An electromagnetic characteristic analysis method, device and equipment of a target object and a medium

Abstract

The application discloses an electromagnetic characteristic analysis method and device of a target object, an electronic device and a computer readable storage medium. The method comprises the following steps: performing simulation modeling according to boundary condition information of the target object to obtain a simulation model of the target object; performing grid division on the simulation model by using a preset structure, and establishing a time-varying electromagnetic field of a Maxwell equation group based on the simulation model after the grid division; implicitly solving the time-varying electromagnetic field of the Maxwell equation group based on double iteration of physical time and virtual time; and outputting an electromagnetic characteristic analysis result of the target object when the time-varying electromagnetic field of the Maxwell equation group converges. The electromagnetic characteristic analysis method provided by the application improves the electromagnetic characteristic analysis efficiency of the target object.

Description

Technical Field

[0001] This application relates to the field of time-domain electromagnetics, and more specifically, to a method and apparatus for analyzing the electromagnetic properties of a target object, an electronic device, and a computer-readable storage medium. Background Technology

[0002] For electromagnetic scattering of complex-shaped targets and electromagnetic interference in complex electromagnetic environments, time-domain methods can reliably simulate complex phenomena such as scattering, multiple scattering, hole penetration, and cavity excitation. Furthermore, they can obtain broadband information of the system with only one calculation. Therefore, they have been widely used in electromagnetic field problems. Time-domain methods can accurately simulate time history, unlike traditional high-frequency asymptotic methods which require special processing methods for special components and special electromagnetic phenomena such as diffraction at geometric edges.

[0003] Time-varying electromagnetic fields in the time domain satisfy Maxwell's equations in the time domain. With the development of computer technology, it has become possible to directly solve these equations. The hyperbolic mathematical characteristics, similar to those of Euler's equations, have facilitated the application of computational fluid dynamics (CFD) techniques in electromagnetic field calculations. Among these, the finite-difference time-domain (FDTD) method and the finite-volume time-domain (FVTD) method are the most well-known. In the 1960s, K.S.S.E. published a pioneering FDTD algorithm, directly calculating the time-varying Maxwell's differential equations using finite-difference methods. This successfully simulated the time-domain response of an electromagnetic pulse interacting with an ideal conductor, pioneering a new method for time-domain electromagnetic field calculations. In the Yee algorithm, a Cartesian orthogonal grid is first generated in the region of interest (the target and a certain space around it). The points where the electric and magnetic field components take values ​​in the grid space are placed intersectingly, so that each electric field component is surrounded by a magnetic field component on each coordinate plane, and each magnetic field component is surrounded by an electric field component. This electromagnetic field configuration meets the requirements of Faraday's law of induction and Ampere's circuital law. This type of grid is usually called the Yee grid.

[0004] Traditional finite-difference time-domain (FDTD) and finite-volume time-domain (FVT) methods employ second-order central difference or spatiotemporally coupled Lax-Wendroff schemes and multi-step Runge-Kutta methods for time progression. Their common feature is the explicit format of time computation. Explicit methods, exemplified by the Runge-Kutta method, offer advantages such as ease of programming and high time accuracy, making them reliable time discretization methods for time-domain electromagnetic field calculations. However, explicit time methods have a major drawback: their time step is limited by stability. The entire computational space must use a uniform minimum global computational step size. For example, the body-fitted, refined meshes generated to simulate drastic changes in geometric shape (e.g., the geometric singularities of the leading and trailing edges of an airfoil leading to drastic changes in the electromagnetic field gradient requiring careful simulation of the refined mesh, and electromagnetic multi-scale problems), result in very small global time steps. Larger mesh cells require more time steps to propagate information within that cell, thus requiring a longer computation time to obtain a stable time-varying electromagnetic field. This is particularly problematic when solving time-domain electromagnetic scattering problems of high-frequency, electrically large targets. The small time step, limited by stability, significantly increases the computational load of the time-domain electromagnetic field, consuming substantial computational resources. On the other hand, implicit computation methods can relax the stability restrictions on computation step size, but this comes at the cost of decreased time precision and increased dimension of the coefficient matrix due to encryption, which increases the difficulty of matrix inversion.

[0005] Alternating Diretion Implicit (ADI) overcomes the limitation of the CFL (Courant Friedrichs-Lewy) number, allowing the choice of time step to be determined solely by computational accuracy, independent of the Courant stability condition. This enables a significant increase in the number of time steps and a substantial decrease in computation time. In 1999, Namiki et al. proposed the Alternating Direction Implicit Finite-Difference Time Domain (ADI-FDTD) method, which was subsequently proven to be unconditionally stable. In 2009, Cooke et al. derived the simplified single-step Alternating Direction Implicit Finite-Difference Time Domain (Leapfrog ADI-FDTD) method, reducing the computation to six implicit equations, thus greatly reducing computational complexity and improving simulation efficiency. However, as mentioned above, traditional FDTD uses Cartesian meshes instead of conformal meshes, inevitably introducing step errors when simulating complex shapes. The body-fitted curvilinear coordinate system of FVTD does not have this problem, but currently, an implicit ADI-FVTD for calculating time-varying electromagnetic fields does not exist.

[0006] Therefore, how to improve the efficiency of electromagnetic property analysis of target objects is a technical problem that needs to be solved by those skilled in the art. Summary of the Invention

[0007] The purpose of this application is to provide a method, apparatus, electronic device, and computer-readable storage medium for analyzing the electromagnetic properties of a target object, thereby improving the efficiency of electromagnetic property analysis of the target object.

[0008] To achieve the above objectives, this application provides a method for analyzing the electromagnetic properties of a target object, comprising:

[0009] Simulation modeling is performed based on the boundary condition information of the target object to obtain a simulation model of the target object;

[0010] The simulation model is meshed using a preset structure, and a time-varying electromagnetic field based on Maxwell's equations is established based on the meshed simulation model.

[0011] The time-varying electromagnetic field of Maxwell's equations is implicitly solved using a dual iterative method based on physical time and virtual time.

[0012] When the time-varying electromagnetic field of the Maxwell equations converges, the electromagnetic property analysis results of the target object are output.

[0013] The step of meshing the simulation model using a preset structure includes:

[0014] The simulation model is meshed using a preset quadrilateral or hexahedral structure.

[0015] In the simulation model, the mesh density at the target location is negatively correlated with the distance between the target location and the wall, and negatively correlated with the distance between the target location and the geometric singularity.

[0016] The implicit solution of the time-varying electromagnetic field of Maxwell's equations based on a dual iterative method using both physical and virtual time includes:

[0017] Electromagnetic parameters and control parameters are obtained, and the time-varying electromagnetic field of Maxwell's equations is implicitly solved using the electromagnetic parameters and control parameters based on a dual iterative method of physical time and virtual time.

[0018] The implicit solution of the time-varying electromagnetic field of Maxwell's equations using the electromagnetic parameters and the control parameters based on a dual iterative method of physical time and virtual time includes:

[0019] The physical time step iterative loop continues until the physical time step iterative convergence is achieved.

[0020] During each physical time step iteration, the virtual time step iterates and loops until the virtual time step iteration converges;

[0021] In each virtual time sub-iteration, the electromagnetic parameters and the control parameters are used to implicitly solve the time-varying electromagnetic field of Maxwell's equations based on the physical time step and the virtual time step, so as to update the value of the conserved electromagnetic field for the next virtual time sub-iteration step.

