matrix after the adjacent j+1 grid cells are split; It refers to the coefficient matrix after the adjacent k+1 grid cells are split;

[0063] The electromagnetic field difference ΔW calculated by forward and backward iteration is obtained:

[0064]

[0065] L=D+D -

[0066] U=D+D +

[0067] Among them, D -1 is the inverse matrix of D, L and U are respectively based on D+D - 、D+D + Calculate the upper triangular matrix and lower triangular matrix obtained;

[0068] Forward loop:

[0069] Backward loop:

[0070] in, It is the intermediate transition variable of the difference of electromagnetic conservation variables;

[0071] Finally, the scattered electromagnetic field Q is obtained by subtracting the analytical incident electromagnetic field from the electromagnetic field conservation variable in the medium:

[0072]

[0073] Among them, μ r is the relative magnetic susceptibility, ε r is the relative dielectric constant, B i is the real-number incident magnetic field intensity vector, D i is the real-valued incident electric displacement vector.

[0074] In a second aspect, the present application discloses an implicit calculation device for electromagnetic scattering of a dielectric-coated conductor composite target, comprising:

[0075] A data acquisition and initialization module is used to acquire target data and initialize the calculation of the spatial electromagnetic field; wherein the target data includes a grid data file, a boundary condition file, target calculation electromagnetic parameters, and numerical calculation control parameters; the grid data file is a grid data file obtained by meshing the simulation model, and the simulation model is a model obtained by simulation modeling based on the physical background and boundary condition information of the electromagnetic problem simulated by the dielectric-coated conductor composite target;

[0076] a calculation module for iteratively solving the time-varying electromagnetic field of the dielectric Maxwell equations based on the target data and in an implicit dual-time-step manner based on time iterative advancement of the conserved electromagnetic field in the dielectric and spatial flux residuals, to obtain electromagnetic field parameters of the dielectric-coated conductor composite target;

[0077] Among them, the iterative solution of the time-varying electromagnetic field of the medium Maxwell equations based on the target data and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual includes: using a physical time step loop in the outer layer of the simulation model until the calculation converges; using a virtual time step sub-iteration loop in the inner layer of the simulation model until the sub-iteration converges; in each virtual time sub-iteration process, each edge grid unit in each grid block is sequentially expanded with a virtual image point of the dielectric / conductor boundary according to the boundary conditions, any grid unit in each grid block is decomposed and interpolated according to the discontinuous electromagnetic characteristics, spatial flux calculation and implicit iterative solution calculation are performed, and the conserved electromagnetic field value of the next level virtual time sub-iteration step is updated.

[0078] In a third aspect, the present application discloses an electronic device, including a memory and a processor, wherein:

[0079] The memory is used to store computer programs;

[0080] The processor is used to execute the computer program to implement the aforementioned implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target.

[0081] In a fourth aspect, the present application discloses a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target.

[0082] It can be seen that the present application obtains target data and initializes the calculation of the spatial electromagnetic field; wherein, the target data includes a grid data file, a boundary condition file, target calculation electromagnetic parameters and numerical calculation control parameters; the grid data file is a grid data file obtained by meshing the simulation model, and the simulation model is a model obtained by simulation modeling based on the physical background and boundary condition information of the electromagnetic problem simulated by the dielectric-coated conductor composite target; based on the target data, and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual, the time-varying electromagnetic field of the dielectric Maxwell equations is iteratively solved to obtain the electromagnetic field parameters of the dielectric-coated conductor composite target; wherein, the target data is obtained by meshing the simulation model, and the boundary condition information is obtained by simulation modeling; based on the target data, and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual, the time-varying electromagnetic field of the dielectric Maxwell equations is iteratively solved to obtain the electromagnetic field parameters of the dielectric-coated conductor composite target; wherein, the target Data, and based on the time iterative advancement of the conserved electromagnetic field in the medium and the implicit dual time step method of the spatial flux residual, the time-varying electromagnetic field of the medium Maxwell equations is iteratively solved, including: using a physical time step loop in the outer layer of the simulation model until the calculation converges; using a virtual time step sub-iteration loop in the inner layer of the simulation model until the sub-iteration converges; in each virtual time sub-iteration process, each edge grid unit in each grid block is sequentially expanded according to the boundary conditions of the medium / conductor boundary virtual image points, and any grid unit in each grid block is decomposed and interpolated according to the discontinuous electromagnetic characteristics of the medium / medium boundary, and the spatial flux calculation and implicit iterative solution calculation are performed, and the next level of virtual time sub-iteration step number of conserved electromagnetic field values ​​is updated. That is, the present application uses a time-domain finite volume method with dual (physical and virtual) time iterative advancement of the conserved electromagnetic field in the medium and implicit calculation of the spatial flux residual to replace the time and spatial flux residuals commonly used in the existing method as explicit solution algorithms. In this way, the physical time step is selected according to the physical problem without being restricted by stability, and the stability is satisfied by the implicit virtual time sub-iteration, thereby overcoming the problem of large computational load caused by the time step of the explicit method being restricted by stability and having to adopt a unified minimum global step and an encrypted grid, thereby improving computational efficiency. Finally, this dual-time-step implicit time-domain finite volume method is used to efficiently solve the 2D and 3D Maxwell equations to obtain the time and space distribution of the composite target time-varying electromagnetic field of the dielectric-coated conductor, while ensuring the format accuracy and improving the time advancement efficiency, saving computational cost. In addition, the present application uses four physical and numerical boundary conditions to construct virtual image point electromagnetic field values ​​at the dielectric / conductor boundary as a grid block end face expansion layer, so that the required electromagnetic field values ​​at the block boundary interpolation still exist, so that the flux calculation of all unit interfaces in the block does not require special processing even at the grid block end face, and all maintain a consistent computational processing method, which is beneficial to computational efficiency. In addition, the interpolation follows the physical characteristics of the discontinuous electromagnetic field and can more accurately calculate the spatiotemporal distribution of the electromagnetic field. In this way, the solution provided by this application can improve the computational efficiency of the electromagnetic scattering problem of dielectric-coated conductor composite targets while ensuring accuracy, thereby saving costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without any creative work.

[0084] Figure 1 This is a flow chart of an implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target disclosed in this application;

[0085] Figure 2 This is a specific implicit calculation flow chart of electromagnetic scattering of dielectric-coated conductor composite targets disclosed in this application;

[0086] Figure 3 is a dielectric coating thickness λ disclosed in this application d / 30,ε r =2.56, schematic diagram of the E-plane bistatic radar cross section distribution of a metal sphere;

[0087] Figure 4 This is a schematic diagram of the bistatic radar cross section distribution of a metal sphere (ka=3) with a dielectric coating thickness of 0.01 meters disclosed in this application;

[0088] Figure 5 This is a schematic diagram of electromagnetic scattering of a metal-coated traveling wave tube disclosed in this application;

[0089] Figure 6 A schematic diagram comparing electromagnetic field components at the same spatial point when a traveling wave tube is coated with or without dielectric coating disclosed in this application;

[0090] Figure 7 This is a schematic diagram of the induced current density distribution on the surface of a traveling wave tube without dielectric coating disclosed in this application;

[0091] Figure 8 This is a schematic diagram of the induced current density distribution on the dielectric-coated surface of a traveling wave tube disclosed in this application;

[0092] Figure 9 A schematic diagram comparing the dual-station radar cross sections of a traveling wave tube before and after dielectric coating disclosed in this application;

[0093] Figure 10 This is a schematic structural diagram of an implicit calculation device for electromagnetic scattering of a dielectric-coated conductor composite target disclosed in this application;

[0094] Figure 11 This is a structural diagram of an electronic device disclosed in this application. DETAILED DESCRIPTION

[0095] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0096] See also Figure 1 As shown, the embodiment of the present application discloses an implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target, which is characterized by comprising:

[0097] Step S11: Acquire target data and initialize the calculation space electromagnetic field; wherein, the target data includes a grid data file, a boundary condition file, target calculation electromagnetic parameters and numerical calculation control parameters; the grid data file is a grid data file obtained by meshing the simulation model, and the simulation model is a model obtained by simulation modeling based on the physical background and boundary condition information of the electromagnetic problem simulated by the dielectric-coated conductor composite target.

[0098] In a specific embodiment, the specific process of obtaining the grid data file is to use a quadrilateral or hexahedral structure to mesh the simulation model, the grid is encrypted at the scattering wall and the geometric singularity, and the grid gradually becomes sparse away from the scattering wall; the grid of the corresponding area is numerically calculated to obtain the grid data file.

