Grid frequency domain electromagnetic field finite volume convergence acceleration method, equipment and medium

Abstract

The invention discloses a finite volume convergence acceleration method and device for a grid frequency domain electromagnetic field and a medium, and belongs to the field of calculation of electromagnetic frequency domain numerical values, and the method comprises the steps: carrying out the iterative solution of a Maxwell equation set frequency domain electromagnetic field based on virtual time advance and space flux residual splitting calculation and correction; performing steady virtual time step circulation on the simulation model until convergence is finished; in each virtual time iteration process, space flux calculation and correction and implicit iterative solution calculation are carried out on each grid block grid and each grid unit in sequence, and a next-level virtual time iteration step number conservation electromagnetic field numerical value is updated; and finally, outputting real part and imaginary part spatial distribution of the electromagnetic field, and outputting surface induced current and radar cross section spatial distribution data. According to the method, the problem of large-scale electromagnetic scattering of any complex-shape and high-frequency electrically large-size target can be solved.

Description

Technical Field

[0001] The present invention relates to the frequency domain numerical field of computational electromagnetics, and more specifically, to a grid frequency domain electromagnetic field finite volume convergence acceleration method, device and medium. Background Art

[0002] Electromagnetic scattering, electromagnetic interference, and electromagnetic compatibility of various aircraft require high-precision spatial distribution data of electromagnetic fields. The electromagnetic field is controlled by Maxwell's equations. The development of computer technology has begun to numerically simulate this set of equations. In the 1990s, the finite volume method of computational fluid dynamics (CFD) was introduced into computational electromagnetic field science, forming the finite volume time domain method (FVTD) for electromagnetic field calculation. FVTD uses a body-fitting curved coordinate system grid, which has a conformal effect on complex shapes and is superior to the traditional finite difference time domain method.

[0003] Time domain calculation can simulate broadband pulse electromagnetic waveforms, which is more intuitive and dynamic. For single-frequency simple harmonic electromagnetic waves, frequency domain calculation is more convenient. Traditional frequency domain full-wave numerical methods mainly include the method of moment (MOM) that solves integral equations with current as a variable, and the finite element method (FEM) of the Helmholtz wave equation that solves the electromagnetic field.

[0004] FVTD is extended to the frequency domain to form the finite volume frequency domain method (FVFD). This field calculation differential method can simulate fine structures and inhomogeneous media, but the frequency domain differential classification algorithm is not yet mature. For example, there are problems of cumbersome and difficult calculations. In practical applications, some calculation states have long-term oscillations and slow convergence.

[0005] In CFD, there are also selective frequency dissipation or modal space filtering to truncate high-frequency components, and filter dynamic instability modes to achieve high-frequency filtering and dissipation effects. Steady-state FVFD is derived from the mathematical characteristics of the hyperbolic equation group. The electromagnetic information propagation and numerical algorithm design are derived from the upwind characteristic line theory through the eigenvalue. Since the Maxwell equation group contains two zero eigenvalues, the numerical viscosity dissipation of the corresponding characteristic invariant in the flux calculated by Steger-Warming splitting or Roe splitting based on the eigenvalue is also 0. The numerical difficulties caused by zero artificial viscosity will bring non-physical oscillations and convergence stability problems, which have not been considered in the time domain / frequency domain finite volume method of electromagnetic field calculation in the early stage. In order to solve the numerical oscillation and slow convergence caused by the default of some numerical viscosity in FVFD, smooth out the numerical jump of clutter and improve the application efficiency, especially to improve the application efficiency of parallel large grid and electrically large target electromagnetic problems, this application proposes an electromagnetic flux correction algorithm to maintain the numerical viscosity dissipation effect, maintain the stability of the numerical solution process and suppress the numerical oscillation of the electromagnetic field quantity in the convergence process.

