Method for analyzing electromagnetic scattering of metal scatterer based on electric field integral equation

Abstract

The application provides a metal scatterer electromagnetic scattering analysis method based on an electric field integral equation, triangular surface patch units are used to discretize a target surface, and RWG base functions are defined to expand and approximate surface currents; the expanded and approximated surface current is substituted into the electric field integral equation, the equation is tested by using a RWG-based test function, a discrete electric field integral equation matrix system is obtained; a Gram matrix corresponding to the RWG base function is constructed, according to a matrix function theory, Chebyshev polynomial approximation expansion suitable for a scalar inverse square root is extended to Chebyshev polynomial approximation expansion suitable for a matrix inverse square root, and numerical calculation of the Gram matrix inverse square root is realized; the Gram matrix inverse square root is used to precondition the discrete electric field integral equation matrix system, a correlation between a solution vector of a preconditioned matrix equation system and a solution vector of an original matrix equation system is established, and a spatial scattering field of the metal scatterer is obtained. The application improves the electromagnetic scattering analysis efficiency of the metal scatterer.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a method for analyzing electromagnetic scattering of metallic scatterers based on an electric field integral equation. Background Technology

[0002] The boundary element method (BEM) is currently widely used for electromagnetic scattering analysis of metallic scattering targets. This method typically requires solving the electric field integral equation. To numerically solve the electric field integral equation, the surface current of the metallic scattering target is first approximated by expanding the equation using basis functions defined on the grid discrete elements. The electric field integral operator is then discretized using basis functions. Next, a test function is used to test the discretized electric field integral equation, resulting in a fully discretized matrix equation system. Finally, this system is solved to obtain the unknown surface current expansion coefficients, thereby revealing the scattering field distribution in the background medium space of the metallic scattering target.

[0003] However, after the discretization process described above, the spectrum and eigenvectors of the boundary element matrix obtained from the electric field integral equation usually cannot represent the spectrum and eigenfunctions of its underlying surface integral operator. This is because the boundary elements obtained from discretizing an electromagnetic scatterer typically cannot form an orthogonal basis space from their expansion, and the eigenvalues ​​of the surface integral operator can only be obtained by solving the generalized eigenvalue problem. Although standard electromagnetic scattering problem-solving strategies generally do not face this problem, some numerical methods that rely on establishing necessary correlations between the spectrum of the operator to be discretized and the spectrum of the corresponding boundary element matrix and performing meticulous spectral manipulation will encounter it. Furthermore, the solution performance of the discretized electric field integral equation matrix system is often affected by the matrix behavior within the system. When the matrix condition number is poor, iterative methods are difficult to solve the system, and convergent solutions are even rarer.

[0004] Currently, there are two main technical approaches to solving the above problems: one is to use orthogonal basis functions, and the other is to construct a preconditioning matrix. However, on the one hand, it is convenient to construct appropriate orthogonal basis functions for electromagnetic scattering targets with regular shapes, but it is difficult to construct corresponding orthogonal basis functions for electromagnetic scattering targets with complex and irregular shapes in practical engineering applications (1. D. Boffi, “Compatible discretizations for eigenvalue problems,” in Compatible Spatial Discretizations, IMA Volumes in Mathematics and its Applications, vol. 142, pp. 121-142, Berlin: Springer, 2006.). On the other hand, the preconditioning matrices currently constructed are usually quite complex in form. For complex large-scale electromagnetic scattering problems in practical engineering applications, it is cumbersome to implement preconditioning for the electric field integral equations, which is not conducive to the rapid and flexible construction of the preconditioning matrix (2. S. Adrian, A. Dely, D. Consoli, A. Merlini, and F. P. Andriulli, “Electromagnetic integral equations: Insights in conditioning and preconditioning,” IEEE Open J. Antennas Propag., vol. 2, pp. 1143-1174, 2021.). Summary of the Invention

[0005] The purpose of this invention is to provide a method for electromagnetic scattering analysis of metallic scatterers based on the electric field integral equation.