[0099] In one embodiment, a user can utilize simulation software to perform simulation modeling based on the physical background of the target electromagnetic problem being simulated, combined with boundary condition information, to obtain a simulation model. The simulation model is then meshed using a quadrilateral or hexahedron structure, with the mesh becoming denser at the walls and geometric singularities and becoming increasingly sparse away from the scattering walls. The mesh in the corresponding area is numerically calculated, a mesh data file is output, and a boundary condition file is set and output. This application obtains the target calculation electromagnetic parameters, numerical calculation control parameters, and input mesh data and boundary condition information files input by the user, and initializes the computational space electromagnetic field.

[0100] In addition, the grid density is guaranteed to be 15-20 grid points per wavelength, the wall density is >300 points / local wavelength in the medium, and the density is encrypted to 50-100 grid points / local wavelength in the medium at geometric singularities; for two-dimensional grids, the right-hand rule is used to advance one layer in the plane perpendicular to the two-dimensional grid, and the calculation is unified as a special case of three-dimensional problems; the grid data file includes the number of structural grid blocks and the three dimensions of each block in the curvilinear coordinate system.

[0101] Furthermore, for the input target calculation electromagnetic parameters and numerical calculation control parameters: the physical time step is pre-set, and for two-dimensional problems, a physical time step of the order of 0.01 is used to dimensionlessly convert the incident electromagnetic wave period to ensure sufficient calculation accuracy, and for three-dimensional problems, a physical time step of the order of 0.001 is selected; at the same time, the sub-iteration convergence standard criterion value is set to the maximum amplitude difference between adjacent sub-iteration time steps in the full grid space <0.001, which is judged as convergence; and the maximum number of sub-iteration steps is set to 30.

[0102] Step S12: Based on the target data, the time-varying electromagnetic field of the dielectric Maxwell equations is iteratively solved using an implicit dual-time-stepping method based on time-based iterative advancement of the conserved electromagnetic field in the dielectric and spatial flux residuals to obtain electromagnetic field parameters of the dielectric-coated conductor composite target. The dielectric Maxwell equations are in the form of scattered fields to be solved and contain dielectric time-domain Maxwell equations.

[0103] Among them, the iterative solution of the time-varying electromagnetic field of the medium Maxwell equations based on the target data and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual includes: using a physical time step loop in the outer layer of the simulation model until the calculation converges; using a virtual time step sub-iteration loop in the inner layer of the simulation model until the sub-iteration converges; in each virtual time sub-iteration process, each edge grid unit in each grid block is sequentially expanded with a virtual image point of the dielectric / conductor boundary according to the boundary conditions, any grid unit in each grid block is decomposed and interpolated according to the discontinuous electromagnetic characteristics, spatial flux calculation and implicit iterative solution calculation are performed, and the conserved electromagnetic field value of the next level virtual time sub-iteration step is updated.

[0104] The physical time step cycle and virtual time step sub-iteration cycle process is:

[0105] Add virtual time derivative term The scattered field form to be solved and the time-domain Maxwell equations containing medium are modified to:

[0106]

[0107]

[0108]

[0109]

[0110] Where W is the electromagnetic field conservation variable, μ r is the relative magnetic susceptibility, μ0 is the vacuum magnetic susceptibility, ε r is the relative dielectric constant, ε0 is the vacuum dielectric constant, σ m is the magnetic permeability, σe is the conductivity. Q is the original variable of the scattered electromagnetic field, τ is the virtual time, t is the normalized physical time, F x 、F y 、F z are the x, y, and z components of the electromagnetic flux in the rectangular coordinate system, S is the external source term caused by the magnetic permeability and electrical conductivity of the medium, J is the external forced current vector, and J x 、J y 、J z are the x, y, and z components of the externally forced current in the rectangular coordinate system, and B i is the real-number incident magnetic field intensity vector, D i is the real number incident field electric displacement vector, B is the real number scattered magnetic induction intensity vector, D is the real number scattered field electric displacement vector, E i is the incident electric field intensity vector, H i is the incident field magnetic field intensity vector, E is the scattered field electric field intensity vector, H is the scattered field magnetic field intensity vector, the scalars with subscripts x, y, and z are the rectangular coordinate system x, y, and z components of the corresponding vectors, respectively, and the superscript t corresponds to the total electromagnetic field form;

[0111] when When converged, the system of equations is equivalent to the original system of equations, and the constant virtual time τ subiteration is expressed as:

[0112]

[0113]

[0114] Among them, W * is the value of the electromagnetic field conservation variable after virtual time iteration, W * It's W n+1 The superscript * represents the value of the conserved variable corresponding to the virtual time sub-iteration, R is the flux residual, and R * is the residual of the flux residual R after adding the physical time derivative term and the source term; n is the number of physical time steps; Δt is the physical time step, W n is the electromagnetic conservation variable at the nth physical time step, W n-1 is the electromagnetic conservation variable at the n-1th physical time step; R * (W * ) is W * The corresponding intermediate state flux residual; the physical time derivative of the backward second-order difference is the second-order time accuracy; the stationary sub-iteration part adopts the implicit algorithm:

[0115]

[0116] Among them, ξ, η, ζ represent the three different directions of the structure grid curve coordinate system; F, G, H are the electromagnetic fluxes corresponding to the ξ, η, ζ directions of the curve coordinate system respectively; is the source term of the corresponding curvilinear coordinate system; ω is the implicit control parameter, which is fully implicit when ω = 1. Other parameters (i.e., ω is not 1) correspond to the explicit and implicit mixed format; subscripts i, j, k are the grid unit numbers, is the electromagnetic conservation variable of the n+1th virtual time step of the i, j, kth grid cell, is the electromagnetic conservation variable of the nth virtual time step of the i, j, kth grid cell, W n+1 is the electromagnetic conservation variable at the n+1th physical time step, W n is the electromagnetic conservation variable at the nth physical time step, W n-1 is the electromagnetic conservation variable at the n-1th physical time step, is the spatial flux residual of the n+1th virtual time step of the i, j, kth grid cell, is the spatial flux residual of the nth virtual time step of the i, j, k-th grid cell, Δτ is the virtual time step controlled by stability, calculated by the CFL number and the local grid cell geometric scale and eigenvalue, which is significantly different from the explicit method. Different grid cells in the steady-state calculation have different local virtual time sub-iteration steps, thereby accelerating the convergence of the electromagnetic field of the unit.

[0117] Furthermore, the spatial flux calculation process is as follows:

[0118] The Steger-Warming splitting method is used to calculate the interface flux of the grid cells.

[0119]

[0120]

[0121]

[0122] Where the subscript k is one of the directions of the curvilinear coordinate system ξ, η, ζ, and the corresponding F k That is, the electromagnetic flux corresponding to the directions of ξ, η, and ζ, represents the electromagnetic flux obtained by splitting the positive eigenvalue in the Steger-Warming splitting in the corresponding directions of the curvilinear coordinate system ξ, η, ζ; represents the electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding directions of the curvilinear coordinate system ξ, η, ζ; S, S - is the similarity matrix, Λ + , Λ - are diagonal matrices composed of positive and negative eigenvalues, Q L , Q RRepresent the left and right state variables at the interface, respectively, and use the MUSCL format to achieve the highest third-order accuracy:

[0123]

[0124]

[0125] Where φ=1 is the limiter, and the subscript i is the grid unit number. Corresponding to the unit interface, κ=1 / 3 is the control parameter of the third-order accuracy format, and Δ are the back-difference and front-difference operators respectively; Represented in grid cells The conserved variables of the left-state electromagnetic field at the interface are: Represented in grid cells The conservation variable of the right state electromagnetic field at the interface; Q i is the conservation variable of the scattered electromagnetic field of the i-th grid unit, Q i+1 is the conservation variable of the scattered electromagnetic field of the i+1th grid cell.

[0126] The interpolation process requires the electromagnetic field values ​​of the adjacent unit centers. The end face numbering of the grid block will overflow the real interval. Therefore, in each dimension of each grid block, two layers are expanded according to the geometric relationship between the grid blocks and the physical boundary conditions, so that the Q required at the block boundary interpolation is i-1 , Q i+1 It still exists, so that the flux calculation of all unit interfaces in the block does not need special treatment even at the end face of the grid block, and the calculation processing method is consistent, which is beneficial to the calculation efficiency.