[0006] In summary, it is necessary to develop an electromagnetic flux correction algorithm that maintains numerical viscosity, maintains the stability of the numerical solution process, and accelerates iterative convergence, forming a new FVFD algorithm with accelerated convergence techniques, which will greatly improve the application efficiency of FVFD in various large-scale electromagnetic problems. Summary of the invention

[0007] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a grid frequency-domain electromagnetic field finite volume convergence acceleration method, device and medium, which can solve large-scale electromagnetic scattering problems of targets with arbitrary complex shapes and high-frequency electrical large sizes, or solve electromagnetic problems that are difficult to handle with multi-scale MOM containing complex electronic detail structures.

[0008] The object of the present invention is achieved through the following solutions: A grid frequency domain electromagnetic field finite volume convergence acceleration method, comprising: Based on virtual time advancement and calculation and correction of spatial flux residual splitting, the frequency domain electromagnetic field of Maxwell's equations is iteratively solved; the simulation model is cycled through a constant virtual time step until convergence is achieved; in each virtual time iteration process, spatial flux calculation and correction and implicit iterative solution calculation are performed on each grid block and each grid unit in turn, and the conserved electromagnetic field value of the next level of virtual time iteration step is updated; finally, the spatial distribution of the real and imaginary parts of the electromagnetic field is output, and the spatial distribution data of the surface induced current and radar scattering cross section are output.

[0009] Furthermore, the simulation model is cycled through a constant virtual time step until convergence is complete; in each virtual time iteration process, spatial flux calculation and correction and implicit iterative solution calculation are performed on each grid block and each grid unit in turn, and the value of the conserved electromagnetic field of the next virtual time iteration step is updated, which specifically includes the following sub-steps: The process of the constant virtual time step cycle until convergence is as follows: Add virtual time derivative , the frequency domain complex rectangular coordinate system Maxwell equations to be solved are modified to: ; (1) ; (2) in, is the complex-valued scattering electromagnetic field conservation variable, It's virtual time. is the sign of the imaginary part, is pi, is the frequency of the incident simple harmonic electromagnetic wave, , , is the electromagnetic flux in rectangular coordinates , , Quantity, is the complex scattered magnetic induction intensity vector, is the complex scattered field electric displacement vector; In the curvilinear coordinate system grid space, the constant iteration adopts a fully implicit algorithm: ; (3) in, is the structural grid curve coordinate system direction 1, is the structural grid curve coordinate system direction 2, is the structural grid curve coordinate system direction 3; They correspond to the curvilinear coordinate system Directional electromagnetic flux; subscript is the grid cell number, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is Grid unit The spatial flux residual at the virtual time step, is the virtual time step controlled by stability, calculated from the CFL number and the local grid cell geometry scale and eigenvalues; The process of calculating and correcting the spatial flux and calculating the implicit iterative solution is as follows: Steger-Warming splitting is used to calculate the interface flux of the grid cells

[0010] ; (4) In the formula, the subscript Take the curvilinear coordinate system One of the directions, corresponding That is the corresponding The direction of the electromagnetic flux, Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the positive eigenvalue in the Steger-Warming splitting in the corresponding direction; Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding direction; For the grid cell interface flux calculated using Steger-Warming splitting Carry out the correction process, including direction: First, truncate the corrected split eigenvalues: ; ; ; In the formula, They are The diagonal matrix of positive and negative eigenvalues ​​of the grid cells, is the local grid cell magnetic permeability, is the relative permittivity of the local grid cell, For local Directional grid geometry stretch factor; is the local cutoff eigenvalue added for the eigenvalue of 0; Secondly, the Steger-Warming splitting method is used to calculate the interface flux of the grid cells. To make corrections: ; ; Specifically, the curve grid direction 1 Direction, that is: ; (5) ; ; in, is the modified flux on top of the flux calculated by the initial Steger-Warming splitting, is the local cutoff eigenvalue, is the control parameter; the other curves in mesh directions 2 and 3 The numerical flux correction is similar; Formula (3) adopts the implicit linearization of spatial flux and the splitting of Jacobi coefficient matrix to solve it by forward and backward iteration. After the Steger-Warming splitting of Jacobi coefficient generated by the conservation variable of flux partial derivative, ; (6) ; in, is the coefficient matrix after splitting, is the spatial flux residual calculated at the previous iterative time step, is the implicit sub-iteration electromagnetic field difference; Finally, based on the LUSGS forward and backward iterative calculation, the electromagnetic field difference is obtained .