[0006] The technical solution to achieve the purpose of this invention is as follows: a method for electromagnetic scattering analysis of metallic scatterers based on the electric field integral equation. Based on the precondition matrix of the inverse square root of the Gram matrix, the electric field integral equation is effectively preconditioned, enabling efficient solution of the electric field integral equation and obtaining the spatial scattering field of the metallic scatterer. The steps are as follows:

[0007] Step 1: For the metal scatterer target, the target surface is discretized using triangular patch elements. Based on this, RWG basis functions are defined, and the surface current is expanded to approximate the surface current.

[0008] Step 2: Substitute the surface current approximate expansion into the electric field integral equation, and use the RWG-based test function to test the equation to obtain the discretized electric field integral equation matrix system.

[0009] Step 3: Construct the Gram matrix corresponding to the RWG basis functions. Based on matrix function theory, extend the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar to the Chebyshev polynomial approximation expansion applicable to the inverse square root of a matrix, thereby realizing the numerical calculation of the inverse square root of the Gram matrix.

[0010] Step 4: Use the inverse square root of the Gram matrix to precondition the discretized electric field integral equation matrix system, and establish the correlation between the solution vector of the matrix equation system after preconditioning and the solution vector of the original matrix equation system, and finally obtain the spatial scattering field of the metal scatterer.

[0011] Furthermore, in step 1, for the metallic scatterer target, the target surface is discretized using triangular patch elements. Based on this, RWG basis functions are defined, and the surface current is approximated by expansion. The specific method is as follows:

[0012] Step 1-1: Use triangular patch elements to geometrically discretize the surface S of the metal scatterer target, and define the RWG basis function f based on this mesh. n (r), its expression is

[0013]

[0014] Where r is a point on surface S, and For two triangular units connected to the nth side, and Triangular units and The free vertex, and Triangular units and The area;

[0015] Steps 1-2: Use RWG base functions f n (r), n = 1, 2, ..., N E The surface current J(r) is approximated by expansion, and its expansion is as follows:

[0016]

[0017] Where, N E denoted as the number of discrete grid edges, and j as the vector containing the expansion coefficients of the unknown current to be solved.

[0018] Further, in step 2, the surface current approximate expansion is substituted into the electric field integral equation, and the equation is tested using a test function based on RWG to obtain the discretized electric field integral equation matrix system. The specific method is as follows:

[0019] Step 2-1: Calculate the scattered electric field E generated by the target surface current J(r) in the background medium. sca (r), its expression is:

[0020]

[0021] Where g(r,r′)=e -jkR / (4πR) is the Green's function. Let ω be the wavenumber, ε be the angular frequency, μ be the permittivity and permeability of the background medium, r be the field point and r′ be the source point, and r′ ∈ S, and R = |rr′| be the Eulerian distance between the field and source points. For surface divergence operators;

[0022] Step 2-2: Based on the electric field boundary conditions of the target surface of the metal scatterer The electric field integral equation is established as follows:

[0023]

[0024] Among them, E inc (r) represents the incident electric field on the surface of the metal scatterer target. Let r be the unit outward normal vector at point r;

[0025] Steps 2-3: Substitute the approximate expansion of the surface current into the above electric field integral equation, and use the RWG-based test function. The equation was tested, and the discretized electric field integral equation matrix system was obtained, which has the following form:

[0026] Tj = v

[0027] Where T is the dimension N E ×N E The boundary element matrix, where v is of dimension N. E The right-hand side of the ×1 vector, and the matrix and vector elements of both are as follows:

[0028]

[0029]

[0030] in, S a Let a(r) be the supporting domain.