[0022] The time-varying electromagnetic field of Maxwell's equations is as follows:

[0023]

[0024] Where Δt is the physical time step and Δτ is the virtual time step. These are the electromagnetic conservation variables at the (n+1)th virtual time step of the j, k, and l grid cells. Q is the electromagnetic conservation variable at the nth virtual time step of the j, k, and l grid cells. n +1 Q is the electromagnetic conservation variable at the (n+1)th physical time step. n Q is the electromagnetic conserved variable at the nth physical time step. n-1 ω is the electromagnetic conservation variable at the (n-1)th physical time step, δ is the implicit control parameter, and ω is the electromagnetic conservation variable at the (n-1)th physical time step. ξ δ η δ ζ These correspond to the difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively. Jacobian coefficient matrices corresponding to the electromagnetic flux in the directions ξ, η, and ζ in the curvilinear coordinate system, respectively, ΔQ n It is the difference in the conserved variables of the scattered field between adjacent physical times. It is the spatial flux residual at the nth physical time step, and RHS is the total spatial flux residual at the previous physical time step plus the corrections from the physical time step and the virtual time step.

[0025] When the time-varying electromagnetic field of Maxwell's equations converges, the electromagnetic property analysis results of the target object are output, including:

[0026] When the time-varying electromagnetic field of Maxwell's equations converges, the output is any one or a combination of any of the following: the time distribution, spatial distribution, surface induced current, and radar cross section spatial distribution data of the target object.

[0027] To achieve the above objectives, this application provides an electromagnetic characteristic analysis device for a target object, comprising:

[0028] The modeling module is used to perform simulation modeling based on the boundary condition information of the target object, and obtain a simulation model of the target object.

[0029] A module is established to perform meshing on the simulation model using a preset structure, and to establish a time-varying electromagnetic field based on the Maxwell equations of the simulation model after meshing.

[0030] The solution module is used to implicitly solve the time-varying electromagnetic field of Maxwell's equations based on a dual iterative method of physical time and virtual time;

[0031] The analysis module is used to output the electromagnetic property analysis results of the target object when the time-varying electromagnetic field of the Maxwell equations converges.

[0032] To achieve the above objectives, this application provides an electronic device, comprising:

[0033] Memory, used to store computer programs;

[0034] A processor is used to execute the computer program to implement the steps of the electromagnetic property analysis method for the target object as described above.

[0035] To achieve the above objectives, this application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the electromagnetic characteristic analysis method for the target object described above.

[0036] As can be seen from the above scheme, the electromagnetic property analysis method for a target object provided in this application includes: performing simulation modeling based on the boundary condition information of the target object to obtain a simulation model of the target object; performing mesh partitioning of the simulation model using a preset structure, and establishing a time-varying electromagnetic field of Maxwell's equations based on the mesh-partitioned simulation model; implicitly solving the time-varying electromagnetic field of Maxwell's equations using a dual iteration method of physical time and virtual time; and outputting the electromagnetic property analysis results of the target object when the time-varying electromagnetic field of Maxwell's equations converges.

[0037] The electromagnetic property analysis method for the target object provided in this application implicitly solves the time-varying electromagnetic field of Maxwell's equations through a dual iterative approach of conserved electromagnetic field physical time and virtual time. This replaces the explicit solution algorithms commonly used in existing methods, where both time and spatial flux residuals are calculated. The physical time step is selected according to the physical problem and is not limited by stability, while stability is satisfied by the implicit virtual time sub-iteration. This overcomes the computational burden caused by the stability limitation of the time step in explicit methods and the necessity of using a uniform minimum global step size and refined mesh, thus improving computational efficiency. Therefore, the electromagnetic property analysis method for the target object provided in this application improves the efficiency of electromagnetic property analysis. This application also discloses an electromagnetic property analysis device, an electronic device, and a computer-readable storage medium, which can achieve the same technical effects.

[0038] It should be understood that the above general description and the following detailed description are merely exemplary and do not limit this application. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The drawings are used to provide a further understanding of this disclosure and constitute a part of the specification. They are used together with the following detailed description to explain this disclosure, but do not constitute a limitation of this disclosure. In the drawings:

[0040] Figure 1 This is a flowchart illustrating an electromagnetic property analysis method for a target object according to an exemplary embodiment;

[0041] Figure 2 A flowchart of an application embodiment provided in this application;

[0042] Figure 3 This is a schematic diagram illustrating the effect of a TM wave physical time step on the radar cross section of a cylinder (ka=5) according to an exemplary embodiment.

[0043] Figure 4 This is a schematic diagram illustrating the effect of a TE wave physical time step on the radar cross section of a cylinder (ka=5) according to an exemplary embodiment.

[0044] Figure 5 This is a schematic diagram illustrating the comparison of the time history of the transverse magnetic field at the same location of a cylindrical (ka=5) TE wave according to an exemplary embodiment;

[0045] Figure 6 This is a schematic diagram illustrating the effect of a physical time step on the radar cross-section of a metal sphere (ka=2) according to an exemplary embodiment.

[0046] Figure 7 This is a cloud map showing the induced current density distribution on the surface of a metal sphere (ka=5) according to an exemplary embodiment;

[0047] Figure 8 This is a schematic diagram comparing the calculation of bistatic radar cross section distribution using an explicit and implicit method with a metal sphere (ka=5) according to an exemplary embodiment.

[0048] Figure 9 This is a structural diagram of an electromagnetic characteristic analysis apparatus for a target object according to an exemplary embodiment;

[0049] Figure 10 This is a structural diagram of an electronic device according to an exemplary embodiment. Detailed Implementation

[0050] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. Furthermore, in the embodiments of this application, "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0051] This application discloses a method for analyzing the electromagnetic properties of a target object, which improves the efficiency of electromagnetic property analysis of the target object.

[0052] See Figure 1 A flowchart illustrating a method for analyzing the electromagnetic properties of a target object according to an exemplary embodiment is shown below. Figure 1 As shown, it includes:

[0053] S101: Perform simulation modeling based on the boundary condition information of the target object to obtain a simulation model of the target object;

[0054] In this step, simulation modeling is performed based on the physical background of the electromagnetic problem being simulated for the target object, combined with boundary condition information, to obtain the simulation model of the target object.

[0055] S102: The simulation model is meshed using a preset structure, and a time-varying electromagnetic field based on Maxwell's equations is established based on the meshed simulation model.

[0056] In this step, the simulation model is meshed using a pre-defined quadrilateral or hexahedral structure. A time-varying electromagnetic field based on Maxwell's equations is then established based on the meshed simulation model. Preferably, the mesh density at the target location in the simulation model is negatively correlated with the distance between the target location and the wall, and negatively correlated with the distance between the target location and geometric singularities. In specific implementations, the mesh is refined at the wall and geometric singularities, and gradually becomes sparser away from the scattering wall. Numerical calculations are performed on the mesh in the corresponding region, and a mesh data file is output. Boundary condition files are set and output. For example, the mesh density is guaranteed to be 15-20 mesh points per wavelength, the wall density is >300 points / local wavelength, and the density at geometric singularities is reduced to 50-100 mesh points / local wavelength. For two-dimensional meshes, one layer is advanced in the plane perpendicular to the two-dimensional mesh using the right-hand rule, and this is treated as a special case for three-dimensional problems and calculated uniformly. The mesh data file includes the number of structural mesh blocks and the three dimensions of each block in a curvilinear coordinate system.