[0011] Furthermore, the control parameters The range is .

[0012] Further, Corresponds to no numerical flux correction.

[0013] A grid frequency domain electromagnetic field finite volume convergence acceleration device comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is loaded by the processor, the method described in any one of the above items is executed.

[0014] A computer-readable storage medium stores a computer program, wherein the computer program is loaded by a processor and executes any of the above methods.

[0015] The beneficial effects of the present invention include: 1. The present invention can simulate large-scale electromagnetic simulation calculations of complex shapes and electrically large targets, or electromagnetic engineering problems such as fine structures and inhomogeneous media that are difficult to handle using the moment method.

[0016] 2. The present invention takes into account the numerical viscosity default and computational oscillation phenomenon caused by the zero eigenvalue of the Jacobian coefficient matrix in the Maxwell equations, and provides a corresponding solution.

[0017] 3. The present invention maintains numerical viscosity, stability of the solution process and suppresses numerical oscillations of electromagnetic field quantities in the convergence process by truncating eigenvalues ​​and using an electromagnetic flux correction algorithm. The calculation of the frequency domain electromagnetic field of a typical two-dimensional cylindrical structure grid shows that, under the same calculation conditions and convergence criteria, the convergence of TM wave polarization drops from 20,400 steps before the numerical flux correction is used to 900 steps after use. It can be seen that the convergence steps of this typical two-dimensional problem using the numerical flux correction algorithm proposed by the present invention are reduced to 1 / 20 of the original, and the efficiency is greatly improved. The calculation of the frequency domain electromagnetic field of a typical three-dimensional metal sphere structure grid shows that, under the same calculation conditions and convergence criteria, the convergence steps of this typical three-dimensional problem using the numerical flux correction algorithm proposed by the present invention are reduced to less than 1 / 3 of the original, and the efficiency is greatly improved.

[0018] 4. The frequency-domain finite volume method for implicit flux zero eigenvalue correction proposed in the present invention can greatly save convergence iteration time and reduce the disadvantages of large computational complexity and low efficiency for electrically large targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0020] Figure 1 A schematic diagram of a process for calculating a frequency domain electromagnetic field using the present invention; Figure 2 The electromagnetic field comparison before and after the numerical flux correction of the FVFD calculation of a metal cylinder (ka=5, TM) by the present invention; Bx in the diagram represents the x-component amplitude of the complex scattered magnetic induction intensity vector, is the artificial viscosity control parameter; Figure 3 The figure shows the convergence curve comparison before and after the correction of the numerical flux of FVFD calculation of metal cylinder (ka=5, TM) by the present invention; dhmax in the figure indicates that the maximum difference of magnetic field intensity in adjacent iteration steps is used as the residual standard, and demax in the figure indicates that the maximum difference of electric field intensity in adjacent iteration steps is used as the residual standard. is the artificial viscosity control parameter; Figure 4 Comparison of the distribution of the dual-station radar cross section before and after the numerical flux correction of the FVFD calculation of the metal cylinder (ka=5, TM) by the present invention; represents the scattering azimuth, and the deg. in brackets indicates the unit is degree; the ordinate It represents the two-dimensional radar scattering width normalized by wavelength, and the dB in brackets represents the decibel unit; in the icon, ExactTM represents the exact solution of 2D TM wave polarization; FVFD represents the frequency domain finite volume method, is the artificial viscosity control parameter; Figure 5 The electromagnetic field comparison before and after the numerical flux correction of the FVFD calculation of a metal ball (ka=2) using the present invention; Dx in the diagram represents the amplitude of the x component of the complex scattered electric displacement vector, is the artificial viscosity control parameter; Figure 6 The figure shows the convergence curve comparison before and after the correction of the numerical flux of FVFD calculation of a metal ball (ka=2) by the present invention; dhmax in the figure indicates that the maximum difference between the magnetic field strengths of adjacent iteration steps is used as the residual standard, and demax in the figure indicates that the maximum difference between the electric field strengths of adjacent iteration steps is used as the residual standard. is the artificial viscosity control parameter. DETAILED DESCRIPTION

[0021] All features disclosed in all embodiments in this specification, or steps in all methods or processes implicitly disclosed, except for mutually exclusive features and / or steps, can be combined and / or expanded or replaced in any manner.

