Method for modeling electromagnetic scattering of planar multilayer medium based on layered medium green function

Abstract

The application belongs to the technical field of electromagnetic modeling of targets in layered media, and specifically provides a plane multilayer medium electromagnetic scattering modeling method based on layered medium Green function, which is used to solve the problems of large number of unknown quantities and low calculation efficiency when analyzing the electromagnetic scattering characteristics of targets in layered media; first, the medium target in the plane multilayer medium is meshed; then, the layered medium Green function is calculated based on the space list and interpolation method, and the matrix equation of the target current and magnetic current is constructed by solving the surface integral equation of the target by using the method of moments; finally, the improved stacked non-diagonal low-rank matrix is used to solve the matrix equation to calculate the target scattering field. The application adopts a direct solving calculation method, effectively solves the problem of ill-conditioned matrix difficult to converge in the conventional iterative method, especially for the multi-port excitation problem, without the need for repeated calculation, improving the solving efficiency of large-scale problems and reducing the consumption of calculation resources.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic modeling technology for targets in layered media, and relates to a method for solving the scattering field of a medium target in a planar multilayered medium. Specifically, it provides a method for electromagnetic scattering modeling of a planar multilayered medium based on the Green's function of the layered medium. Background Technology

[0002] The planar layered medium model is a simplified model of a vertically layered non-homogeneous medium, widely used in planar antenna or circuit design, ground-penetrating radar, and well logging. This model can effectively and comprehensively model the target and its complex environment. Compared to homogeneous media or free space, electromagnetic scattering problems in layered media are more complex. When solved directly using the traditional method of moments, large and dense matrix equations are generated. As the problem size increases, the number of unknowns in the system increases significantly when using conventional RWG basis functions for discretization, leading to a large consumption of computation time and memory resources.

[0003] Higher-order methods discretize targets using larger-sized surface elements, providing better fitting results than planar triangles, thereby reducing the number of elements and unknowns. When dealing with complex electromagnetic targets, different mesh sizes are used for different geometries, often resulting in ill-conditioned system matrices. Conventional iterative methods face problems such as slow convergence, low accuracy, or even non-convergence when solving these matrices. Higher-order stacked vector basis functions offer high flexibility, adaptively selecting the order of basis functions based on the mesh element size, enabling more efficient electromagnetic modeling of complex targets. However, in practical engineering applications, the analysis of the target's monostatic electromagnetic scattering characteristics is often involved, i.e., a problem with multiple right-hand side terms. Iterative solutions require re-iteration for each right-hand side excitation vector, leading to low computational efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a fast calculation method for electromagnetic scattering of targets in planar multilayer media based on the Green's function of layered media, in order to solve the problems of a large number of unknowns and low computational efficiency when analyzing the electromagnetic scattering characteristics of targets in layered media. Specifically, this invention adopts a fast direct solution method, which can quickly solve problems with multiple right-hand side terms.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A planar multilayer dielectric electromagnetic scattering modeling method based on the Green's function of a layered dielectric is characterized by the following steps:

[0007] S01: Mesh the medium target in a planar multilayer medium (PLM) to obtain mesh information;

[0008] S02: Based on the grid information, the Green's function (LMGF) of the layered medium is calculated using spatial listing and interpolation methods;

[0009] S03: Based on the Green's function of the layered medium, the surface integral equation of the medium target is solved using the method of moments, and the matrix equations of the target current and magnetic current are constructed.

[0010] S04: The improved stacked off-diagonal low-rank matrix method (M-HODLR) is applied to solve the matrix equations to obtain the surface current and surface magnetic flux of the medium target. The scattering field of the medium target is then calculated based on the surface current and surface magnetic flux.

[0011] Furthermore, the specific process of step S01 is as follows:

[0012] S011: Discretize the surface region of the medium target using a curved triangular mesh.

[0013] Furthermore, the specific process of step S02 is as follows:

[0014] S021: Read the grid information of the medium target, and set the number of sampling points and interpolation interval required for interpolation;

[0015] S022: Obtain the spatial coordinates of the interpolation nodes based on the number of sampling points and the interpolation interval, and calculate the LMGF of the corresponding interpolation node positions;

[0016] S023: Determine whether the field point and the source point are located in the same medium layer. If they are in the same medium layer, perform two-dimensional spatial listing and interpolation; otherwise, perform three-dimensional spatial listing and interpolation.