[0057] S103: Implicitly solve the time-varying electromagnetic field of Maxwell's equations based on a dual iterative method of physical time and virtual time;

[0058] Specifically, electromagnetic parameters and control parameters are obtained, and the time-varying electromagnetic field of Maxwell's equations is implicitly solved using a dual iterative method based on both physical and virtual time. In practice, the electromagnetic field in the computational space is initialized, and electromagnetic and control parameters are obtained. Electromagnetic parameters may include magnetic susceptibility, dielectric constant, etc., while control parameters may include the maximum amplitude difference between sub-iteration time steps, the maximum number of sub-iteration steps, and implicit control parameters. For example, a physical time step is pre-set; for two-dimensional problems, a dimensionless physical time step of 0.01 (the period of the incident electromagnetic wave is used) is chosen to ensure sufficient computational accuracy, while for three-dimensional problems, a physical time step of 0.001 is selected. Simultaneously, the sub-iteration convergence criterion is set to a maximum amplitude difference of <0.001 between adjacent sub-iteration time steps in the full grid space, indicating convergence; the maximum number of sub-iteration steps is set to 30.

[0059] Specifically, the implicit solution of the time-varying electromagnetic field of Maxwell's equations using the electromagnetic parameters and the control parameters based on a dual iterative method of physical time and virtual time includes: iterating through the physical time step until the physical time step convergence; iterating through the virtual time step sub-iteration during each physical time step iteration until the virtual time step convergence; and implicitly solving the time-varying electromagnetic field of Maxwell's equations using the electromagnetic parameters and the control parameters based on the physical time step and the virtual time step during each virtual time sub-iteration to update the value of the conserved electromagnetic field for the next virtual time sub-iteration step.

[0060] The outer layer of the simulation model is a physical time-step loop until the computation converges; the inner layer is a virtual time-step sub-iteration loop until the sub-iteration converges. During each virtual time sub-iteration, the spatial flux and implicit iterative solution are calculated sequentially for each grid cell and each grid unit, updating the conserved electromagnetic field values ​​for the next level of virtual time sub-iteration steps. The sub-iteration convergence criterion is the absolute value of the maximum amplitude difference between the electric and magnetic fields in the computational space, and a maximum number of sub-iteration steps is set in the numerical calculation.

[0061] The physical time step loop and the virtual time step iteration loop process are as follows:

[0062] Add virtual time derivative term The source-free time-domain Maxwell's equations in the form of the scattered field to be solved are modified as follows:

[0063]

[0064]

[0065]

[0066] Where Q is the conserved variable of the scattered electromagnetic field, τ is the virtual time, t is the normalized physical time, and F x F y F z The x, y, and z components of the electromagnetic flux in the Cartesian coordinate system are: B is the real-number scattered magnetic flux density vector, D is the real-number scattered electric displacement vector, E is the scattered electric field intensity vector, and H is the scattered magnetic field intensity vector. The subscripts x, y, and z scalars are the Cartesian coordinate system x, y, and z components of the corresponding vectors.

[0067] It is obvious that when Upon convergence, the system of equations is equivalent to the original system of equations, and the time-invariant virtual time sub-iteration is expressed as:

[0068]

[0069]

[0070] Among them, Q * Q is the value of the electromagnetic field conservation variable after virtual time sub-iteration. * It is Q n+1 The approximation is given by the superscript *, which represents the value of the conserved variable corresponding to the virtual time sub-iteration. R is the flux residual. * The flux residual R is the residual after adding the physical time derivative term and the source term; n is the physical time step; Δt is the physical time step size; Q n Q is the electromagnetic conservation variable at the nth physical time step. n-1 R is the electromagnetic conservation variable at the (n-1)th physical time step; * (Q · ) for Q * The corresponding intermediate state flux residual; the physical time derivative using backward second-order differencing has second-order time precision; the constant sub-iteration part uses an implicit algorithm:

[0071]

[0072] Where ξ represents direction 1 of the curved coordinate system of the structured grid, η represents direction 2 of the curved coordinate system of the structured grid, ζ represents direction 3 of the curved coordinate system of the structured grid, F, G, and H are the electromagnetic fluxes in the directions ξ, η, and ζ of the curved coordinate system, respectively, ω is an implicit control parameter, taking the form of fully implicit ω = 1, and other parameters correspond to a mixed explicit and implicit format; the subscripts i, j, and k are the grid cell numbers. These are the electromagnetic conservation variables at the (n+1)th virtual time step of the i, j, k-th grid cells. Q is the electromagnetic conservation variable at the nth virtual time step of the i, j, k-th grid cell.n+1 Q is the electromagnetic conservation variable at the (n+1)th physical time step. n Q is the electromagnetic conserved variable at the nth physical time step. n-1 It is the electromagnetic conservation variable at the (n-1)th physical time step. It is the spatial flux residual of the (n+1)th virtual time step in the i, j, k-th grid cell. Δτ is the spatial flux residual of the nth virtual time step of the i, j, k grid cells. Δτ is the virtual time step size controlled by stability and is calculated by the CFL number and the local grid cell geometry and eigenvalues. It is significantly different from the explicit method. Different grid cells calculated in a steady-state manner have different local virtual time step sizes, thereby accelerating the convergence of the electromagnetic field of the cell.

[0073] The time-varying electromagnetic field of Maxwell's equations is:

[0074]

[0075] Where Δt is the physical time step and Δτ is the virtual time step. These are the electromagnetic conservation variables at the (n+1)th virtual time step of the j, k, and l grid cells. Q is the electromagnetic conservation variable at the nth virtual time step of the j, k, and l grid cells. n+1 Q is the electromagnetic conservation variable at the (n+1)th physical time step. n Q is the electromagnetic conserved variable at the nth physical time step. n-1 ω is the electromagnetic conservation variable at the (n-1)th physical time step, δ is the implicit control parameter, and ω is the electromagnetic conservation variable at the (n-1)th physical time step. ξ δ η δ ζ These correspond to the difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively. Jacobian coefficient matrices corresponding to the electromagnetic flux in the directions ξ, η, and ζ in the curvilinear coordinate system, respectively, ΔQ n It is the difference in the conserved variables of the scattered field between adjacent physical times. It is the spatial flux residual at the nth physical time step, and RHS is the total spatial flux residual at the previous physical time step plus the corrections from the physical time step and the virtual time step.

[0076]

[0077]

[0078]

[0079] ΔQ n =Q n+1 -Q n ;

[0080]

[0081] Spatial flux is calculated as follows:

[0082] The flux at the interface of the grid cells is calculated using Steger-Warming splitting.

[0083]

[0084]

[0085]

[0086] In the formula, the subscript k takes one of the directions ξ, η, ζ in the curvilinear coordinate system, and the corresponding F k That is, the electromagnetic flux corresponding to the directions ξ, η, and ζ. The electromagnetic flux obtained after splitting the positive eigenvalues ​​in the Steger-Warming splitting process in the corresponding directions of ξ, η, ζ in the curvilinear coordinate system; S,S represents the electromagnetic flux obtained after splitting the negative eigenvalues ​​in the Steger-Warming splitting process in the corresponding directions of ξ, η, ζ in the curvilinear coordinate system; - Let Λ be a similar matrix. + ,Λ - Q is a diagonal matrix composed of positive and negative eigenvalues. L Q R These represent the left and right state variables at the interface, respectively, and can be formatted using the MUSCL format to achieve the highest third-order precision.