[0022] The specific implementation process of the present invention is as follows: In a preferred embodiment, the present invention relates to a numerical simulation method for calculating the distribution of electromagnetic fields in the frequency domain of grid space based on the implicit frequency domain finite volume method FVFD (Finite Volume Frequency Domain, FVFD), and in particular to an acceleration technique for improving the iterative convergence efficiency of steady-state complex scattering fields. In a specific embodiment, the present invention provides an electromagnetic flux correction method for maintaining numerical viscosity and accelerating iterative convergence in the process of calculating electromagnetic fields using a structured grid and an implicit frequency domain finite volume method, including simulation modeling based on the physical background of the electromagnetic problem simulated by the target and combined with boundary condition information; the quadrilateral or hexahedral structured grid in the numerical calculation area is encrypted at the wall and geometric singularities, and the grid gradually moves away from the scattering wall and becomes sparse; the grid data file is output and the boundary condition file is set and output; the target calculation electromagnetic parameters and numerical calculation control parameters are input; the grid data and boundary condition information file are input to initialize the calculation space electromagnetic field; the electromagnetic flux of the grid unit interface is corrected to maintain numerical viscosity; the frequency domain electromagnetic field of the Maxwell equations is iteratively solved; the real and imaginary spatial distribution of the electromagnetic field is output, and the surface induced current and radar cross-section spatial distribution data are output. The invention can solve the large-scale electromagnetic scattering problem of targets with arbitrary complex shapes, high frequencies and large sizes.

[0023] Further, see Attachment Figure 1The entire structural grid frequency domain electromagnetic field finite volume convergence acceleration algorithm software can be divided into three parts according to the 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, pre-processing is performed to provide calculation support for electromagnetic field calculation; electromagnetic field calculation includes: spatial electromagnetic field MUSCL format interpolation, unit interface flux calculation and correction, time advancement, and convergence judgment module; post-processing is mainly used to output the spatial real and imaginary distribution of the electromagnetic field, the target surface induced current density, and the radar scattering cross section output.

[0024] Next, we combine the two curl equations (time factor) of the frequency domain Maxwell equations to be numerically simulated. ), Faraday's law of electromagnetic induction: ; Ampere's theorem: , introduces the numerical calculation process of implicit frequency domain finite volume method. is the imaginary sign corresponding to the complex variable, is the frequency of the simple harmonic electromagnetic wave, is the complex scattered magnetic induction intensity vector, is the complex scattered field electric displacement vector, is the electric field intensity vector of the scattered field, Scattering field magnetic field intensity vector, It is an external forced current.

[0025] The conservative form of the two curl equations of the frequency domain Maxwell equations under the condition of no source is:

[0026]

[0027] in, is the conservation variable of the scattered electromagnetic field, It's virtual time. is the sign of the imaginary part, is pi, is the frequency of the incident simple harmonic electromagnetic wave, , , is the electromagnetic flux in rectangular coordinates , , Quantity, is the complex scattered magnetic induction intensity vector, is the complex scattered field electric displacement vector, is the electric field intensity vector of the scattered field, Scattering field magnetic field intensity vector, including subscripts , , The scalars are the rectangular coordinates of the corresponding vectors , , Quantity.

[0028] Clearly visible when When converged, this system of equations is equivalent to the original system of equations.