[0127] Furthermore, at the medium / conductor boundary, the electromagnetic field value of the virtual image point expansion layer is constructed using physical and numerical boundary conditions;

[0128] The physical and numerical boundary conditions used are:

[0129]

[0130]

[0131]

[0132]

[0133] in, is the unit external normal vector of the conductor wall, E t is the total electric field strength vector on the conductor wall, B t is the total magnetic induction field vector of the conductor wall, E tn is the normal component of the total electric field intensity on the conductor wall, H t is the total magnetic field strength vector on the conductor wall;

[0134] The electromagnetic field value of the constructed virtual image point expansion layer is:

[0135]

[0136]

[0137] E x-2 t =E x-1 t

[0138] H x-2 t =H x-1 t

[0139] The cells in the grid block are numbered x, the two expansion layers are numbered x-1 and x-2 respectively, and the superscript t represents the total field.

[0140] For example, combining these four physical and numerical medium / conductor boundary conditions, construct the electromagnetic field value of the virtual image point expansion layer. Assuming that the unit number in the grid block is 2, the corresponding numbers of the two expansion layers are 1 and 0:

[0141]

[0142]

[0143] E0 t =E1 t

[0144] H0 t =H1 t

[0145] Among them, the subscripts 0, 1, and 2 represent the corresponding numbered field quantities, and the superscript t represents the total field.

[0146] The above MUSCL format calculation The electromagnetic field Q is required during the process i , Q i+1 Continuous differentiability is essential for maintaining numerical accuracy, but discontinuities exist between units with different wave resistance media. Non-continuous differentiability and arbitrary interpolation along spatial directions can lead to large numerical errors. Therefore, the present embodiment corrects adjacent units with different electromagnetic parameters (wave resistance) based on the following physical boundary conditions between the media:

[0147]

[0148]

[0149]

[0150]

[0151] Among them, the superscripts s and t represent the scattered field and the total field respectively, and the subscripts L and R represent the left and right states of the interface with different wave resistances respectively. is the unit normal vector of the dielectric interface. The specific correction method of MUSCL interpolation for dielectric interfaces with different wave resistance is as follows: perform MUSCL interpolation on the tangential components of the adjacent electric field intensity and magnetic field intensity respectively; perform MUSCL interpolation on the normal components of the adjacent electric displacement vector and magnetic induction intensity vector respectively; finally, combine the two MUSCL interpolation results to obtain the dielectric interfaces with different wave resistance.

[0152] Furthermore, the specific process of implicit iterative solution calculation and updating the value of the conserved electromagnetic field at the next level of virtual time sub-iteration step includes:

[0153] The solution is solved by using the implicit iteration of spatial flux and the splitting forward and backward iteration of the Jacobi coefficient matrix. The Jacobi coefficient Steger-Warming splitting generated by the flux partial derivative conservation variable is obtained.

[0154]

[0155] Among them, A + , A - , B + , B - , C + , C - is the coefficient matrix after splitting, RHS is the spatial flux residual calculated in the previous physical time step, ΔW n is the implicit sub-iteration electromagnetic field difference;

[0156]

[0157] Expressed as LDU (i.e. upper triangle, lower triangle, diagonal), the approximate factorization is:

[0158]

[0159]

[0160]

[0161]

[0162] Wherein, the subscripts i, j, and k are the grid cell numbers, β is the maximum eigenvalue splitting parameter of the Jacobian coefficient matrix, and γ A , γB , γ C is the maximum eigenvalue of the Jacobian coefficient matrix, I is the unit diagonal matrix, D is the diagonal matrix calculated as above, D + is the upper triangular matrix formed after the negative eigenvalue split, D - is the lower triangular matrix formed after the positive eigenvalue splitting, ΔW + is the difference in electromagnetic conservation variables in the upper triangle corresponding to the split, ΔW - The difference of electromagnetic conservation variables in the lower triangle corresponding to the split; ΔW i-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i-1; ΔW j-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j-1; ΔW k-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k-1; ΔW i+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i+1; ΔW j+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j+1; ΔW k+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k+1; It refers to the coefficient matrix after the adjacent i-1 grid cells are split; It refers to the coefficient matrix after the adjacent j-1 grid cells are split; It refers to the coefficient matrix after the adjacent k-1 grid cells are split; It refers to the coefficient matrix after the adjacent i+1 grid cells are split; It refers to the coefficient matrix after the adjacent j+1 grid cells are split; It refers to the coefficient matrix after the adjacent k+1 grid cells are split;

[0163] The electromagnetic field difference ΔW calculated by forward and backward iteration is obtained:

[0164]

[0165] L=D+D -

[0166] U=D+D +

[0167] Among them, D -1 is the inverse matrix of D, L and U are respectively based on D+D - 、D+D + Calculate the upper triangular matrix and lower triangular matrix obtained;

[0168] Forward loop:

[0169] Backward loop:

[0170] in, It is the intermediate transition variable of the difference of electromagnetic conservation variables;

[0171] Finally, the scattered electromagnetic field Q is obtained by subtracting the analytical incident electromagnetic field from the electromagnetic field conservation variable in the medium:

[0172]

[0173] Among them, μ r is the relative magnetic susceptibility, ε r is the relative dielectric constant, B i is the real-number incident magnetic field intensity vector, D i is the real-valued incident electric displacement vector.

[0174] Furthermore, in a specific embodiment, the sub-iteration convergence criterion is the absolute value of the maximum amplitude difference between the electric field and the magnetic field in the calculation space, and a maximum number of sub-iteration steps is set in the numerical calculation.

[0175] It is understandable that there is a need for an efficient direct solution to the time-domain Maxwell equations, which not only relaxes the restrictions of very small grid scales on iterative physical time steps while maintaining high numerical accuracy, but also accurately simulates the electromagnetic reflection and refraction physical properties of media / conductors and media / media, thereby improving computing performance. In order to achieve efficient time-domain electromagnetic numerical methods to solve large-scale electromagnetic scattering problems of complex shapes, high frequencies, and dielectric-coated conductor composite targets, the computing efficiency is improved while ensuring high accuracy of time and space calculation formats. The present application provides an implicit time-domain numerical technology for the electromagnetic scattering problem of dielectric-coated conductor composite targets, involving implicit dual-time-step time advancement, virtual image point processing of dielectric conductor physical boundary conditions, and electromagnetic numerical methods for decomposing and calculating the electromagnetic flux according to physical conditions at the dielectric interface corresponding to the electromagnetic field discontinuity. First, by introducing a steady-state virtual time derivative term into the governing equations, the physical time derivative is linearized within each physical time segment. This allows the physical time marching step size to be selected based on the physical problem, without being constrained by stability. The computational stability requirement is satisfied by the virtual time sub-iterations, and the steady-state computations of the sub-iterations can be accelerated using local time steps, significantly reducing the computational time required to obtain the stable electromagnetic field within the medium. Secondly, by expanding each grid block by two layers in each dimension, the physical boundaries of the virtual image points / conductors are uniformly treated. This eliminates the need for special treatment of fluxes at the grid block endpoints, allowing them to be calculated in the same manner as cells within the grid, thereby improving program execution and parallel computing efficiency. Finally, fluxes are constructed based on the discontinuity characteristics of the electromagnetic field at the dielectric interface, reflecting the physical characteristics and enabling more accurate calculation of the spatiotemporal distribution of the electromagnetic field. This dual-time-step implicit time-domain finite volume method efficiently solves the 2D and 3D Maxwell equations, obtaining the temporal and spatial distributions of the electromagnetic scattering field of the composite medium / conductor target, while ensuring format accuracy and improving time marching efficiency, thus saving computational cost.

[0176] Compared with the prior art, the beneficial effects of this application mainly include:

[0177] 1. This application uses a time-domain finite volume method that uses a dual (physical and virtual) time iterative advancement of the conserved electromagnetic field in the medium and an implicit calculation of the spatial flux residual to replace the existing methods that usually use explicit solution algorithms for both time and spatial flux residuals. In this way, the physical time step can be selected according to the physical problem without being restricted by stability.

[0178] 2. This application adopts a conservative electromagnetic field method consisting of a scattered field in a medium and a partial incident field, wherein the incident field is given analytically, which is equivalent to solving the Maxwell equations in the form of a scattered field. This eliminates the need to numerically calculate the propagation of the incident electromagnetic wave in the entire computational grid space, thereby avoiding dissipation and dispersion of the incident electromagnetic field and helping to maintain numerical accuracy.

[0179] 3. This application supports structured grids and multi-region decomposition. The integral form of the conservation law of Maxwell's equations can be directly applied to discrete curvilinear coordinate grid cells using body-fitting grids.

[0180] 4. This application is different from traditional FDTD. FDTD uses Cartesian rectangular orthogonal grids to simulate the wall surface, which has a step effect that affects the numerical accuracy, and uses the cross-time and space placement of electromagnetic field components to add artificial viscosity to the second-order central difference format. FVTD uses a body-fitting curve coordinate system grid to better fit the object surface and encrypt the grid at geometric singularities. The electromagnetic field quantities are placed at the center of the grid unit in the grid space, and the upwind format is used to maintain artificial viscosity, which is more conducive to maintaining accuracy and algorithm design.