[0087]

[0088]

[0089] Where φ = 1 is the limiter, and the subscript i is the grid cell number. At the corresponding unit interface, κ = 1 / 3 is the control parameter for the 3rd order precision format. Δ and Δ are the after-difference and front-difference operators, respectively; Indicated in grid cell The electromagnetic field is conserved in the left state at the interface. Indicated in grid cell The electromagnetic field conserved variable at the right state of the interface; Q i Q is the conserved variable of the scattered electromagnetic field in the i-th grid cell. i+1 It is the conserved variable of the electromagnetic field scattered by the (i+1)th grid cell.

[0090] The calculation process for the implicit iterative solution in alternating directions is as follows:

[0091]

[0092] Where I is the identity matrix, The superscript k is the virtual time step number, and rhs is the new flux residual.

[0093] The approximation factor AF is decomposed as follows:

[0094]

[0095] in, The difference operator performs pre- and post-difference decompositions based on the Steger-Warming split:

[0096]

[0097] in, It is the coefficient matrix after splitting; δ ξ - δ η - δ ζ - These correspond to the backward difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively; δ ξ + δ η + δ ζ + These correspond to the forward difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively.

[0098] The solution is obtained by iteratively solving in the three directions ξ, η, and ζ one dimension at a time. For two-dimensional problems, iteration in the ζ direction is not required. The sequence of iterative solutions in the three directions ξ, η, and ζ one dimension at a time is as follows:

[0099]

[0100]

[0101]

[0102] ΔQ k =ΔQ *** ;

[0103] Where, ΔQ * ΔQ ** ΔQ *** These are the differences in electromagnetic conservation variables of the scattered field at adjacent virtual time steps during the intermediate iteration processes in the three directions: ξ, η, and ζ.

[0104] Taking the ξ direction as an example, the other two directions follow the same logic. For each direction, the same forward and backward iteration algorithm for L and U is used to calculate the intermediate iteration value ΔQ. * ΔQ ** ΔQ*** :

[0105] LUΔQ * =-rhs

[0106]

[0107]

[0108]

[0109]

[0110] Where L is the forward iteration operator and U is the backward iteration operator; It is the intermediate value of the electromagnetic conservation variable in the forward and backward iterations of L and U; It is the splitting coefficient matrix corresponding to the positive eigenvalue of the Steger-Warming split in the i-th unit. It is the splitting coefficient matrix corresponding to the positive eigenvalue of the (i-1)th unit Steger-Warming split. It is the splitting coefficient matrix corresponding to the negative eigenvalues ​​of the i-th Steger-Warming split. It is the splitting coefficient matrix corresponding to the negative feature of the Steger-Warming split in the (i+1)th unit; It is the difference in electromagnetic conservation variables of the scattered field between adjacent virtual time steps after the L iteration of the i-th unit; It is the difference in electromagnetic conservation variables of the scattered field at adjacent virtual time steps after iteration of unit i-1 L; ΔQ i * It is the difference in electromagnetic conservation variables of the scattered field between adjacent virtual time steps after the iteration of unit i in U; It is the difference in electromagnetic conservation variables of the scattered field at adjacent virtual time steps after the (i+1)th unit U iteration.

[0111] Required The inverse matrix is:

[0112]

[0113]

[0114] in, μ is the magnetic susceptibility, and ε is the dielectric constant.

[0115] S104: When the time-varying electromagnetic field of the Maxwell equations converges, output the electromagnetic property analysis results of the target object.

[0116] In this step, when the time-varying electromagnetic field of Maxwell's equations converges, any one or a combination of any of the following data is output: the time distribution, spatial distribution, surface induced current, and radar cross section spatial distribution of the target object.

[0117] The electromagnetic property analysis method for target objects provided in this application implicitly solves the time-varying electromagnetic field of Maxwell's equations through a dual iterative approach of conserved electromagnetic field physical time and virtual time. This replaces the explicit solution algorithms commonly used in existing methods, where both time and spatial flux residuals are calculated. The physical time step is selected based on the physical problem and is not limited by stability, while stability is satisfied by the implicit virtual time sub-iteration. This overcomes the computational burden caused by the stability limitations of explicit methods and the necessity of using a uniform minimum global step size and a refined mesh, thus improving computational efficiency. Therefore, the electromagnetic property analysis method for target objects provided in this application improves the efficiency of electromagnetic property analysis for target objects.

[0118] The following describes an application embodiment provided in this application; see [link to application example]. Figure 2 The entire software for calculating electromagnetic fields using the finite volume time-domain method can be structurally divided into three parts: preprocessing, electromagnetic field calculation, and post-processing. Preprocessing mainly includes three modules: mesh data input, calculation parameter data input, and control parameter input. These modules are primarily used to read in mesh data, calculation parameter data, and control parameter files, and then perform preprocessing to provide computational support for electromagnetic field calculations. Electromagnetic field calculations consist of modules for spatial electromagnetic field MUSCL format interpolation, element interface flux calculation, time progression, and convergence judgment. Post-processing is mainly used to output the temporal and spatial distribution of the electromagnetic field, the target surface induced current density, and the radar cross section.

[0119] The following section combines two curl equations from the passive Maxwell equations to be numerically simulated. Where ▽ is the gradient symbol, B is the real-valued magnetic flux density vector of the scattered field, D is the real-valued electric displacement vector of the scattered field, E is the real-valued electric field intensity vector of the scattered field, H is the real-valued magnetic field intensity vector of the scattered field, and t is the normalized physical time.

[0120] This paper introduces the iterative numerical calculation of the electromagnetic scattering process of a target using the two-time-step time-domain finite volume method. The scattered field is represented in Cartesian coordinates by the time-domain Maxwell's equations as follows:

[0121]

[0122]

[0123]

[0124] Where Q is the conserved variable of the scattered electromagnetic field, τ is the virtual time, t is the normalized physical time, and F x F y F z The x, y, and z components of the electromagnetic flux in the Cartesian coordinate system are: B is the real-number scattered magnetic flux density vector, D is the real-number scattered electric displacement vector, E is the scattered electric field intensity vector, and H is the scattered magnetic field intensity vector. The subscripts x, y, and z scalars are the Cartesian coordinate system x, y, and z components of the corresponding vectors.

[0125] For objects with complex shapes, a computationally oriented, multi-block structured mesh is used, thus requiring coordinate transformations: k = k(x,y,z)k = ξ,η,ζ. Here, k represents the three directions ξ, η, and ζ in the curvilinear coordinate system. Taking one of ξ, η, or ζ yields the conserved form of Maxwell's equations in the curvilinear coordinate system to be numerically simulated.

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] In the formula, V is the Jacobian matrix of the coordinate transformation, and the superscript variable ^ represents the value in the curvilinear coordinate system, which is obtained by the coordinate transformation. For conserved variables in a curvilinear coordinate system, That is, the electromagnetic flux in the curvilinear coordinate system when k takes one of the directions ξ, η, and ζ respectively.

[0134] To overcome the computational burden inherent in traditional explicit time-domain finite-volume global minimum physical time step methods, this paper proposes a fully implicit dual-time-step computation method to improve the time-propagation efficiency of the target time-varying electromagnetic field. This method uses dual time steps to ensure time accuracy while selecting the physical time step based on physical characteristics. Combined with implicit spatial flux residuals, a stable and efficient computational process is obtained, including the following steps:

[0135] Step 1: Based on the physical background of the electromagnetic problem to be simulated, and combined with the boundary condition information, perform simulation modeling.