[0029] For objects with complex shapes, the computational space body-fitting multi-block structure grid is used, so there is a coordinate transformation:

[0030]

[0031] in Represents a curvilinear coordinate system In three directions, the conservation form of Maxwell's equations in the curvilinear coordinate system for numerical simulation is obtained:

[0032]

[0033]

[0034]

[0035] In the formula, is the Jacobian matrix of the coordinate transformation. The corresponding ^ superscript variables represent the values ​​in the curvilinear coordinate system, which are obtained by the coordinate transformation. is the electromagnetic conservation variable in the curvilinear coordinate system; is the structural grid curve coordinate system direction 1, is the structural grid curve coordinate system direction 2, is the structural grid curve coordinate system direction 3; is the electromagnetic flux in the curvilinear coordinate system. Take separately One of three curvilinear coordinate directions.

[0036] In order to get rid of the drawback of large amount of calculation caused by the global limitation of iterative time step of traditional explicit finite volume, a structured grid frequency domain electromagnetic field finite volume convergence acceleration algorithm of the present invention utilizes the local time step constant iterative advancement, combined with implicit spatial flux residual calculation and correction to obtain a stable and efficient calculation process, which includes the following steps: Step 1: Perform simulation modeling based on the physical background of the target electromagnetic problem and boundary condition information.

[0037] Step 2: Use quadrilateral (2D) or hexahedral (3D) structures to mesh the simulation model. The mesh is encrypted on the wall and geometric singularities, and the mesh becomes sparser as it moves away from the scattering wall. Numerically calculate the mesh of the corresponding area, output the mesh data file, set and output the boundary condition file. The mesh density ensures 13-20 grid points per wavelength, the wall density is >300 points per wavelength, and the geometric singularities are encrypted to 50-100 grid points per wavelength. The two-dimensional grid is advanced one layer according to the right-hand rule in the plane perpendicular to the two-dimensional grid, and is calculated uniformly as a special case of the three-dimensional problem. The mesh data file includes the number of structural grid blocks and the dimensions of each block in the three curvilinear coordinate system.

[0038] Step 3: Preprocessing: Input the target calculation electromagnetic parameters, numerical calculation control parameters, and the corresponding flow field parameter file if there is a plasma external flow field. The virtual time iteration is implicit and its CFL number is not constrained by explicit stability requirements.

[0039] Step 4: Input the mesh data and boundary condition information file to initialize the calculation of the spatial electromagnetic field.

[0040] Step 5: Iteratively solve the frequency domain electromagnetic field of Maxwell's equations based on virtual time advancement and spatial flux residual splitting calculation and correction.

[0041] Step 5-1: Cycle the constant virtual time step until the calculation converges.

[0042]

[0043]

[0044]

[0045] in, is the conservation variable of the scattered electromagnetic field, It's virtual time. is the frequency of the incident simple harmonic electromagnetic wave, , , is the electromagnetic flux in rectangular coordinates , , Quantity, is the complex scattered magnetic induction intensity vector, is the complex scattered field electric displacement vector, is the electric field intensity vector of the scattered field, Scattering field magnetic field intensity vector, including subscripts , , The scalars are the rectangular coordinates of the corresponding vectors , , Quantity.

[0046] In the curvilinear coordinate system grid space, the constant iteration adopts the implicit algorithm:

[0047] in, is the structural grid curve coordinate system direction 1, is the structural grid curve coordinate system direction 2, is the structural grid curve coordinate system direction 3; They correspond to the curvilinear coordinate system Directional electromagnetic flux; is an implicit control parameter, The fully implicit form of the other parameters corresponds to the explicit and implicit mixed format; subscript is the grid cell number, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is Electromagnetic conservation variables for virtual time steps, It is Electromagnetic conservation variables for virtual time steps, It is Grid unit The spatial flux residual at the virtual time step, It is Grid unit The spatial flux residual at the virtual time step, It is a virtual time step controlled by stability, calculated by the CFL number and the local grid unit geometric scale and eigenvalue, which is significantly different from the explicit method. Different grid units in the steady-state calculation have different local virtual time sub-iteration steps, thereby accelerating the convergence of the electromagnetic field of the unit.

[0048] Step 5-2: In each virtual time iteration process, the spatial flux calculation and correction and implicit iterative solution calculation are performed grid block by grid block and grid cell by grid cell, and the conservative electromagnetic field value of the next virtual time iteration step is updated.