[0017] S024: Calculate the LMGF at the point to be interpolated using the Lagrange interpolation method (LIM).

[0018] Furthermore, the specific process of step S03 is as follows:

[0019] S031: The surface integral equation of the target is obtained based on the principle of surface equivalence, and the dielectric target in PLM is replaced by the equivalent surface current and the equivalent surface magnetic current.

[0020] S032: Discretize the equivalent surface current and equivalent surface magnetic current, and select a high-order stacked vector basis function to expand the surface current and surface magnetic current to be solved;

[0021] S033: Using the Galerkin matching method, the higher-order stacked vector basis function in step S032 is selected as the weight function to construct the matrix equation of the medium target in PLM;

[0022] S034: Use the LMGF obtained in step S02 to calculate the element values ​​of the impedance matrix and the right-hand vector in the matrix equation.

[0023] Furthermore, the specific process of step S04 is as follows:

[0024] S041: Based on the spatial location of the basis functions, the basis function group is grouped and sorted using the binary tree method, thereby obtaining the H-matrix of the impedance matrix in the matrix equation;

[0025] S042: Determine whether the matrix blocks in the off-diagonal position after partitioning satisfy the expansion compatibility condition. For matrix blocks that satisfy the condition, perform ACA low-rank compression, and for matrix blocks that do not satisfy the condition, perform down-segmentation until the leaf layer is reached. For off-diagonal matrix blocks in the leaf layer, perform ACA low-rank compression directly, and for diagonal matrix blocks, perform full-rank filling.

[0026] S043: Re-aggregate the matrix blocks that were split down in step S042 into a single matrix block by uplink aggregation to obtain the updated H-matrix stacked structure.

[0027] S044: Using the SMW (Sherman-Morrison-Woodbury) formula to solve for the approximate inverse of the impedance matrix, the original matrix of the stacked structure is decomposed into the form of a product of multiple block diagonal matrices;

[0028] S045: Multiply the inverse of the impedance matrix obtained in step S044 with the vector on the right to obtain the current coefficient and the magnetocurrent coefficient. Calculate the surface current and surface magnetocurrent of the medium target from the current coefficient and the magnetocurrent coefficient. Calculate the scattering field of the medium target based on the surface current and surface magnetocurrent.

[0029] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0030] This invention provides a planar multilayer dielectric electromagnetic scattering modeling method based on the Green's function of a layered dielectric, which has the following advantages:

[0031] 1) Replacing the traditional RWG basis function with a higher-order stacked vector basis function effectively reduces the number of unknowns, lowers the dimension of the system matrix, and further improves the solution efficiency;

[0032] 2) The direct solution method effectively solves the problem of convergence of ill-conditioned matrices in conventional iterative methods; especially for multi-port excitation problems, it eliminates the need for repeated calculations, greatly improving computational efficiency.

[0033] 3) The M-HODLR method was introduced to analyze the electromagnetic scattering problem of targets in layered media, which significantly reduced the complexity of solving the matrix, improved the efficiency of solving large-scale problems, and reduced the consumption of computing resources. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the planar multilayer dielectric electromagnetic scattering modeling method based on the Green's function of the layered dielectric in this invention.

[0035] Figure 2 This is a schematic diagram of the curved triangular mesh element used in this invention.

[0036] Figure 3 This is a schematic diagram of the Lagrange interpolation (LIM) method used in this invention, where (a) is a three-dimensional LIM and (b) is a two-dimensional LIM.

[0037] Figure 4 This is a schematic diagram of the equivalent problem of the target when electromagnetic waves are incident in this invention, wherein (a) is a schematic diagram of the external equivalent problem and (b) is a schematic diagram of the internal equivalent problem.

[0038] Figure 5 This is a schematic diagram illustrating the process of constructing the M-HODLR matrix by dividing the basis function group using the binary tree method in this invention.

[0039] Figure 6 This is a schematic diagram illustrating the decomposition of the M-HODLR matrix into a product of multiple block diagonal matrices in this invention.

[0040] Figure 7 This is a schematic diagram of a dielectric sphere model in a planar multilayer medium in Embodiment 1 of the present invention.