[0136] Step 2: Mesh the simulation model using a quadrilateral (2D) or hexahedral (3D) structure. The mesh is denser at the walls and geometric singularities, gradually thinning out away from the scattering walls. Numerical calculations are performed on the corresponding regions' meshes, and the mesh data file is output. Boundary condition files are set and output. The mesh density is maintained at 15-20 mesh points per wavelength, with a wall density >300 points / wavelength. At geometric singularities, the mesh density is reduced to 50-100 mesh points / wavelength. For 2D meshes, one layer is advanced perpendicular to the plane using the right-hand rule, treating this as a special case of the 3D problem for unified calculation. The mesh data file includes the number of structural mesh blocks and the three dimensions of each block in a curvilinear coordinate system.

[0137] Step 3: Preprocessing section. Input the target electromagnetic parameters and numerical calculation control parameters. Since the virtual time sub-iteration is an implicit CFL number, it is not constrained by the above explicit stability requirements. The physical time step is preset. For two-dimensional problems, a dimensionless physical time step Δt = 0.01 of the incident electromagnetic wave period is sufficient for calculation accuracy. For three-dimensional problems, Δt ≈ 0.001 is chosen. At the same time, the sub-iteration convergence criterion value is set (e.g., the maximum amplitude difference between adjacent sub-iteration time steps in the full mesh space is <0.001, which is considered convergence) and the maximum number of sub-iteration steps are set (e.g., ifusmax = 30).

[0138] Step 4: Input the grid data and boundary condition information file to initialize the computational space electromagnetic field.

[0139] Step 5: Iteratively solve the time-varying electromagnetic field of Maxwell's equations for the medium using an implicit dual-time-step approach based on the time-iterative progression of the conserved electromagnetic field and the spatial flux residual.

[0140] Step 5-1: Loop through the outer physical time step until the calculation converges.

[0141] Step 5-2: Iterate through the inner virtual time step until either the sub-iteration converges or the maximum number of sub-iteration steps is met. The time accuracy of unsteady computation using the dual-time method is also constrained by the number of sub-iteration steps in each physical time step. A larger number of iterations and stricter convergence control ensures higher time accuracy. A smaller real time step allows for fewer sub-iterations. In numerical computation, to prevent situations with drastic field changes or excessively large CFL numbers in sub-iterations, which could prevent the residual from failing to decrease and leading to an infinite loop, a maximum number of sub-iteration steps is given. Furthermore, the convergence of sub-iterations is judged and controlled to end the iteration as quickly as possible while maintaining a certain level of 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.

[0142] The following describes the specific algorithms for steps 5-1 and 5-2: MUSCL (Monotonic Upstream Schemes for Conservation Laws) interpolation is used.

[0143] Add virtual time derivative term The Maxwell's equations in the time domain, which are to be solved in the form of the scattered field, are modified as follows:

[0144]

[0145] It is obvious that when Upon convergence, the system of equations is equivalent to the original system of equations, and the time-invariant virtual time sub-iteration is expressed as:

[0146]

[0147]

[0148] Among them, Q * Q is the value of the electromagnetic field conservation variable after virtual time sub-iteration. * It is Q n+1 The approximation is given by the superscript *, which represents the value of the conserved variable corresponding to the virtual time sub-iteration. R is the flux residual. * The flux residual R is the residual after adding the physical time derivative term and the source term; n is the physical time step; Δt is the physical time step size; Q n Q is the electromagnetic conservation variable at the nth physical time step. n-1 R is the electromagnetic conservation variable at the (n-1)th physical time step; * (Q · ) for Q * The corresponding intermediate state flux residual; the physical time derivative using backward second-order differencing has second-order time precision; the constant sub-iteration part uses an implicit algorithm:

[0149]

[0150] Where ξ represents direction 1 of the curved coordinate system of the structured grid, η represents direction 2 of the curved coordinate system of the structured grid, ζ represents direction 3 of the curved coordinate system of the structured grid, F, G, and H are the electromagnetic fluxes in the directions ξ, η, and ζ of the curved coordinate system, respectively, ω is an implicit control parameter, taking the form of fully implicit ω = 1, and other parameters correspond to a mixed explicit and implicit format; the subscripts i, j, and k are the grid cell numbers. These are the electromagnetic conservation variables at the (n+1)th virtual time step of the i, j, k-th grid cells. Q is the electromagnetic conservation variable at the nth virtual time step of the i, j, k-th grid cell. n+1 Q is the electromagnetic conservation variable at the (n+1)th physical time step. nQ is the electromagnetic conserved variable at the nth physical time step. n-1 It is the electromagnetic conservation variable at the (n-1)th physical time step. It is the spatial flux residual of the (n+1)th virtual time step in the i, j, k-th grid cell. Δτ is the spatial flux residual of the nth virtual time step of the i, j, k grid cells. Δτ is the virtual time step size controlled by stability and is calculated by the CFL number and the local grid cell geometry and eigenvalues. It is significantly different from the explicit method. Different grid cells calculated in a steady-state manner have different local virtual time step sizes, thereby accelerating the convergence of the electromagnetic field of the cell.

[0151] Implicit time-progressive iterative equation:

[0152]

[0153]

[0154]

[0155]

[0156] ΔQ n =Q n+1 -Q n ;

[0157]

[0158] Where Δτ is the virtual time step; δ ξ δ η δ ζ These correspond to the difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively. Jacobian coefficient matrices corresponding to the electromagnetic flux in the directions ξ, η, and ζ in the curvilinear coordinate system, respectively; ΔQ n It is the difference in the conserved variables of the scattered field between adjacent physical times; RHS is the spatial flux residual at the nth physical time step, and RHS is the total spatial flux residual at the previous physical time step plus the corrections from the two time steps.

[0159] Spatial flux is calculated as follows:

[0160] The flux at the interface of the grid cells is calculated using Steger-Warming splitting.

[0161]

[0162]

[0163]

[0164] In the formula, the subscript k takes one of the directions ξ, η, ζ in the curvilinear coordinate system, and the corresponding F k That is, the electromagnetic flux corresponding to the directions ξ, η, and ζ. The electromagnetic flux obtained after splitting the positive eigenvalues ​​in the Steger-Warming splitting process in the corresponding directions of ξ, η, ζ in the curvilinear coordinate system; S,S represents the electromagnetic flux obtained after splitting the negative eigenvalues ​​in the Steger-Warming splitting process in the corresponding directions of ξ, η, ζ in the curvilinear coordinate system; - Let Λ be a similar matrix. + ,Λ - Q is a diagonal matrix composed of positive and negative eigenvalues. L Q R These represent the left and right state variables at the interface, respectively, and can be formatted using the MUSCL format to achieve the highest third-order precision.

[0165]

[0166]

[0167] Where φ = 1 is the limiter, and the subscript i is the grid cell number. At the corresponding unit interface, κ = 1 / 3 is the control parameter for the 3rd order precision format. Δ and Δ are the after-difference and front-difference operators, respectively; Indicated in grid cell The electromagnetic field is conserved in the left state at the interface. Indicated in grid cell The electromagnetic field conserved variable at the right state of the interface; Q i Q is the conserved variable of the scattered electromagnetic field in the i-th grid cell. i+1 It is the conserved variable of the electromagnetic field scattered by the (i+1)th grid cell.

[0168] The calculation process for the implicit iterative solution in alternating directions is as follows:

[0169]

[0170] Where I is the identity matrix, The superscript k is the virtual time step number.

[0171] The approximation factor AF is decomposed as follows:

[0172]

[0173] in, The difference operator performs pre- and post-difference decompositions based on the Steger-Warming split:

[0174]

[0175] in, It is the coefficient matrix after splitting; δ ξ - δ η - δ ζ - These correspond to the backward difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively; δ ξ + δ η + δ ζ + These correspond to the forward difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively.