[0049] The spatial accuracy of the finite volume method is reflected in whether it can accurately simulate the conserved variables. The state variables at the grid cell interface are used to obtain the corresponding accurate interface flux , Steger-Warming splitting is used to calculate the interface flux of the grid cells.

[0050]

[0051]

[0052]

[0053] In the formula, the subscript Take the curvilinear coordinate system One of the directions, corresponding That is the corresponding The direction of the electromagnetic flux, Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the positive eigenvalue in the Steger-Warming splitting in the corresponding direction; Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding direction; is the similarity matrix, are diagonal matrices consisting of positive and negative eigenvalues, respectively. They represent the left and right state variables at the interface respectively, and they can use the MUSCL format to achieve the highest third-order accuracy.

[0054]

[0055]

[0056] in is a limiter, subscript is the grid cell number, Corresponding unit interface, is the control parameter in third-order precision format, and are the post-difference and pre-difference operators respectively; Represented in grid cells The left state electromagnetic field conservation variable at the interface, Represented in grid cells Conservation variables of the right-state electromagnetic field at the interface; It is The conservation variables of the electromagnetic field scattered by each grid cell are: It is The grid cells scatter the electromagnetic field conservation variables.

[0057] For the grid cell interface flux calculated using Steger-Warming splitting Carry out the correction process to direction as an example, and the other two directions are analogous.

[0058] First truncate the eigenvalues ​​after the modified split:

[0059] in They are The diagonal matrix of positive and negative eigenvalues ​​of the grid cells, is the local grid cell magnetic permeability, is the relative permittivity of the local grid cell.

[0060] Secondly, the grid cell interface flux calculated by Steger-Warming splitting To make corrections:

[0061]

[0062] With the curved grid direction 1 Taking direction as an example,

[0063]

[0064]

[0065] in, is the local cutoff eigenvalue, is the control parameter. The remaining curves in grid directions 2 and 3 Numerical flux corrections follow similarly.

[0066] The spatial flux implicit iteration and the splitting of the Jacobi coefficient matrix are solved by forward and backward iteration, and the Jacobi coefficient Steger-Warming splitting generated by the flux partial derivative conservation variable is obtained.

[0067]

[0068] in is the coefficient matrix after splitting, is the spatial flux residual calculated at the previous iterative time step, is the implicit sub-iteration electromagnetic field difference.

[0069] Will Expressed as LDU approximate factorization

[0070] Among them, the subscript is the grid cell number, is the maximum eigenvalue splitting parameter of the Jacobi coefficient matrix, is the largest eigenvalue of the Jacobian coefficient matrix. is the unit diagonal matrix, is a diagonal matrix, is an upper triangular matrix, is a lower triangular matrix, is the difference of the electromagnetic conservation variables corresponding to the upper triangular matrix, is the difference of electromagnetic conservation variables corresponding to the lower triangular matrix; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; refer to The difference of electromagnetic conservation variables in adjacent iteration time steps of the grid cells; It refers to adjacent The coefficient matrix after the grid cell splitting; means The coefficient matrix after the adjacent grid cells are split; It refers to adjacent The coefficient matrix after the grid cell splitting; It refers to adjacent The coefficient matrix after the grid cell splitting; means The coefficient matrix after the adjacent grid cells are split; means The coefficient matrix after the adjacent grid cells are split; Finally, the electromagnetic field difference calculated by forward and backward iteration is obtained :

[0071]

[0072]

[0073] in, is a diagonal matrix The inverse matrix of , According to , The calculated upper triangular matrix and lower triangular matrix; Forward loop:

[0074] Backward loop:

[0075] in, It is the intermediate transition variable of the difference of electromagnetic conservation variables.

[0076] The above is the iterative process of calculating the frequency domain electromagnetic field controlled by the Maxwell equations using implicit FVFD with numerical flux correction to accelerate convergence.

[0077] Step 6: Convergence judgment, post-processing process, output the spatial distribution of the real and imaginary parts of the electromagnetic field, output the spatial distribution data of the surface induced current and radar scattering cross section, etc.