[0041] Figure 8 The figures show a comparison of the scattering field calculation results of the medium sphere model in the planar multilayer medium in Embodiment 1 of the present invention, where (a) is a comparison of the scattering electric field results and (b) is a comparison of the scattering magnetic field results. Detailed Implementation

[0042] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0043] Example 1

[0044] This embodiment provides a planar multilayer dielectric electromagnetic scattering modeling method based on the Green's function of a layered dielectric. The specific implementation process is as follows: Figure 1 As shown, the main steps include: performing high-order mesh generation on the target in the layered medium, establishing a Green's function interpolation table for the layered medium, constructing the matrix equations of the target surface current and surface magnetic current using the method of moments, solving the constructed matrix equations using a fast direct solution method, and calculating the target's scattered field; detailed steps are as follows:

[0045] S01: Mesh generation for media targets in planar multilayer media (PLM);

[0046] S02: Calculation of the Green's function (LMGF) of layered media based on spatial listing and interpolation methods;

[0047] S03: The surface integral equation of the target is solved using the method of moments, and the matrix equations of the target current and magnetic current are constructed.

[0048] S04: Solve the matrix equations using the improved stacked off-diagonal low-rank matrix method (M-HODLR) to calculate the target scattering field.

[0049] Furthermore, in step S01, the specific process of meshing the medium target in the planar multilayer medium is as follows:

[0050] S011: Discretize the target surface region using a curved triangular mesh.

[0051] Furthermore, the curved triangular mesh elements used in step S01, such as... Figure 2 As shown:

[0052] The target surface region is discretized using a curved triangular mesh; this mesh element is a second-order parametric surface, defined by six parametric control points, such as... Figure 2 As shown in (a), a standard triangle can be transformed to a parametric coordinate system through projection, as follows: Figure 2 As shown in (b); any point r on the surface triangle is represented in the parameter space as:

[0053]

[0054] Where, r j Let ξ1, ξ2, ξ3 be the spatial coordinates of the parametric control points, satisfying 0 < ξ < 1 and ξ1 + ξ2 + ξ3 = 1. It is a shape function, and its specific expression is:

[0055]

[0056] Furthermore, in step S02, the specific process of calculating the Green's function of the layered medium based on the spatial list and interpolation method is as follows:

[0057] S021: Read the mesh information of the target model, and set the number of sampling points and interpolation interval required for interpolation;

[0058] S022: Obtain the spatial coordinates of the interpolation nodes based on the number of sampling points and the interpolation interval, and calculate the LMGF of the corresponding interpolation node positions;

[0059] S023: Determine whether the field point and the source point are located in the same medium layer. If they are in the same medium layer, perform two-dimensional spatial listing and interpolation; otherwise, perform three-dimensional spatial listing and interpolation.

[0060] S024: Calculate the LMGF at the point to be interpolated using the Lagrange interpolation method (LIM).

[0061] Furthermore, in step S02, the specific process of calculating the Green's function of the layered medium based on the spatial list and interpolation method is as follows:

[0062] After meshing the target in step S011, the mesh information is read, the interpolation interval is set according to the error requirements, and the spatial coordinates of the interpolation nodes are obtained. The Sommerfeld integral at the interpolation point is calculated by the direct numerical integration method, and then the LMGF at the node is obtained.

[0063] LMGF represents the field point coordinates. Coordinates of the source point The function, in planar layered media, can be further expressed as lateral distance. The function of vertical axis coordinates z, z′, when the field point and source point are located in different media layers, requires three-dimensional spatial listing and interpolation of ρ, z, z′. The LMGF at the point to be determined within the frame is calculated using LMGF interpolation at the eight vertices of the hexahedron frame, such as... Figure 3 As shown in (a); when both are in the same dielectric layer, LMGF can be represented as a bivariate function of ρ and z±z′. A two-dimensional spatial table and interpolation of ρ and z±z′ are required. The LMGF at the point to be determined within the rectangle is calculated by interpolating the LMGF at the four vertices of the rectangle, as shown in (a). Figure 3 As shown in (b); the interpolation method used is Lagrange interpolation, and its interpolation basis function is defined as:

[0064]

[0065] interpolation function L n (x) can be calculated from the interpolation basis functions and the function values ​​at the interpolation nodes:

[0066]

[0067] The computational time of impedance elements is mainly due to the numerical calculation of the Sommerfeld integral. This method can replace the point-by-point calculation of the Sommerfeld integral with a simpler interpolation calculation, thereby reducing the number of numerical integration calculations while meeting accuracy requirements, thus significantly improving computational efficiency.