[0176] The solution is obtained by iteratively solving in the three directions ξ, η, and ζ. For two-dimensional problems, iteration in the ζ direction is not required. The sequence of iterative solutions in the three directions ξ, η, and ζ is as follows:

[0177]

[0178]

[0179]

[0180] ΔQ k =ΔQ ***

[0181] Where, ΔQ * ΔQ ** ΔQ *** These are the differences in electromagnetic conservation variables of the scattered field at adjacent virtual time steps during the intermediate iteration process in the three directions: ξ, η, and ζ.

[0182] Taking the ξ direction as an example, the other two directions follow the same logic. For each direction, the same forward and backward iteration algorithm for L and U is used to calculate the intermediate iteration value ΔQ. * ΔQ ** ΔQ *** :

[0183] LUΔQ * =-rhs

[0184]

[0185]

[0186]

[0187]

[0188] Where L is the forward iteration operator and U is the backward iteration operator; It is the intermediate value of the electromagnetic conservation variable in the forward and backward iterations of L and U; It is the splitting coefficient matrix corresponding to the positive eigenvalue of the Steger-Warming split in the i-th unit. It is the splitting coefficient matrix corresponding to the positive eigenvalue of the (i-1)th unit Steger-Warming split. It is the splitting coefficient matrix corresponding to the negative eigenvalues ​​of the i-th Steger-Warming split. It is the splitting coefficient matrix corresponding to the negative feature of the Steger-Warming split in the (i+1)th unit; It is the difference in electromagnetic conservation variables of the scattered field between adjacent virtual time steps after the L iteration of the i-th unit; It is the difference in electromagnetic conservation variables of the scattered field at adjacent virtual time steps after iteration of unit i-1 L; ΔQ i * It is the difference in electromagnetic conservation variables of the scattered field between adjacent virtual time steps after the iteration of unit i in U; It is the difference in electromagnetic conservation variables of the scattered field at adjacent virtual time steps after the (i+1)th unit U iteration.

[0189] Required The inverse matrix is:

[0190]

[0191]

[0192] in: μ is the magnetic susceptibility, and ε is the dielectric constant.

[0193] The above describes the implicit dual-time-step, alternating-direction calculation process of the time-varying electromagnetic field controlled by Maxwell's equations.

[0194] Step 6: Convergence judgment, post-processing, outputting the temporal and spatial distribution of the electromagnetic field, and outputting surface induced current and radar cross section spatial distribution data, etc.

[0195] like Figure 3 and Figure 4 As shown, the effects of different physical time steps for TM and TE waves on the RCS results of a cylinder (ka=5) were compared. k is the wavenumber, a is the cylinder radius, and the computational grid is 91x46. The object surface grid has 18 grid points per wavelength, the far-field boundary is beyond 3 wavelengths, and the radial grid is fined at the wall, averaging approximately 15 grid points per wavelength. With increasing physical time intervals, the difference between the calculated results and the reference values ​​gradually increases. Under excessively large physical time steps, the computational accuracy of the dual-time-step method decreases. For the two-dimensional problem of the cylinder, the ADI-FVTD software with alternating direction implicit iteration was used. Figure 3 , Figure 4 It can be seen that when the physical time step is taken to the order of 0.01, the numerical calculation results can match the analytical series solution very well.

[0196] like Figure 5 As shown, and Figure 4 Under the same calculation conditions (TE polarization, ka = 5, a is the cylinder radius), the time oscillation history of the scattered electromagnetic field at the same spatial point is almost identical when calculated using the explicit 4th-order Runge-Kutta method and the two-time-step ADI-FVTD method. This indicates that the accuracy of the physical-time backward difference, 2nd-order precision two-time ADI-FVTD method meets the requirements of Fourier transform.

[0197] like Figure 6 As shown, the electromagnetic scattering calculation of a metal sphere (ka = 2, a is the radius of the metal sphere) is compared with the numerical calculation results of the time-domain finite volume in alternating directions with different physical time steps. The error is significantly greater when the physical time step is 0.005 than when dt = 0.001. It can be seen that for typical three-dimensional problems, the physical time step must be as small as 0.001 to ensure sufficient calculation accuracy.

[0198] Figure 7 It is the induced current density distribution on the surface of a metal sphere (ka = 5, a is the radius of the metal sphere). Figure 8 The distribution of the radar cross section of the metal sphere in the E-plane and H-plane bistatic radar cross section was compared with the analytical series solution using the explicit 4-step Runge-Kutta method and the implicit alternating direction finite volume method. It is obvious that the ADI-FVTD method for calculating the time-varying electromagnetic field alternating direction fully implicit finite volume also has high numerical calculation accuracy.

[0199] Table 1 compares the time steps required to calculate the above examples using the explicit 4th-order Runge-Kutta FVTD and the implicit alternating direction ADI-FVTD:

[0200] Table 1

[0201]

[0202] It is evident that, due to the requirements of grid refinement and explicit methods that the entire computational space adopts the minimum step size that satisfies stability requirements, the step size of explicit methods is significantly smaller, resulting in a larger computational workload.

[0203] These numerical examples demonstrate that the ADI-FVTD method for calculating time-varying electromagnetic fields with alternating directions, corresponding to this patent, can not only relax the time step constraints while ensuring the accuracy of the format numerical values ​​and accurately obtain the temporal and spatial distribution of the target electromagnetic scattering field, but also improve the time advancement efficiency and save computational costs.

[0204] This application replaces existing methods that typically employ explicit solutions for both time and spatial flux residuals with a time-domain finite volume method that uses dual-time (physical and virtual) time-iterative progression of the conserved electromagnetic field and implicit computation of spatial flux residuals. This allows the physical time step to be selected based on the physical problem without being constrained by stability, while stability is satisfied by the implicit virtual time sub-iteration. This overcomes the computational burden of explicit methods, which are limited by stability and require a uniform minimum global step size and refined mesh, thus improving computational efficiency. Finally, this dual-time-step implicit time-domain finite volume method efficiently solves 2D and 3D Maxwell's equations to obtain the temporal and spatial distributions of the target time-varying electromagnetic field, improving time progression efficiency while maintaining scheme accuracy and saving computational costs.

[0205] The incident field in this application is given analytically, and the Maxwell equations in the form of the scattered field are solved. The propagation of the incident electromagnetic wave does not need to be numerically calculated in the entire computational grid space, thus avoiding the dissipation and dispersion of the incident electromagnetic field and helping to maintain numerical accuracy.

[0206] This application supports structured meshes and multi-domain decomposition. Using a body-fitted mesh, the integral form of the conservation laws of Maxwell's equations can be directly applied to discrete curvilinear coordinate system mesh elements. This application's method differs from traditional FDTD. FDTD uses Cartesian orthogonal meshes to simulate the step effect on the wall surface, which affects numerical accuracy. It also adds artificial viscosity to the second-order central difference scheme by placing electromagnetic field components in a spatiotemporal cross-referenced manner. FVTD, using a body-fitted curvilinear coordinate system mesh, can better fit the object surface and refine the mesh at geometric singularities. Furthermore, the electromagnetic field quantities are co-located at the center of the mesh elements in the mesh space, and an upwind scheme is used to maintain artificial viscosity, which is more conducive to maintaining accuracy and algorithm design.