[0078] like Figures 2 to 4 The figure shows the FVFD calculation case of TM polarization and metal cylinder (ka=5), where k is the wave number, a is the cylinder radius, CFL=2, It is fully implicit, and the computational grid is 91x46. The object surface grid selects 18 grid points per wavelength, the far field boundary is outside 3 wavelengths, and the radial grid wall is encrypted, with an average of about 15 grid points per wavelength. The convergence criterion is that the maximum amplitude difference of the electromagnetic field in adjacent iteration steps in the whole space is <0.02. Figure 2 The electromagnetic field BX of the metal cylinder (ka=5, TM) is compared before and after the numerical flux correction of the FVFD calculation of the present invention. It can be seen that the numerical oscillation is compressed after the numerical flux correction; Figure 3 The convergence curves of the FVFD calculation of a metal cylinder (ka=5, TM) before and after the numerical flux correction are compared by using the present invention. It can be seen that the TM wave polarization convergence is reduced from 20400 steps before the numerical flux correction is used to 900 steps after the use, and the number of convergence steps is reduced to less than 1 / 20 of the original number. Figure 4 The comparison of the dual-station radar cross-section distribution before and after the numerical flux correction of the FVFD calculation of a metal cylinder (ka=5, TM) using the present invention shows that even though the convergence is greatly accelerated, the final output has the same calculation accuracy.

[0079] like Figure 5 to Figure 6 The figure shows the FVFD calculation of a metal sphere (ka=2), where k is the wave number, a is the radius of the metal sphere, and CFL=2. It is fully implicit, the computational grid is 46x61 x31, and the convergence criterion is that the maximum amplitude difference of the electromagnetic field in adjacent iteration steps in the whole space is less than 0.02. Figure 5The electromagnetic field Dx of the metal ball (ka=2) is compared before and after the numerical flux correction of the FVFD calculation of the present invention. It can be seen that the numerical oscillation is compressed after the numerical flux correction. Figure 6 The convergence curves of the FVFD calculation of a metal sphere (ka=2) before and after the numerical flux correction are compared using the present invention. It can be seen that the convergence is reduced from 19200 steps before the numerical flux correction is used to 6000 steps after the use of the numerical flux correction. It can be seen that the number of convergence steps for this typical three-dimensional problem is reduced to less than 1 / 3 of the original when the numerical flux correction algorithm proposed in the present invention is used.

[0080] These numerical examples show that the structural grid frequency-domain electromagnetic field finite volume FVFD convergence acceleration algorithm corresponding to the invention can maintain numerical viscosity and solution process stability through the electromagnetic flux correction algorithm, and can suppress numerical oscillations of the electromagnetic field during the convergence process, thereby greatly improving computational efficiency while ensuring numerical accuracy, which is conducive to application in the computational analysis of larger-scale electromagnetic problems.

[0081] The units involved in the embodiments of the present invention may be implemented by software or hardware, and the units described may also be arranged in a processor. The names of these units do not, in some cases, limit the units themselves.

[0082] According to one aspect of an embodiment of the present invention, a computer program product or a computer program is provided, the computer program product or the computer program includes a computer instruction, and the computer instruction is stored in a computer-readable storage medium. A processor of a computer device reads the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the method provided in the above various optional implementations.

[0083] As another aspect, an embodiment of the present invention further provides a computer-readable medium, which may be included in the electronic device described in the above embodiment; or may exist independently without being assembled into the electronic device. The above computer-readable medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the method described in the above embodiment.

Claims

1. A grid frequency domain electromagnetic field finite volume convergence acceleration method, characterized in that: include: Based on virtual time advancement and calculation and correction of spatial flux residual splitting, the frequency domain electromagnetic field of Maxwell equations is iteratively solved; The simulation model is cycled through constant virtual time steps until convergence. In each virtual time iteration, spatial flux calculation and correction and implicit iterative solution calculation are performed on each grid block and each grid unit in turn, and the conserved electromagnetic field value of the next virtual time iteration step is updated. Finally, the spatial distribution of the real and imaginary parts of the electromagnetic field is output, and the spatial distribution data of the surface induced current and radar scattering cross section are output.