[0068] Furthermore, in step S03, the specific process of using the method of moments to solve the surface integral equation of the target and construct the matrix equations of the target current and magnetic current is as follows:

[0069] S031: The surface integral equation of the target is obtained based on the principle of surface equivalence, and the dielectric target in PLM is replaced by the equivalent surface current and the equivalent surface magnetic current.

[0070] S032: Discretize the equivalent surface current and equivalent surface magnetic current, and select a high-order stacked vector basis function to expand the current and magnetic current to be determined;

[0071] S033: Using the Galerkin matching method, the higher-order stacked vector basis function in step S032 is selected as the weight function to construct the matrix equation of the medium target in PLM;

[0072] S034: Calculate the element values ​​of the system matrix and excitation vector using the LMGF obtained in step S024.

[0073] Furthermore, in step S03, the specific process of using the method of moments to solve the surface integral equation of the target and construct the matrix equations of the target current and magnetic current is as follows:

[0074] Based on the equivalence principle of LMGF and Love field, we can obtain the following respectively: Figure 4 The external equivalence problem shown in (a) is similar to... Figure 4 The surface electric field integral equation for the internal equivalent problem shown in (b) is:

[0075]

[0076] Where r and r ′ These represent the field point coordinates and the source point coordinates, respectively. The superscript "o" indicates external equivalence, and the superscript "i" indicates internal equivalence. J and M represent the surface current and surface magnetic current, respectively. The operator is defined as follows:

[0077]

[0078] Where μ represents the permeability, ε represents the permittivity, and ω represents the angular frequency. These represent the electric dextral Green's function and the magnetic dextral Green's function in the PLM, respectively, which are calculated by step S02;

[0079] By using high-order stacked vector basis functions to expand the surface current and surface magnetic current, and employing the Galerkin matching method, a set of linear equations about the expansion coefficients is obtained.

[0080] From the duality principle, we can obtain as follows: Figure 4 The external equivalence problem shown in (a) is similar to... Figure 4 The surface magnetic field integral equation for the internal equivalent problem shown in (b) is:

[0081]

[0082] Similarly, another set of linear equations about the expansion coefficients is obtained, which, when combined, yields the PMCHWT (Poggio-Miller-Chang-Harrington-Wu-Tsai) equations for the medium target in PLM:

[0083]

[0084] Based on the LMGF obtained in step S02, the impedance matrix (system matrix) and the right-hand vector (excitation vector) are calculated.

[0085] Furthermore, in step S04, the improved stacked off-diagonal low-rank matrix method (M-HODLR) is applied to solve the matrix equations, and the specific process for calculating the target scattering field is as follows:

[0086] S041: Based on the spatial location of the basis functions, the basis function group is grouped and sorted using the binary tree method, thereby obtaining the H-matrix stacked structure of the impedance matrix in step S034.

[0087] S042: Determine whether the matrix blocks in the off-diagonal position after partitioning satisfy the expansion compatibility condition. For matrix blocks that satisfy the condition, perform ACA low-rank compression, and for matrix blocks that do not satisfy the condition, perform down-segmentation until the leaf layer is reached. For off-diagonal matrix blocks in the leaf layer, perform ACA low-rank compression directly, and for diagonal matrix blocks, perform full-rank filling.

[0088] S043: The matrix blocks that were split in step S042 are re-aggregated into a single matrix block by uplink aggregation, and finally the updated stacked structure H-matrix is ​​obtained.

[0089] S044: Using the SMW (Sherman-Morrison-Woodbury) formula to solve for the approximate inverse of the impedance matrix, the original matrix of the stacked structure is decomposed into the form of a product of multiple block diagonal matrices;

[0090] S045: Solve for surface current and surface magnetic current, and calculate the target scattering field: Multiply the inverse of the impedance matrix obtained in step S044 with the vector on the right to obtain the current coefficient and magnetic current coefficient, thereby obtaining the surface current and surface magnetic current, and calculate the target scattering field of the medium based on the surface current and surface magnetic current.