[0181] 5. This application expands two layers in each dimension of each grid block at both end faces based on the geometric relationship and physical boundary conditions between the grid blocks. This ensures that the required electromagnetic field values ​​are still present at the block boundary interpolation points. This allows for the calculation of fluxes at all unit interfaces within the block, even at the grid block end faces, without requiring special processing, maintaining a consistent computational approach, which is beneficial for computational efficiency. It should be noted that without the expanded grid, special processing would be required at each time step at the dielectric / conductor boundary, which would inconvenience field interpolation, information exchange, and parallelization, thus affecting computational efficiency.

[0182] 6. This application uses four physical and numerical boundary conditions to construct the electromagnetic field values ​​of virtual image points at the dielectric / conductor boundary as a grid block end face expansion layer.

[0183] 7. This application requires that at the interface between different wave-resistance media / medium grid units, that is, adjacent units with different electromagnetic parameters (wave resistance) need to correct the MUSCL interpolation according to the physical conditions of electromagnetic wave reflection and refraction between the media: MUSCL interpolation is performed on the tangential components of the adjacent electric field intensity and magnetic field intensity respectively, and MUSCL interpolation is performed on the normal components of the adjacent electric displacement vector and magnetic induction intensity vector respectively. Finally, the two are combined to obtain the left and right state variables of the interface between different wave-resistance media. Such interpolation follows the physical characteristics of the discontinuous electromagnetic field and can more accurately calculate the spatiotemporal distribution of the electromagnetic field. It should be pointed out that due to the discontinuous characteristics of the electromagnetic field between grid units with different electromagnetic parameters, the electromagnetic field value of the interface required for calculating the electromagnetic flux (obtained by interpolation of the field values ​​at the center of the adjacent units) will not be able to accurately simulate the physical characteristics between the media if the physical characteristics are not considered purely like free space and interpolated according to the spatial direction, resulting in large numerical errors.

[0184] 8. This application adopts the spatial flux implicit iteration and the split forward and backward iterative solution of the Jacobi coefficient matrix, and replaces the sparse matrix inversion with two loops, which is simple and easy to use in engineering.

[0185] 9. This application replaces the traditional Runge-Kutta time-domain finite volume method in which time is explicitly advanced and spatial flux is also explicitly calculated, thereby relaxing the extreme restrictions of the grid and explicit algorithm on the physical time step. This dual-time-step implicit time-domain finite volume method can efficiently solve the 2D and 3D Maxwell equations, and obtain the spatiotemporal distribution of the time-varying electromagnetic field of the dielectric-coated conductor composite target, thereby improving the time advancement efficiency and enhancing the computing performance while ensuring the format accuracy.

[0186] For further information, see Figure 2 As shown, Figure 2 A specific implicit calculation flow chart of electromagnetic scattering of a dielectric-coated conductor composite target provided in an embodiment of the present application. Figure 2 The entire time-domain finite volume method for electromagnetic field calculation software can be divided into three parts according to its structure: preprocessing, electromagnetic field calculation, and post-processing. Preprocessing mainly includes three modules: grid data input, calculation parameter data input, and control parameter input. It is mainly used to read grid data, calculation parameter data input, and control parameter files, and on this basis, perform pre-processing to provide calculation support for electromagnetic field calculation. Electromagnetic field calculation includes: spatial electromagnetic field MUSCL format interpolation, unit interface flux calculation, time advancement, and convergence judgment module. Post-processing is mainly used to output the time and space distribution of the electromagnetic field, the target surface induced current density, and the radar scattering cross section output.

[0187] The following two curl equations of the Maxwell equations to be numerically simulated are combined:

[0188]

[0189]

[0190] in, is the gradient symbol, B t is the real total magnetic field intensity vector, D t is the real total electric displacement vector, E t is the real total electric field strength vector, H t is the real total magnetic field intensity vector, J is the external forced current vector, J m is the magnetizing current vector, J e is the conduction current vector, and t is the normalized physical time.

[0191] The dual-time-step time-domain finite volume method is introduced to iteratively calculate the electromagnetic scattering process of a dielectric-coated conductor composite target. The scattered field form and the dielectric-containing time-domain Maxwell equations are expressed in rectangular coordinates as follows:

[0192]

[0193]

[0194]

[0195]

[0196] Where W is the electromagnetic field conservation variable, μ r is the relative magnetic susceptibility, μ0 is the vacuum magnetic susceptibility, ε r is the relative dielectric constant, ε0 is the vacuum dielectric constant, σ m is the magnetic permeability, σ e is the conductivity. Q is the original variable of the scattered electromagnetic field, τ is the virtual time, t is the normalized physical time, F x 、F y 、F z are the x, y, and z components of the electromagnetic flux in the rectangular coordinate system, S is the external source term caused by the magnetic permeability and electrical conductivity of the medium, J is the external forced current vector, and J x 、J y 、J z are the x, y, and z components of the externally forced current in the rectangular coordinate system, and B i is the real-number incident magnetic field intensity vector, D i is the real number incident field electric displacement vector, B is the real number scattered magnetic induction intensity vector, D is the real number scattered field electric displacement vector, E i is the incident electric field intensity vector, H i is the incident field magnetic field intensity vector, E is the scattered field electric field intensity vector, H is the scattered field magnetic field intensity vector, the scalars with subscripts x, y, and z are the rectangular coordinate system x, y, and z components of the corresponding vectors, respectively, and the superscript t corresponds to the total electromagnetic field form;

[0197] For objects with complex shapes, the computational space body-fitting multi-block structure grid is used, so there is a coordinate transformation:

[0198] k=k(x, y, z) k=ξ, η, ζ

[0199] Where k represents the three directions of the curvilinear coordinate system ξ, η, and ζ, and takes one of ξ, η, and ζ respectively. The conservation form of the Maxwell equations in the curvilinear coordinate system for numerical simulation is obtained:

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206] Where V is the Jacobian matrix of the coordinate transformation, and variables with superscript ^ represent values ​​in the curvilinear coordinate system, which are obtained by the coordinate transformation. is the conserved variable in the curvilinear coordinate system, That is, it is the electromagnetic flux in the curvilinear coordinate system when k takes one of the curvilinear coordinate system directions ξ, η, ζ.

[0207] In order to get rid of the drawback of large computational complexity caused by the limitation of the global minimum physical time step in the traditional explicit time domain finite volume, a fully implicit dual-time-step calculation method is invented to improve the time marching efficiency of the dielectric / conductor composite target time-varying electromagnetic field. The dual time step is used to ensure time accuracy while selecting the physical time step according to the physical characteristics. Combined with the implicit spatial flux residual, a stable and efficient calculation process is obtained, which includes the following steps:

[0208] Step 1: Perform simulation modeling based on the physical background of the target electromagnetic problem and boundary condition information.

[0209] Step 2: Mesh the simulation model using quadrilaterals (2D) or hexahedrons (3D). The mesh is denser at walls and geometric singularities, becoming increasingly sparse away from the scattering walls. Numerically calculate the mesh for the corresponding area, output the mesh data file, and set and output the boundary condition file. The mesh density is maintained at 15-20 points per wavelength, with >300 points per wavelength on walls. The mesh is denser at geometric singularities to 50-100 points per wavelength. The 2D mesh is advanced one level perpendicular to the plane using the right-hand rule, and the calculation is unified as a special case of the 3D problem. The mesh data file includes the number of structural grid blocks and the three curvilinear coordinate dimensions of each block.

[0210] Step 3: Preprocessing: Input the target electromagnetic parameters and numerical control parameters. Because the virtual time sub-iteration is an implicit CFL number and is not subject to the explicit stability requirements mentioned above, a pre-set physical time step is required. For two-dimensional problems, a dimensionless physical time step of Δt = 0.01, representing the period of the incident electromagnetic wave, provides sufficient computational accuracy. For three-dimensional problems, a Δt of ≈ 0.001 is used. Also, set the sub-iteration convergence criterion (e.g., convergence is determined when the maximum amplitude difference between adjacent sub-iteration time steps in the full grid space is < 0.001) and the maximum number of sub-iteration steps (e.g., isubmax = 30).

[0211] Step 4: Input the grid data and boundary condition information file to initialize the calculation of the space electromagnetic field.

[0212] Step 5: The time-varying electromagnetic field of the medium Maxwell equations is iteratively solved using an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual.

[0213] Step 5-1: Loop the outer physical time step until the calculation converges.