[0207] This application employs a time-progressive dual-time-step iteration, implicit spatial flux iteration, and Jacobian coefficient matrix splitting, with alternating direction dimension-wise forward and backward iterations. The time-domain finite volume method, combining dual-time-step time and implicit spatial flux, can stably, accurately, and efficiently obtain the temporal and spatial distributions of electromagnetic fields. It is suitable for numerical simulations of electromagnetic wave propagation and reflection, and is particularly well-suited for large-scale, computationally intensive electromagnetic field calculations and scattering stealth characteristic calculations for electrically large targets.

[0208] This application employs implicit iteration of spatial flux and forward and backward iteration of splitting the Jacobian coefficient matrix to solve the problem. It replaces the inversion of sparse matrices with dimension-wise summation and two loops, which is simple and easy to use in engineering.

[0209] This application improves computational performance by relaxing the restrictions on iterative physical time steps at very small grid scales while maintaining high numerical accuracy.

[0210] This application is used to calculate time-varying electromagnetic fields and corresponding target electromagnetic properties. By introducing a steady virtual time derivative term into the governing equations, the physical time derivative is linearized within each physical time interval. This allows the physical time step size to be selected according to the physical problem without being limited by stability. The stability requirements of the calculation are met by the virtual time sub-iteration. The steady calculation of the sub-iteration can be accelerated by using a local time step, which greatly shortens the calculation time required to obtain a stable electromagnetic field.

[0211] This application provides a solution for iterative calculation of conserved variables in time-varying electromagnetic fields using an alternating direction fully implicit finite volume method: a dual-time-step progression formula combining virtual time and physical time for Maxwell's equations, and a formula and steps for inverting the spatial flux residuals of the dimension-wise forward and backward iterative matrix. This forms a novel software for alternating direction fully implicit finite volume of time-varying electromagnetic fields. Compared with traditional Runge-Kutta explicit time-step progression and explicit calculation of spatial flux in time-domain finite volume methods, this method relaxes the extreme restrictions on physical time steps imposed by the mesh and explicit algorithms. This dual-time-step implicit time-domain finite volume method can efficiently solve 2D and 3D Maxwell's equations to obtain the spatiotemporal distribution of time-varying electromagnetic fields, improving time-step progression efficiency and enhancing computational performance while ensuring format accuracy.

[0212] The electromagnetic characteristic analysis device for a target object provided in the embodiments of this application is described below. The electromagnetic characteristic analysis device for a target object described below and the electromagnetic characteristic analysis method for a target object described above can be referred to each other.

[0213] See Figure 9 A structural diagram of an electromagnetic characteristic analysis device for a target object is shown according to an exemplary embodiment, as follows: Figure 9 As shown, it includes:

[0214] Modeling module 901 is used to perform simulation modeling based on the boundary condition information of the target object to obtain a simulation model of the target object;

[0215] Module 902 is used to mesh the simulation model using a preset structure and to establish a time-varying electromagnetic field based on Maxwell's equations on the meshed simulation model.

[0216] The solver module 903 is used to implicitly solve the time-varying electromagnetic field of Maxwell's equations based on a dual iterative method of physical time and virtual time.

[0217] Analysis module 904 is used to output the electromagnetic property analysis results of the target object when the time-varying electromagnetic field of the Maxwell equations converges.

[0218] The electromagnetic property analysis device for target objects provided in this application implicitly solves the time-varying electromagnetic field of Maxwell's equations through a dual iterative approach of conserved electromagnetic field physical time and virtual time. This replaces the explicit solution algorithms commonly used in existing methods, where both time and spatial flux residuals are calculated. The physical time step is selected based on the physical problem and is not limited by stability, while stability is satisfied by the implicit virtual time sub-iteration. This overcomes the computational burden caused by the stability limitations of explicit methods and the necessity of using a uniform minimum global step size and a refined mesh, thus improving computational efficiency. Therefore, the electromagnetic property analysis device for target objects provided in this application improves the efficiency of electromagnetic property analysis for target objects.

[0219] Based on the above embodiments, as a preferred implementation, the establishment module 902 is specifically used to: mesh the simulation model using a preset quadrilateral structure or hexahedral structure, and establish a time-varying electromagnetic field of Maxwell's equations based on the meshed simulation model.

[0220] Based on the above embodiments, as a preferred implementation, the mesh density at the target location in the simulation model is negatively correlated with the distance between the target location and the wall, and negatively correlated with the distance between the target location and the geometric singularity.

[0221] Based on the above embodiments, as a preferred implementation, the solution module 903 is specifically used to: obtain electromagnetic parameters and control parameters, and implicitly solve the time-varying electromagnetic field of Maxwell's equations using the electromagnetic parameters and the control parameters based on a dual iteration method of physical time and virtual time.

[0222] Based on the above embodiments, as a preferred implementation, the solution module 903 is specifically used for: iterating through the physical time step until the physical time step iteration converges; during each physical time step iteration, iterating through the virtual time step until the virtual time step iteration converges; during each virtual time step iteration, implicitly solving the time-varying electromagnetic field of Maxwell's equations based on the physical time step and the virtual time step using the electromagnetic parameters and the control parameters, so as to update the value of the conserved electromagnetic field for the next virtual time step iteration.

[0223] Based on the above embodiments, as a preferred implementation, the time-varying electromagnetic field of Maxwell's equations is:

[0224]

[0225] Where Δt is the physical time step and Δτ is the virtual time step. These are the electromagnetic conservation variables at the (n+1)th virtual time step of the j, k, and l grid cells. Q is the electromagnetic conservation variable at the nth virtual time step of the j, k, and l grid cells. n +1 Q is the electromagnetic conservation variable at the (n+1)th physical time step. n Q is the electromagnetic conserved variable at the nth physical time step. n-1 ω is the electromagnetic conservation variable at the (n-1)th physical time step, δ is the implicit control parameter, and ω is the electromagnetic conservation variable at the (n-1)th physical time step. ξ δ η δ ζ These correspond to the difference operators in the directions ξ, η, and ζ of the curvilinear coordinate system, respectively. Jacobian coefficient matrices corresponding to the electromagnetic flux in the directions ξ, η, and ζ in the curvilinear coordinate system, respectively, ΔQ n It is the difference in the conserved variables of the scattered field between adjacent physical times. It is the spatial flux residual at the nth physical time step, and RHS is the total spatial flux residual at the previous physical time step plus the corrections from the physical time step and the virtual time step.

[0226] Based on the above embodiments, as a preferred implementation, the analysis module 904 is specifically used to: when the time-varying electromagnetic field of the Maxwell equations converges, output any one or a combination of any of the time distribution, spatial distribution, surface induced current, and radar cross section spatial distribution data of the target object.

[0227] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0228] Based on the hardware implementation of the above program modules, and in order to implement the method of the embodiments of this application, the embodiments of this application also provide an electronic device. Figure 10 This is a structural diagram of an electronic device according to an exemplary embodiment, such as... Figure 10 As shown, the electronic device includes:

[0229] Communication interface 1 enables information exchange with other devices, such as network devices;

[0230] Processor 2, connected to communication interface 1, enables information exchange with other devices and, when running a computer program, executes the electromagnetic characteristic analysis method for the target object provided by one or more of the above-mentioned technical solutions. The computer program is stored in memory 3.

[0231] Of course, in practical applications, the various components in an electronic device are coupled together through bus system 4. It can be understood that bus system 4 is used to achieve communication and connection between these components. In addition to the data bus, bus system 4 also includes a power bus, a control bus, and a status signal bus. However, for clarity, in... Figure 10 The general will label all buses as Bus System 4.