2. The grid frequency domain electromagnetic field finite volume convergence acceleration method according to claim 1 is characterized in that: The simulation model is cycled by constant virtual time steps until convergence is completed; in each virtual time iteration process, spatial flux calculation and correction and implicit iterative solution calculation are performed on each grid block and each grid unit in turn, and the value of the conserved electromagnetic field of the next virtual time iteration step is updated, which specifically includes the following sub-steps: The process of the constant virtual time step cycle until convergence is as follows: Add virtual time derivative , the frequency domain complex rectangular coordinate system Maxwell equations to be solved are modified to: ；(1) ；(2) in, is the complex-valued scattering electromagnetic field conservation variable, It's virtual time. is the sign of the imaginary part, is pi, is the frequency of the incident simple harmonic electromagnetic wave, , , is the electromagnetic flux in rectangular coordinates , , Quantity, is the complex scattered magnetic induction intensity vector, is the complex scattered field electric displacement vector; In the curvilinear coordinate system grid space, the constant iteration adopts a fully implicit algorithm: ； (3) in, is the structural grid curve coordinate system direction 1, is the structural grid curve coordinate system direction 2, is the structural grid curve coordinate system direction 3; They correspond to the curvilinear coordinate system Directional electromagnetic flux; subscript is the grid cell number, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is Grid unit Electromagnetic conservation variables for virtual time steps, It is Grid unit The spatial flux residual at the virtual time step, is the virtual time step controlled by stability, calculated from the CFL number and the local grid cell geometry scale and eigenvalues; The process of calculating and correcting the spatial flux and calculating the implicit iterative solution is as follows: Steger-Warming splitting is used to calculate the interface flux of the grid cells ；(4) In the formula, the subscript Take the curvilinear coordinate system One of the directions, corresponding That is the corresponding The direction of the electromagnetic flux, Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the positive eigenvalue in the Steger-Warming splitting in the corresponding direction; Represents a curvilinear coordinate system The electromagnetic flux obtained by splitting the negative eigenvalue in the Steger-Warming splitting in the corresponding direction; For the grid cell interface flux calculated using Steger-Warming splitting Carry out the correction process, including direction: First, truncate the corrected split eigenvalues: ； ； ； In the formula, They are The diagonal matrix of positive and negative eigenvalues ​​of the grid cells, is the local grid cell magnetic permeability, is the relative permittivity of the local grid cell, For local Directional grid geometry stretch factor; is the local cutoff eigenvalue added for the eigenvalue of 0; Secondly, the Steger-Warming splitting method is used to calculate the interface flux of the grid cells. To make corrections: ； ； Specifically, the curve grid direction 1 Direction, that is: ；(5) ； ； in, is the modified flux on top of the flux calculated by the initial Steger-Warming splitting, is the local cutoff eigenvalue, is the control parameter; the other curves in mesh directions 2 and 3 The numerical flux correction is similar; Formula (3) adopts the implicit linearization of spatial flux and the splitting of Jacobi coefficient matrix to solve it by forward and backward iteration. After the Steger-Warming splitting of Jacobi coefficient generated by the conservation variable of flux partial derivative, ；(6) ； in, is the coefficient matrix after splitting, is the spatial flux residual calculated at the previous iterative time step, is the implicit sub-iteration electromagnetic field difference; Finally, based on the LUSGS forward and backward iterative calculation, the electromagnetic field difference is obtained .

3. The grid frequency domain electromagnetic field finite volume convergence acceleration method according to claim 2, characterized in that: Control parameters The range is .

4. The grid frequency domain electromagnetic field finite volume convergence acceleration method according to claim 3, characterized in that: Corresponds to no numerical flux correction.

5. A grid frequency domain electromagnetic field finite volume convergence acceleration device, characterized in that: The method comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is loaded by the processor, the method according to any one of claims 1 to 4 is executed.

6. A computer-readable storage medium, characterized in that: A computer program is stored in a readable storage medium, and the computer program is loaded by a processor to execute the method according to any one of claims 1 to 4.

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