[0214] Step 5-2: The inner virtual time step sub-iteration loop continues until the sub-iteration converges or the maximum number of sub-iteration steps is met. The time accuracy of unsteady calculations using the dual-time method is also constrained by the number of sub-iteration steps in each physical time step. A large number of iterations and strict convergence control guarantee time accuracy. A small real time step allows for fewer sub-iterations. In numerical calculations, the maximum number of sub-iteration steps is set to prevent drastic field changes and excessively large sub-iteration CFL numbers, where the residual may not be able to converge, leading to an infinite loop. Furthermore, the sub-iteration convergence is judged and controlled, terminating the iteration as quickly as possible while ensuring a certain time accuracy. The sub-iteration convergence criterion uses the absolute value of the maximum amplitude difference between the electric and magnetic fields in the computational space.

[0215] The specific algorithms for steps 5-1 and 5-2 are introduced below: MUSCL (Monotonic Upstream Schemes for Conservation Laws, MUSCL) interpolation is used.

[0216] Add virtual time derivative term The scattered field form to be solved and the time-domain Maxwell equations containing medium are modified to:

[0217]

[0218] Obviously, when When converged, the system of equations is equivalent to the original system of equations, and the constant virtual time τ subiteration is expressed as:

[0219]

[0220]

[0221] Among them, W * is the value of the electromagnetic field conservation variable after W undergoes virtual time iteration, W * It's W n+1 The superscript * represents the value of the conserved variable corresponding to the virtual time sub-iteration, R is the flux residual, and R * is the residual of the flux residual R after adding the physical time derivative term and the source term; n is the number of physical time steps; Δt is the physical time step length, W n is the electromagnetic conservation variable at the nth physical time step, W n-1is the electromagnetic conservation variable at the n-1th physical time step; R * (W * ) is W * The corresponding intermediate state flux residual; the physical time derivative using backward second-order difference is second-order time accuracy.

[0222] The constant sub-iteration part adopts implicit algorithm:

[0223]

[0224] Among them, ξ is the direction 1 of the structural grid curve coordinate system, η is the direction 2 of the structural grid curve coordinate system, and ζ is the direction 3 of the structural grid curve coordinate system; F, G, and H are the electromagnetic fluxes corresponding to the directions of the curve coordinate system ξ, η, and ζ respectively; is the source term of the corresponding curvilinear coordinate system; ω is the implicit control parameter, which is fully implicit when ω = 1. Other parameters (i.e., ω is not 1) correspond to the explicit and implicit mixed format; subscripts i, j, k are the grid unit numbers, is the electromagnetic conservation variable of the n+1th virtual time step of the i, j, kth grid cell, is the electromagnetic conservation variable of the nth virtual time step of the i, j, kth grid cell, W n+1 is the electromagnetic conservation variable at the n+1th physical time step, W n is the electromagnetic conservation variable at the nth physical time step, W n-1 is the electromagnetic conservation variable at the n-1th physical time step, is the spatial flux residual of the n+1th virtual time step of the i, j, kth grid cell, is the spatial flux residual of the nth virtual time step of the i, j, k-th grid cell, Δτ is the virtual time step controlled by stability, calculated by the CFL number and the local grid cell geometric scale and eigenvalue, which is significantly different from the explicit method. Different grid cells in the steady-state calculation have different local virtual time sub-iteration steps, thereby accelerating the convergence of the electromagnetic field of the unit.

[0225] Step 5-3: In each virtual time sub-iteration process, the spatial flux calculation and implicit iterative solution calculation are performed on a grid block by grid block and grid cell by grid cell basis, and the conservative electromagnetic field value of the next level virtual time sub-iteration step is updated.

[0226] The spatial accuracy of the finite volume method is reflected in whether it can accurately simulate the state variables of the conserved variable W at the interface of the grid unit to obtain the corresponding accurate interface fluxes F, G, and H. The Steger-Warming splitting method is used to calculate the interface fluxes of the grid unit.

[0227]

[0228]

[0229]

[0230] Where the subscript k is one of the directions of the curvilinear coordinate system ξ, η, ζ, and the corresponding F k That is, the electromagnetic flux F, G, H corresponding to the directions of ξ, η, ζ, represents the electromagnetic flux obtained by splitting the positive eigenvalues ​​in the Steger-Warming splitting in the curvilinear coordinate system ξ, η, ζ; represents the electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding directions of the curvilinear coordinate system ξ, η, ζ; S, S - is the similarity matrix, Λ + , Λ - are diagonal matrices composed of positive and negative eigenvalues, Q L , Q R Represent the left and right state variables at the interface, respectively, and use the MUSCL format to achieve the highest third-order accuracy:

[0231]

[0232]

[0233] Where φ=1 is the limiter, and the subscript i is the grid unit number. Corresponding to the unit interface, κ=1 / 3 is the control parameter of the third-order accuracy format, and Δ are the back-difference and front-difference operators respectively; Represented in grid cells The conserved variables of the left-state electromagnetic field at the interface are: Represented in grid cells The conservation variable of the right state electromagnetic field at the interface; Q i is the conservation variable of the scattered electromagnetic field of the i-th grid unit, Q i+1 is the conservation variable of the scattered electromagnetic field of the i+1th grid cell.

[0234] Step 5-3-1: Prepare for MUSCL interpolation by expanding each grid block, especially constructing virtual image points at the dielectric / conductor boundary:

[0235] The interpolation process requires the electromagnetic field values ​​of the adjacent unit centers. The end face numbering of the grid block will overflow the real interval. Therefore, in each dimension of each grid block, two layers are expanded according to the geometric relationship between the grid blocks and the physical boundary conditions, so that the Q required at the block boundary interpolation is i-1 , Q i+1Still exists, so that the flux calculation of all unit interfaces in the block does not need special treatment even at the end of the grid block, and the calculation processing method is consistent, which is beneficial to the calculation efficiency. At the dielectric / conductor boundary, physical and numerical boundary conditions are used:

[0236]

[0237]

[0238]

[0239]

[0240] in, is the unit external normal vector of the conductor wall, E t is the total electric field strength vector on the conductor wall, B t is the total magnetic induction field vector of the conductor wall, E t n is the normal component of the total electric field intensity on the conductor wall, H t is the total magnetic field strength vector on the conductor wall.

[0241] Combining these four physical and numerical medium / conductor boundary conditions, the electromagnetic field value of the virtual image point expansion layer is constructed (assuming the cell number in the grid block is 2, then the two expansion layers are numbered 1 and 0 respectively):

[0242]

[0243]

[0244] E0 t =E1 t

[0245] H0 t =H1 t

[0246] Among them, the subscripts 0, 1, and 2 correspond to the field quantity numbers respectively, and the superscript t represents the total field.

[0247] Step 5-3-2: There is discontinuity in the electromagnetic field between different wave-resistance media / dielectric units. To better simulate the reflection and refraction characteristics of electromagnetic waves between media, a special MUSCL interpolation is performed at the interface between different wave-resistance media:

[0248] The above MUSCL format calculation The electromagnetic field Q is required during the process i , Q i+1Continuous differentiability is essential for maintaining numerical accuracy, but discontinuities exist between units with different wave resistance media. Non-continuous differentiability and arbitrary interpolation along spatial directions can lead to large numerical errors. Therefore, adjacent units with different electromagnetic parameters (wave resistance) need to be corrected based on the following physical boundary conditions between the media:

[0249]

[0250]

[0251]

[0252]

[0253] Among them, the superscripts s and t represent the scattered field and the total field respectively, and the subscripts L and R represent the left and right states of the interface with different wave resistances respectively. is the unit normal vector of the dielectric interface. The specific correction method of MUSCL interpolation for dielectric interfaces with different wave resistance is as follows: perform MUSCL interpolation on the tangential components of the adjacent electric field intensity and magnetic field intensity respectively; perform MUSCL interpolation on the normal components of the adjacent electric displacement vector and magnetic induction intensity vector respectively; finally, combine the two to obtain the dielectric interface with different wave resistance.