[0232] The memory 3 in this embodiment is used to store various types of data to support the operation of the electronic device. Examples of such data include any computer program used to operate on the electronic device.

[0233] It is understood that memory 3 can be volatile memory or non-volatile memory, or both. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), ferromagnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc, or compact disc read-only memory (CD-ROM); magnetic surface memory can be disk storage or magnetic tape storage. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Synchronous Static Random Access Memory (SSRAM), Dynamic Random Access Memory (DRAM), Synchronous Dynamic Random Access Memory (SDRAM), Double Data Rate Synchronous Dynamic Random Access Memory (DDRSDRAM), Enhanced Synchronous Dynamic Random Access Memory (ESDRAM), SyncLink Dynamic Random Access Memory (SLDRAM), and Direct Rambus Random Access Memory (DRRAM).The memory 3 described in the embodiments of this application is intended to include, but is not limited to, these and any other suitable types of memory.

[0234] The methods disclosed in the embodiments of this application can be applied to processor 2, or implemented by processor 2. Processor 2 may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the integrated logic circuit of the hardware in processor 2 or by instructions in the form of software. The processor 2 may be a general-purpose processor, DSP, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Processor 2 can implement or execute the methods, steps and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor may be a microprocessor or any conventional processor, etc. The steps of the methods disclosed in the embodiments of this application can be directly manifested as being executed by a hardware decoding processor, or being executed by a combination of hardware and software modules in the decoding processor. The software modules may be located in a storage medium, which is located in memory 3. Processor 2 reads the program in memory 3 and completes the steps of the aforementioned method in combination with its hardware.

[0235] When processor 2 executes the program, it implements the corresponding processes in the various methods of the embodiments of this application. For the sake of brevity, these will not be described in detail here.

[0236] In an exemplary embodiment, this application also provides a storage medium, namely a computer storage medium, specifically a computer-readable storage medium, such as a memory 3 that stores a computer program, which can be executed by a processor 2 to complete the steps described in the aforementioned method. The computer-readable storage medium may be a memory such as FRAM, ROM, PROM, EPROM, EEPROM, Flash Memory, magnetic surface memory, optical disc, or CD-ROM.

[0237] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0238] Alternatively, if the integrated units described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0239] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for analyzing the electromagnetic properties of a target object, characterized in that, include: Simulation modeling is performed based on the boundary condition information of the target object to obtain a simulation model of the target object; The simulation model is meshed using a preset structure, and a time-varying electromagnetic field based on Maxwell's equations is established based on the meshed simulation model. The time-varying electromagnetic field of Maxwell's equations is implicitly solved using a dual iterative method based on physical time and virtual time. When the time-varying electromagnetic field of the Maxwell equations converges, the electromagnetic property analysis results of the target object are output. The implicit solution of the time-varying electromagnetic field of Maxwell's equations based on a dual iterative method using both physical and virtual time includes: Electromagnetic parameters and control parameters are obtained, and the time-varying electromagnetic field of Maxwell's equations is implicitly solved using the electromagnetic parameters and control parameters based on a dual iterative method of physical time and virtual time. The implicit solution of the time-varying electromagnetic field of Maxwell's equations using the electromagnetic parameters and the control parameters based on a dual iterative method of physical time and virtual time includes: The physical time step iterative loop continues until the physical time step iterative convergence is achieved. During each physical time step iteration, the virtual time step iterates and loops until the virtual time step iteration converges; In each virtual time sub-iteration, the electromagnetic parameters and the control parameters are used to implicitly solve the time-varying electromagnetic field of Maxwell's equations based on the physical time step and the virtual time step, so as to update the value of the conserved electromagnetic field for the next virtual time sub-iteration step. The time-varying electromagnetic field of Maxwell's equations is as follows: ； in, For physical time step, For virtual time step, It is the j-th, k-th, l-th grid cell. Electromagnetic conserved variables at the virtual time step It is the j-th, k-th, l-th grid cell. Electromagnetic conserved variables at the virtual time step It is the first Electromagnetic conserved variables at the physical time step It is the first Electromagnetic conserved variables at the physical time step It is the first Electromagnetic conserved variables at the physical time step These are implicit control parameters. , , Corresponding to curvilinear coordinate systems , , Directional difference operator, , , Corresponding to curvilinear coordinate systems , , Jacobian coefficient matrix of directional electromagnetic flux It is the difference in the conserved variables of the scattered field between adjacent physical times. It is the first The physical time step spatial flux residual, RHS, is the total spatial flux residual of the previous physical time step plus the corrections from the physical time step and the virtual time step.

2. The electromagnetic property analysis method according to claim 1, characterized in that, The step of meshing the simulation model using a preset structure includes: The simulation model is meshed using a preset quadrilateral or hexahedral structure.

3. The electromagnetic property analysis method according to claim 1, characterized in that, In the simulation model, the mesh density at the target location is negatively correlated with the distance between the target location and the wall, and negatively correlated with the distance between the target location and the geometric singularity.

4. The electromagnetic property analysis method according to claim 1, characterized in that, When the time-varying electromagnetic field of the Maxwell's equations converges, the electromagnetic property analysis results of the target object are output, including: When the time-varying electromagnetic field of Maxwell's equations converges, the output is any one or a combination of any of the following: the time distribution, spatial distribution, surface induced current, and radar cross section spatial distribution data of the target object.

5. An electromagnetic characteristic analysis device for a target object, characterized in that, include: The modeling module is used to perform simulation modeling based on the boundary condition information of the target object, and obtain a simulation model of the target object. A module is established to perform meshing on the simulation model using a preset structure, and to establish a time-varying electromagnetic field based on the Maxwell equations of the simulation model after meshing. The solution module is used to implicitly solve the time-varying electromagnetic field of Maxwell's equations based on a dual iterative method of physical time and virtual time; The analysis module is used to output the electromagnetic property analysis results of the target object when the time-varying electromagnetic field of the Maxwell equations converges; Specifically, the solution module is used to: obtain electromagnetic parameters and control parameters, and implicitly solve the time-varying electromagnetic field of Maxwell's equations using the electromagnetic parameters and control parameters based on a dual iterative method of physical time and virtual time; Specifically, the solution module is used for: iterating through the physical time step until the physical time step converges; iterating through the virtual time step sub-iteration during each physical time step iteration until the virtual time step converges; and implicitly solving the time-varying electromagnetic field of Maxwell's equations based on the physical time step and the virtual time step using the electromagnetic parameters and the control parameters during each virtual time sub-iteration, so as to update the value of the conserved electromagnetic field for the next virtual time sub-iteration step. The time-varying electromagnetic field of Maxwell's equations is as follows: ； in, For physical time step, For virtual time step, It is the j-th, k-th, l-th grid cell. Electromagnetic conserved variables at the virtual time step It is the j-th, k-th, l-th grid cell. Electromagnetic conserved variables at the virtual time step It is the first Electromagnetic conserved variables at the physical time step It is the first Electromagnetic conserved variables at the physical time step It is the first Electromagnetic conserved variables at the physical time step These are implicit control parameters. , , Corresponding to curvilinear coordinate systems , , Directional difference operator, , , Corresponding to curvilinear coordinate systems , , Jacobian coefficient matrix of directional electromagnetic flux It is the difference in the conserved variables of the scattered field between adjacent physical times. It is the first The physical time step spatial flux residual, RHS, is the total spatial flux residual of the previous physical time step plus the corrections from the physical time step and the virtual time step.

6. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the electromagnetic property analysis method for the target object as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the electromagnetic property analysis method for the target object as described in any one of claims 1 to 4.

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