[0091] Furthermore, in step S04, the specific process of applying the M-HODLR matrix equation to calculate the target scattering field is as follows:

[0092] To construct the impedance matrix obtained in step S03 into an H-matrix form, a binary tree method is used to group the basis functions. The basis function groups are continuously divided downwards based on spatial distance until the number of basis functions contained in a child node is less than a preset minimum value, such as... Figure 5 As shown; unlike matrix equations that only contain unknown current coefficients, the PMCHWT equations involve both current and magnetic current, requiring multi-level grouping of the current and magnetic current basis functions. Each matrix block in each level is represented as a form where current and magnetic current are coupled together:

[0093]

[0094] The traditional HODLR method treats all constructed H-matrix off-diagonal submatrix blocks as satisfying the compatibility condition and approximates them using a low-rank compression method. This method is often inefficient and inaccurate when dealing with submatrix blocks that are spatially close and have poor low-rank properties. The improved M-HODLR method, on the other hand, applies an extended compatibility condition.

[0095]

[0096] Where, m i Represents a subset of basis functions, n j The weight function subgroup is represented by diam(·), the geometric diameter of the basis (weight) function subgroup is represented by dim(·), the geometric distance between the basis function subgroup and the weight function subgroup is represented by dist(·), and η is a preset positive real number.

[0097] The off-diagonal submatrix blocks after partitioning are evaluated. Submatrix blocks that satisfy the expansion compatibility condition are subjected to ACA low-rank compression. Submatrix blocks that do not satisfy the condition are split into smaller submatrix blocks. The expansion compatibility condition is then evaluated on the smaller submatrix blocks. This process is repeated until the number of basis functions contained in a submatrix block is less than a preset minimum value. At this point, the smallest submatrix block is directly subjected to ACA low-rank compression. The matrix after ACA compression can be represented as:

[0098]

[0099] in, Let r be a low-rank approximation matrix;

[0100] To restore the low-rank approximate matrix formed after downlink segmentation to the H-matrix structure, uplink aggregation is required. This step can be represented as:

[0101]

[0102] in, This is the low-rank decomposition matrix obtained after upward aggregation. At this point, the matrix still has a relatively large rank and contains a large number of zero elements. The rank of the matrix can be further reduced using the QR-SVD recompression method. Reduced to k mnThis completes the construction of the M-HODLR matrix for the PMCHWT equation;

[0103] like Figure 6 As shown, the M-HODLR matrix can be further decomposed into the following form:

[0104]

[0105] Where the subscript 'l' represents the layer number, and Z l Represents the diagonal matrix of the l-th block. This represents the block diagonal matrix containing the main diagonal; therefore, solving the matrix equation Z·I=V can be transformed into solving for the inverse of the block diagonal matrix of each layer:

[0106]

[0107] Block diagonal matrix The inverse matrix Z can be obtained through LU decomposition. l The inverse matrix can be obtained using the SMW formula:

[0108]

[0109] Thus, the calculation of the coefficient vector is transformed into multiplying the inverse of a multi-layered block diagonal matrix with the right-hand vector by the M-HODLR fast direct solution method. Since it is relatively easy to invert a block diagonal matrix, the computational efficiency can be significantly improved, especially for problems with multiple right-hand terms. After obtaining the coefficient vector, its scattering field can be obtained by the target equivalent surface current and equivalent surface magnetic current.

[0110] like Figure 8 The figure shows the target electromagnetic properties calculated by the method of the present invention, where (a) is the scattered electric field and (b) is the scattered magnetic field; the dielectric sphere model in the planar multilayer medium is as follows. Figure 7 As shown, the proposed method is compared with the traditional MoM method using CG iteration. The results show that the method of the present invention has higher accuracy in calculating the scattering field of the medium target in PLM. At the same time, in this embodiment, the number of facets required by the traditional planar triangular mesh is 3924, while the number of facets required by the high-order curved triangular mesh in the present method is reduced to 776. The traditional CG iteration method takes 348.326s to calculate, while the M-HODLR method takes 63.125s, which improves the calculation efficiency by 81.88%.