[0254] The spatial flux implicit iteration and the splitting of the Jacobi coefficient matrix are solved by forward and backward iteration. Two loops are used to replace the sparse matrix inversion, which is simple and easy to use in engineering. The Jacobi coefficient Steger-Warming splitting generated by the flux partial derivative conservation variable is obtained:

[0255]

[0256] Among them, A + , A - , B + , B - , C + , C - is the coefficient matrix after splitting, RHS is the spatial flux residual calculated in the previous physical time step, ΔW n is the implicit sub-iteration electromagnetic field difference; expressed as LDU, the approximate factorization is:

[0257]

[0258]

[0259]

[0260]

[0261] Wherein, the subscripts i, j, and k are the grid cell numbers, β is the maximum eigenvalue splitting parameter of the Jacobian coefficient matrix, and γ A , γ B , γ C is the maximum eigenvalue of the Jacobian coefficient matrix, I is the unit diagonal matrix, D is the diagonal matrix calculated as above, D + is the upper triangular matrix formed after the negative eigenvalue split, D - is the lower triangular matrix formed after the positive eigenvalue splitting, ΔW + is the difference in electromagnetic conservation variables in the upper triangle corresponding to the split, ΔW - The difference of electromagnetic conservation variables in the lower triangle corresponding to the split; ΔW i-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i-1; ΔW j-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j-1; ΔW k-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k-1; ΔW i+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i+1; ΔW j+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j+1; ΔW k+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k+1; It refers to the coefficient matrix after the adjacent i-1 grid cells are split; It refers to the coefficient matrix after the adjacent j-1 grid cells are split; It refers to the coefficient matrix after the adjacent k-1 grid cells are split; It refers to the coefficient matrix after the adjacent i+1 grid cells are split; It refers to the coefficient matrix after the adjacent j+1 grid cells are split; It refers to the coefficient matrix after the adjacent k+1 grid cells are split;

[0262] The electromagnetic field difference ΔW calculated by forward and backward iteration is obtained:

[0263]

[0264] L=D+D -

[0265] U=D+D +

[0266] Among them, D -1 is the inverse matrix of D, L and U are respectively based on D+D - 、D+D + Calculate the upper triangular matrix and lower triangular matrix obtained;

[0267] Forward loop:

[0268] Backward loop:

[0269] in, It is the intermediate transition variable of the difference of electromagnetic conservation variables.

[0270] Finally, the scattered electromagnetic field Q is obtained by subtracting the analytical incident electromagnetic field from the electromagnetic field conservation variable in the medium:

[0271]

[0272] Among them, μ r is the relative magnetic susceptibility, ε r is the relative dielectric constant, B i is the real-number incident magnetic field intensity vector, D i is the real-valued incident electric displacement vector.

[0273] The above is the implicit dual-time-step calculation of the Maxwell equations to control the iterative process of the electromagnetic field in the medium.

[0274] Step 6: Convergence judgment, post-processing process, output of time and space distribution of electromagnetic field, output of surface induced current and radar cross section spatial distribution data, etc.

[0275] like Figure 3 As shown, Figure 3 is the dielectric coating thickness λ d / 30,ε r =2.56, E-plane bistatic radar cross section distribution of the metal sphere, calculate the coating thickness of λ d / 30,λ d is the local wavelength of the medium, the relative dielectric constant ε r = 2.56, and the E-plane bistatic radar cross section distribution of a metallic sphere with a radius equal to the incident wavelength is compared with the analytical Mie series solution, showing good agreement. dt is chosen to be 0.001, and the computational grid consists of four blocks: two within the dielectric layer, both with dimensions of 16x91x91, and two in the free space outside the dielectric, both with dimensions of 52x91x91. The dielectric thickness is assumed to be 0.0208 times the incident wavelength. The object plane grid has 30 points per wavelength, and the far-field boundary has an average of 17 points per wavelength beyond three wavelengths. The radial grid is denser, with the first layer of the wall grid having a thickness of approximately 1 / 500 of the free-incident electromagnetic wavelength, less than 1 / 300 of the local wavelength.

[0276] like Figure 4 As shown, Figure 4The dielectric coating thickness is 0.01 meters, the metal ball (ka = 3) bi-station radar cross section distribution, the electromagnetic scattering of the coated metal ball is calculated, where the incident electromagnetic wave wavelength is 0.32 meters, the metal ball radius is 0.1528 meters, which is equivalent to the metal ball electrical size ka = 3, the coating thickness is 0.01 meters, and the dielectric relative permittivity ε r =2+j, relative magnetic susceptibility μ r = 1.5 + 0.5j. The electromagnetic parameters of the dielectric layer reveal not only the refraction of electromagnetic waves, but also the imaginary parts of the relative permittivity and relative magnetic susceptibility, which inevitably lead to electromagnetic energy loss. A two-layer computational grid was used: a 12x73x37 dielectric layer and a 38x73x37 outer free-space grid. dt was selected as 0.0018, and the FVTD method with conserved electromagnetic variables was used. The E-plane and H-plane bistatic radar cross-section distributions agree well with the analytical Mie series solution.

[0277] like Figure 5-Figure 9 As shown, the changes in the electromagnetic scattering characteristics of a metal traveling wave tube before and after dielectric coating are compared. The calculation conditions are: X-band incident electromagnetic wave f = 9.41GHz, wavelength 31.88mm, HH polarization, wave vector incident at an angle of 45 degrees to the +X axis in the XY plane, dielectric coating thickness d = 0.4mm covering the upper surface of the traveling wave tube metal wall, electromagnetic parameters: relative dielectric constant ε r =2.56+j4. The entire grid computation space has 35 grid blocks and 4.6 million grid points. Figure 5 It is a schematic diagram of electromagnetic scattering of a metal-coated traveling wave tube; Figure 6 The comparison of the electromagnetic field components at the same spatial point with and without the traveling wave tube coated with dielectric shows that the coating lossy material absorbs part of the incident electromagnetic energy, reducing the electromagnetic field intensity in the scattering grid space. Figure 7 It is the induced current density distribution on the surface of the traveling wave tube without dielectric coating. Figure 8 The traveling wave tube has a dielectric-coated surface that induces current density distribution; Figure 7 and Figure 8 By comparison, it can be seen that at the same geometric position, the coated lossy material absorbs part of the incident electromagnetic energy, causing the surface induced current to decrease; Figure 9 This figure compares the bistatic radar cross section of a traveling wave tube before and after dielectric coating. PEC stands for Perfectly Conductive Electron Condensing Material (PEC), and RAM stands for Radar Absorbing Material (RAM). After coating, the electromagnetic energy is absorbed, resulting in a corresponding reduction in electromagnetic reflections at the same spatial location. In the bistatic RCS distribution in the XY plane, at the primary reflection lobe φ = 135°, the RCS drops by 7dB, from 5.33dB for a perfectly conductive wall to -1.71dB for dielectric coating. RCS reductions also vary at other angles.

[0278] These numerical examples demonstrate that the implicit time-domain numerical technique for the electromagnetic scattering problem of dielectric-coated conductor composite targets, as applied in this application, can both ensure numerical accuracy and improve computational efficiency while relaxing time-step restrictions. Virtual image points in the grid block expansion layer simulate the physical and numerical boundaries of the dielectric / conductor, eliminating the need for special processing of grid block endpoint fluxes, thereby improving program execution and parallelization efficiency. This application constructs flux based on the discontinuous electromagnetic field characteristics of the dielectric interface, accurately calculating the spatiotemporal distribution of the electromagnetic field within the dielectric. Combining these techniques, this application can accurately obtain the temporal and spatial distribution of the electromagnetic scattering field of dielectric / conductor composite targets, ensuring format accuracy while improving time-marching efficiency and saving computational costs.

[0279] It can be seen that the solution provided by this application involves an electromagnetic numerical method for implicit dual-time-step time advancement of electromagnetic fields in media, virtual image point processing of physical boundary conditions of media / conductors, medium interfaces corresponding to electromagnetic field discontinuities, and decomposition and calculation of electromagnetic flux according to physical conditions. Through the time-domain finite volume method of dual (physical and virtual) time iterative advancement of conserved electromagnetic fields in media and implicit calculation of spatial flux residuals, the explicit solution algorithm of time and space residuals commonly used in existing methods is replaced (especially when the electromagnetic wavelength in the medium is smaller than the electromagnetic wavelength in vacuum, the stability requirements of the explicit format make the physical time step smaller than the vacuum electromagnetic scattering problem, resulting in longer calculation time). The physical time step is selected according to the physical problem and is not restricted by stability. Stability is satisfied by implicit virtual time sub-iteration, thereby overcoming the problem of large computational complexity caused by the time step of explicit methods being restricted by stability and the necessity of using a unified minimum global step size and encrypted grid, thereby improving computational efficiency. Second, by constructing virtual image points that uniformly handle the physical boundaries of dielectrics / conductors by expanding each grid block by two layers, the program eliminates the need for special processing of flux at grid block endpoints, instead calculating them in the same manner as cells within the grid, thereby improving program execution and parallel computing efficiency. Finally, fluxes are constructed based on the discontinuity characteristics of the electromagnetic field at dielectric interfaces, reflecting physical characteristics and enabling more accurate calculation of the spatiotemporal distribution of the electromagnetic field. This dual-time-step implicit time-domain finite volume method efficiently solves Maxwell's equations to obtain the temporal and spatial distribution of the electromagnetic scattering field of dielectric / conductor composite targets, ensuring format accuracy while improving time marching efficiency and saving computational costs. This method can be applied to the calculation and analysis of the stealth properties of absorbing materials, the electromagnetic properties of dielectrics, and the radiation characteristics of dielectric antennas.

[0280] See also Figure 10 As shown, the embodiment of the present application discloses an implicit calculation device for electromagnetic scattering of a dielectric-coated conductor composite target, comprising:

[0281] The data acquisition and initialization module 11 is used to acquire target data and initialize the calculation of the spatial electromagnetic field; wherein the target data includes a grid data file, a boundary condition file, target calculation electromagnetic parameters, and numerical calculation control parameters; the grid data file is a grid data file obtained by meshing the simulation model, and the simulation model is a model obtained by simulation modeling based on the physical background and boundary condition information of the electromagnetic problem simulated by the dielectric-coated conductor composite target;

[0282] A calculation module 12 is configured to iteratively solve the time-varying electromagnetic field of the dielectric Maxwell equations based on the target data and in an implicit dual-time-step method based on time iterative advancement of the conserved electromagnetic field in the dielectric and spatial flux residuals, to obtain electromagnetic field parameters of the dielectric-coated conductor composite target;

[0283] Among them, the iterative solution of the time-varying electromagnetic field of the medium Maxwell equations based on the target data and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual includes: using a physical time step loop in the outer layer of the simulation model until the calculation converges; using a virtual time step sub-iteration loop in the inner layer of the simulation model until the sub-iteration converges; in each virtual time sub-iteration process, each edge grid unit in each grid block is sequentially expanded with a virtual image point of the dielectric / conductor boundary according to the boundary conditions, any grid unit in each grid block is decomposed and interpolated according to the discontinuous electromagnetic characteristics, spatial flux calculation and implicit iterative solution calculation are performed, and the conserved electromagnetic field value of the next level virtual time sub-iteration step is updated.

[0284] See also Figure 11 , an embodiment of the present application discloses an electronic device 20, including a processor 21 and a memory 22; wherein, the memory 22 is used to store a computer program; the processor 21 is used to execute the computer program, the implicit calculation method of electromagnetic scattering of a dielectric-coated conductor composite target disclosed in the above embodiment.

[0285] The specific process of the implicit calculation method for electromagnetic scattering of a composite target of a dielectric-coated conductor can be referred to the corresponding content disclosed in the aforementioned embodiments, and will not be repeated here.

[0286] Furthermore, the memory 22 as a carrier for resource storage may be a read-only memory, a random access memory, a magnetic disk or an optical disk, etc., and the storage method may be temporary storage or permanent storage.

[0287] In addition, the electronic device 20 also includes a power supply 23, a communication interface 24, an input / output interface 25 and a communication bus 26; wherein the power supply 23 is used to provide an operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and an external device, and the communication protocol it follows is any communication protocol that can be applied to the technical solution of the present application, and is not specifically limited here; the input / output interface 25 is used to obtain external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs and is not specifically limited here.

[0288] Furthermore, an embodiment of the present application also discloses a computer-readable storage medium for storing a computer program, wherein when the computer program is executed by a processor, the implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target disclosed in the aforementioned embodiment is implemented.

[0289] The specific process of the implicit calculation method for electromagnetic scattering of a composite target of a dielectric-coated conductor can be referred to the corresponding content disclosed in the aforementioned embodiments, and will not be repeated here.

[0290] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from the other embodiments. Reference can be made to the descriptions of the identical or similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and the relevant parts can be referred to the descriptions of the methods.

[0291] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be implemented directly using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0292] The above is a detailed introduction to the implicit calculation method and device for electromagnetic scattering of a dielectric-coated conductor composite target provided by this application. Specific examples are used in this article to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core idea of ​​this application. At the same time, for general technical personnel in this field, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on this application.

Claims

1. An implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target, characterized in that: include: Acquire target data and initialize the calculation space electromagnetic field; wherein the target data includes a grid data file, a boundary condition file, target calculation electromagnetic parameters, and numerical calculation control parameters; the grid data file is a grid data file obtained by meshing a simulation model, and the simulation model is a model obtained by simulation modeling based on the physical background and boundary condition information of the electromagnetic problem simulated by the dielectric-coated conductor composite target; Based on the target data, and in an implicit dual-time-step method based on time iterative advancement of the conserved electromagnetic field in the medium and spatial flux residual, the time-varying electromagnetic field of the medium Maxwell equations is iteratively solved to obtain the electromagnetic field parameters of the dielectric-coated conductor composite target; Wherein, the iterative solution of the time-varying electromagnetic field of the medium Maxwell equations based on the target data and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual includes: adopting a physical time step loop in the outer layer of the simulation model until the calculation converges; adopting a virtual time step sub-iteration loop in the inner layer of the simulation model until the sub-iteration converges; in each virtual time sub-iteration process, expanding the virtual image points of the medium / conductor boundary of each edge grid cell in each grid block according to the boundary conditions, performing medium / medium boundary decomposition and interpolation on any grid cell in each grid block according to the discontinuous electromagnetic characteristics, performing spatial flux calculation and implicit iterative solution calculation, and updating the conserved electromagnetic field value of the next level virtual time sub-iteration step; At the boundary of medium / conductor, the electromagnetic field value of virtual image point expansion layer is constructed using physical and numerical boundary conditions; The physical and numerical boundary conditions used are: in, is the unit external normal vector of the conductor wall, E t is the total electric field strength vector on the conductor wall, B t is the total magnetic induction field vector of the conductor wall, E t n is the normal component of the total electric field intensity on the conductor wall, H t is the total magnetic field strength vector on the conductor wall; The electromagnetic field value of the constructed virtual image point expansion layer is: AND x-2 t =And x-1 t H x-2 t =H x-1 t The cells in the grid block are numbered x, the two expansion layers are numbered x-1 and x-2 respectively, and the superscript t represents the total field.

2. The implicit calculation method for electromagnetic scattering of dielectric-coated conductor composite targets according to claim 1 is characterized in that: Get the mesh data file, including: The simulation model is meshed using a quadrilateral or hexahedron structure. The mesh is denser at the scattering wall and geometric singularities, and becomes increasingly sparse away from the scattering wall. The mesh of the corresponding area is numerically calculated to obtain a mesh data file.

3. The implicit calculation method for electromagnetic scattering of dielectric-coated conductor composite targets according to claim 1, characterized in that: The physical time step cycle and virtual time step sub-iteration cycle process is: Add virtual time derivative term The time-domain Maxwell equations of the medium to be solved are modified as follows: Where W is the electromagnetic field conservation variable, μ r is the relative magnetic susceptibility, μ0 is the vacuum magnetic susceptibility, ε r is the relative dielectric constant, ε0 is the vacuum dielectric constant, σ m is the magnetic permeability, σ e is the conductivity, Q is the original variable of the scattered electromagnetic field, τ is the virtual time, t is the normalized physical time, F x 、F y 、F z are the x, y, and z components of the electromagnetic flux in the rectangular coordinate system, S is the external source term caused by the magnetic permeability and electrical conductivity of the medium, J is the external forced current vector, and J x 、J y 、J z are the x, y, and z components of the externally forced current in the rectangular coordinate system, and B i is the real-number incident magnetic field intensity vector, D i is the real number incident field electric displacement vector, B is the real number scattered magnetic induction intensity vector, D is the real number scattered field electric displacement vector, E i is the incident electric field intensity vector, H i is the incident field magnetic field intensity vector, E is the scattered field electric field intensity vector, H is the scattered field magnetic field intensity vector, the scalars with subscripts x, y, and z are the rectangular coordinate system x, y, and z components of the corresponding vectors, respectively, and the superscript t corresponds to the total electromagnetic field form; when When converged, the system of equations is equivalent to the original system of equations, and the constant virtual time τ subiteration is expressed as: Among them, W * is the value of the electromagnetic field conservation variable after virtual time iteration, W * It's W n+1 The superscript * represents the value of the conserved variable corresponding to the virtual time sub-iteration, R is the flux residual, and R * is the residual of the flux residual R after adding the physical time derivative term and the source term; n is the number of physical time steps; Δt is the physical time step, W n is the electromagnetic conservation variable at the nth physical time step, W n-1 is the electromagnetic conservation variable at the n-1th physical time step; R * (W * ) is W * The corresponding intermediate state flux residual; the physical time derivative of the backward second-order difference is the second-order time accuracy; the stationary sub-iteration part adopts the implicit algorithm: Among them, ξ, η, ζ represent the three different directions of the structure grid curve coordinate system; F, G, H are the electromagnetic fluxes corresponding to the ξ, η, ζ directions of the curve coordinate system respectively; is the source term of the corresponding curvilinear coordinate system; ω is the implicit control parameter, which is fully implicit when ω = 1; the subscripts i, j, and k are the grid unit numbers. is the electromagnetic conservation variable of the n+1th virtual time step of the i, j, kth grid cell, is the electromagnetic conservation variable of the nth virtual time step of the i, j, kth grid cell, W n+1 is the electromagnetic conservation variable at the n+1th physical time step, W n is the electromagnetic conservation variable at the nth physical time step, W n-1 is the electromagnetic conservation variable at the n-1th physical time step, is the spatial flux residual of the n+1th virtual time step of the i, j, kth grid cell, is the spatial flux residual of the nth virtual time step of the i, j, k-th grid cell, Δτ is the virtual time step controlled by stability, which is calculated by the CFL number and the local grid cell geometric scale and eigenvalue. Different local virtual time sub-iteration steps are used to calculate different grid cells.