[0111] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A planar multilayer dielectric electromagnetic scattering modeling method based on the Green's function of a layered dielectric, characterized in that, Includes the following steps: S01: Mesh the medium target in a planar multilayer medium (PLM) to obtain mesh information; The specific process is as follows: The surface region of the medium target is discretized using a curved triangular mesh. The mesh element is a second-order parametric surface, defined by six parameter control points. Any point on the curved triangle... In parameter space, it is represented as: ， in, The spatial coordinates of the parameter control points. For the parametric coordinates, satisfying , It is a shape function, and its specific expression is: ； S02: Based on the grid information, the Green's function (LMGF) of the layered medium is calculated using spatial listing and interpolation methods; S03: Based on the Green's function of the layered medium, the surface integral equation of the medium target is solved using the method of moments, and the matrix equations of the target current and magnetic current are constructed. The specific process is as follows: S031: The surface integral equation of the target is obtained based on the principle of surface equivalence, replacing the dielectric target in PLM with equivalent surface current and equivalent surface magnetic current; the surface integral equation adopts the PMCHWT equation, expressed as: ； Among them, the superscript " "Represents external equivalence, superscript" "Represents internal equivalence; Represents the surface electric field. Indicates the surface magnetic field. and These represent surface current and surface magnetic current, respectively. , and , Both represent electric field operators. , and , Both represent magnetic field operators; S032: Discretize the equivalent surface current and equivalent surface magnetic current, and select a high-order stacked vector basis function to expand the surface current and surface magnetic current to be solved; S033: Using the Galerkin matching method, the higher-order stacked vector basis function in step S032 is selected as the weight function to construct the matrix equation of the medium target in PLM; S034: Calculate the element values ​​of the impedance matrix and the right-hand vector in the matrix equation using the LMGF obtained in step S02; S04: The improved stacked off-diagonal low-rank matrix method (M-HODLR) is applied to solve the matrix equations to obtain the surface current and surface magnetic flux of the medium target. The scattering field of the medium target is then calculated based on the surface current and surface magnetic flux.

2. The planar multilayer dielectric electromagnetic scattering modeling method based on the Green's function of a layered dielectric as described in claim 1, characterized in that: The specific process of step S02 is as follows: S021: Read the grid information of the medium target, and set the number of sampling points and interpolation interval required for interpolation; S022: Obtain the spatial coordinates of the interpolation nodes based on the number of sampling points and the interpolation interval, and calculate the LMGF of the corresponding interpolation node positions; S023: Determine whether the field point and the source point are located in the same medium layer. If they are in the same medium layer, perform two-dimensional spatial listing and interpolation; otherwise, perform three-dimensional spatial listing and interpolation. S024: Calculate the LMGF at the point to be interpolated using the Lagrange interpolation method (LIM).

3. The planar multilayer dielectric electromagnetic scattering modeling method based on the Green's function of a layered dielectric as described in claim 1, characterized in that, The specific process of step S04 is as follows: S041: Based on the spatial location of the basis functions, the basis function group is grouped and sorted using the binary tree method, thereby obtaining the H-matrix of the impedance matrix in the matrix equation; S042: Determine whether the matrix blocks in the off-diagonal position after partitioning satisfy the expansion compatibility condition. For matrix blocks that satisfy the condition, perform ACA low-rank compression, and for matrix blocks that do not satisfy the condition, perform down-segmentation until the leaf layer is reached. For off-diagonal matrix blocks in the leaf layer, perform ACA low-rank compression directly, and for diagonal matrix blocks, perform full-rank filling. S043: Re-aggregate the matrix blocks that were split down in step S042 into a single matrix block by uplink aggregation to obtain the updated H-matrix stacked structure. S044: Using the SMW (Sherman-Morrison-Woodbury) formula to solve for the approximate inverse of the impedance matrix, the original matrix of the stacked structure is decomposed into the form of a product of multiple block diagonal matrices; S045: Multiply the inverse of the impedance matrix obtained in step S044 with the vector on the right to obtain the current coefficient and the magnetocurrent coefficient. Calculate the surface current and surface magnetocurrent of the medium target from the current coefficient and the magnetocurrent coefficient. Calculate the scattering field of the medium target based on the surface current and surface magnetocurrent.

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