4. The implicit calculation method for electromagnetic scattering of dielectric-coated conductor composite targets according to claim 1 is characterized in that: The spatial flux calculation process is as follows: Steger-Warming splitting is used to calculate the interface flux of the grid cell: Where the subscript k is one of the directions of the curvilinear coordinate system ξ, η, ζ, and the corresponding F k That is, the electromagnetic flux corresponding to the directions of ξ, η, and ζ, represents the electromagnetic flux obtained by splitting the positive eigenvalue in the Steger-Warming splitting in the corresponding directions of the curvilinear coordinate system ξ, η, ζ; represents the electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding directions of the curvilinear coordinate system ξ, η, ζ; S, S - is the similarity matrix, Λ + , Λ - are diagonal matrices composed of positive and negative eigenvalues, Q L , Q R Respectively represent the left and right state variables at the interface, using the MUSCL format: Where φ=1 is the limiter, and the subscript i is the grid unit number. Corresponding to the unit interface, κ=1 / 3 is the control parameter of the third-order accuracy format, and Δ are the back-difference and front-difference operators respectively; Represented in grid cells The conserved variables of the left-state electromagnetic field at the interface are: Represented in grid cells The conservation variable of the right state electromagnetic field at the interface; Q i is the conservation variable of the scattered electromagnetic field of the i-th grid unit, Q i+1 is the conservation variable of the scattered electromagnetic field of the i+1th grid cell.

5. The implicit calculation method for electromagnetic scattering of dielectric-coated conductor composite targets according to claim 1 is characterized in that: Corrections are made to adjacent cells with different wave resistances based on the following physical boundary conditions between media: Among them, the superscripts s and t represent the scattered field and the total field respectively, and the subscripts L and R represent the left and right states of the interface with different wave resistances respectively. is the unit normal vector of the dielectric interface. The specific correction method of MUSCL interpolation for dielectric interfaces with different wave resistance is as follows: perform MUSCL interpolation on the tangential components of the adjacent electric field intensity and magnetic field intensity respectively; perform MUSCL interpolation on the normal components of the adjacent electric displacement vector and magnetic induction intensity vector respectively; finally, combine the two MUSCL interpolation results to obtain the dielectric interfaces with different wave resistance.

6. The implicit calculation method for electromagnetic scattering of dielectric-coated conductor composite targets according to claim 5 is characterized in that: The solution is solved by using the implicit iteration of spatial flux and the splitting forward and backward iteration of the Jacobi coefficient matrix. The Jacobi coefficient Steger-Warming splitting generated by the flux partial derivative conservation variable is obtained. Among them, A + , A - , B + , B - , C + , C - is the coefficient matrix after splitting, RHS is the spatial flux residual calculated in the previous physical time step, ΔW n is the implicit sub-iteration electromagnetic field difference; Expressed as LDU, the approximate factorization is: Wherein, the subscripts i, j, and k are the grid cell numbers, β is the maximum eigenvalue splitting parameter of the Jacobian coefficient matrix, and γ A , γ B , γ C is the maximum eigenvalue of the Jacobian coefficient matrix, I is the unit diagonal matrix, D is the diagonal matrix calculated as above, D + is the upper triangular matrix formed after the negative eigenvalue split, D - is the lower triangular matrix formed after the positive eigenvalue splitting, ΔW + is the difference in electromagnetic conservation variables in the upper triangle corresponding to the split, ΔW - The difference of electromagnetic conservation variables in the lower triangle corresponding to the split; ΔW i-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i-1; ΔW j-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j-1; ΔW k-1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k-1; ΔW i+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell i+1; ΔW j+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell j+1; ΔW k+1 Refers to the difference in electromagnetic conservation variables between adjacent iteration time steps of grid cell k+1; It refers to the coefficient matrix after the adjacent i-1 grid cells are split; It refers to the coefficient matrix after the adjacent j-1 grid cells are split; It refers to the coefficient matrix after the adjacent k-1 grid cells are split; It refers to the coefficient matrix after the adjacent i+1 grid cells are split; It refers to the coefficient matrix after the adjacent j+1 grid cells are split; It refers to the coefficient matrix after the adjacent k+1 grid cells are split; The electromagnetic field difference ΔW calculated by forward and backward iteration is obtained: L=D+D - U=D+D + Among them, D -1 is the inverse matrix of D, L and U are respectively based on D+D - 、D+D + Calculate the upper triangular matrix and lower triangular matrix obtained; Forward loop: Backward loop: in, It is the intermediate transition variable of the difference of electromagnetic conservation variables; Finally, the scattered electromagnetic field Q is obtained by subtracting the analytical incident electromagnetic field from the electromagnetic field conservation variable in the medium: Among them, μ r is the relative magnetic susceptibility, ε r is the relative dielectric constant, B i is the real-number incident magnetic field intensity vector, D i is the real-valued incident electric displacement vector.

7. A device for implicit calculation of electromagnetic scattering of dielectric-coated conductor composite targets, characterized in that: include: A data acquisition and initialization module is used to acquire target data and initialize the calculation of the spatial electromagnetic field; wherein the target data includes a grid data file, a boundary condition file, target calculation electromagnetic parameters, and numerical calculation control parameters; the grid data file is a grid data file obtained by meshing the simulation model, and the simulation model is a model obtained by simulation modeling based on the physical background and boundary condition information of the electromagnetic problem simulated by the dielectric-coated conductor composite target; a calculation module for iteratively solving the time-varying electromagnetic field of the dielectric Maxwell equations based on the target data and in an implicit dual-time-step manner based on time iterative advancement of the conserved electromagnetic field in the dielectric and spatial flux residuals, to obtain electromagnetic field parameters of the dielectric-coated conductor composite target; Wherein, the iterative solution of the time-varying electromagnetic field of the medium Maxwell equations based on the target data and in an implicit dual-time-step method based on the time iterative advancement of the conserved electromagnetic field in the medium and the spatial flux residual includes: adopting a physical time step loop in the outer layer of the simulation model until the calculation converges; adopting a virtual time step sub-iteration loop in the inner layer of the simulation model until the sub-iteration converges; in each virtual time sub-iteration process, expanding the virtual image points of the medium / conductor boundary of each edge grid cell in each grid block according to the boundary conditions, performing medium / medium boundary decomposition and interpolation on any grid cell in each grid block according to the discontinuous electromagnetic characteristics, performing spatial flux calculation and implicit iterative solution calculation, and updating the conserved electromagnetic field value of the next level virtual time sub-iteration step; The device is further used to: construct electromagnetic field values ​​of a virtual image point expansion layer at a medium / conductor boundary using physical and numerical boundary conditions; The physical and numerical boundary conditions used are: in, is the unit external normal vector of the conductor wall, E t is the total electric field strength vector on the conductor wall, B t is the total magnetic induction field vector of the conductor wall, E t n is the normal component of the total electric field intensity on the conductor wall, H t is the total magnetic field strength vector on the conductor wall; The electromagnetic field value of the constructed virtual image point expansion layer is: AND x-2 t =And x-1 t H x-2 t =H x-1 t The cells in the grid block are numbered x, the two expansion layers are numbered x-1 and x-2 respectively, and the superscript t represents the total field.

8. An electronic device, characterized in that: comprising a memory and a processor, wherein: The memory is used to store computer programs; The processor is configured to execute the computer program to implement the implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that Used to store a computer program, wherein when the computer program is executed by a processor, the implicit calculation method for electromagnetic scattering of a dielectric-coated conductor composite target according to any one of claims 1 to 6 is implemented.

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