[0031] Further, in step 3, construct the Gram matrix corresponding to the RWG basis functions. Based on matrix function theory, extend the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar to the Chebyshev polynomial approximation expansion applicable to the inverse square root of a matrix, thus realizing the numerical calculation of the inverse square root of the Gram matrix. The specific method is as follows:

[0032] Step 3-1: Define the inverse square root function of a matrix. Based on this, its scalar dual form is defined, namely the scalar inverse square root function. Where X is a symmetric positive definite matrix with dimension N. E ×N E x is a positive real scalar;

[0033] Step 3-2: Construct the Gram matrix G corresponding to the RWG basis functions. f,f Its matrix dimension is N E ×N E Its matrix elements are:

[0034] {G f,f} mn = <f m (r),f n (r)>

[0035] Step 3-3: Calculate the Gram matrix G f,f condition number cond(G) f,f Based on this, the Chebyshev polynomial approximation interval [n0,1] for the scalar inverse square root is determined, where n0=1 / cond(G f,f );

[0036] Steps 3-4: The inverse square root of the scalar is approximated by Chebyshev polynomial expansion in the interval [n0,1] as follows:

[0037]

[0038] Where, N C Let T be the order of the Chebyshev polynomial expansion. n (x) is a Chebyshev polynomial defined in the interval [n0,1], and its recursive expression is:

[0039]

[0040] also, Let n be the nth expansion coefficient of the Chebyshev polynomial approximation expansion of the inverse square root of the scalar, and its specific form is:

[0041]

[0042] Steps 3-5: Based on matrix function theory, apply the Chebyshev polynomial T to scalars. n (x) extends to the Chebyshev polynomial T applicable to matrices. n (X):

[0043]

[0044] Where I represents a dimension of N E ×N E The identity matrix;

[0045] Steps 3-6: Based on this, the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar is extended to the Chebyshev polynomial approximation expansion applicable to the inverse square root of a matrix:

[0046]

[0047] Step 3-7: Let X = G in the above formula. f,f / ||G f,f ||2, calculated based on the above approximate Chebyshev polynomial expansion. Based on this, the Gram matrix G is calculated according to the following formula. f,f Find the inverse square root and calculate its numerical value:

[0048]

[0049] Among them, ||G f,f ||2 is G f,f The matrix norm 2.

[0050] Furthermore, in step 4, the inverse square root of the Gram matrix is ​​used to precondition the discretized electric field integral equation matrix system, and the correlation between the solution vector of the preconditioned matrix equation system and the solution vector of the original matrix equation system is established. Finally, the spatial scattering field of the metal scatterer is obtained. The specific method is as follows:

[0051] Step 4-1, using G f,f Applying the inverse square root as a precondition to the discretized matrix system of electric field integral equations, we obtain the preconditioned matrix equation system as follows:

[0052]

[0053] in, The solution vector of the matrix equation system after preconditioning;

[0054] Step 4-2: Solve the matrix equation system under the above preconditions to obtain the solution vector. Based on this, the solution vector j of the original electric field integral equation system is calculated, and its correlation is:

[0055]

[0056] Step 4-3: Substitute the solution vector j obtained above into the surface current approximation expansion in Step 1-2 to calculate J(r). Then, substitute the calculated J(r) into Step 2-1 to calculate the background spatial scattering electric field E of the metallic scatterer target. sca (r).

[0057] An electromagnetic scattering analysis system for metal scatterers based on an electric field integral equation is provided, which implements the electromagnetic scattering analysis method for metal scatterers based on the electric field integral equation to achieve electromagnetic scattering analysis of metal scatterers.

[0058] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the electromagnetic scattering analysis method for metal scatterers based on the electric field integral equation, thereby realizing the electromagnetic scattering analysis of metal scatterers.

[0059] A computer-readable storage medium storing a computer program thereon, wherein when the computer program is executed by a processor, the method for electromagnetic scattering analysis of metal scatterers based on the electric field integral equation is implemented to realize electromagnetic scattering analysis of metal scatterers.

[0060] Compared with the prior art, the present invention has the following significant advantages: (1) For electromagnetic scattering targets with complex and irregular shapes in practical engineering applications, it avoids the construction of cumbersome orthogonal basis functions. (2) For complex large-scale electromagnetic scattering problems in practical engineering applications, it avoids the use of complex precondition matrices, and instead uses a precondition matrix based on the inverse square root of the Gram matrix to achieve efficient preconditioning of the electric field integral equation.

[0061] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the overall process of the electromagnetic scattering analysis method for metal scatterers based on the electric field integral equation of the present invention.

[0063] Figure 2 This is a flowchart of step one.

[0064] Figure 3 This is a flowchart of steps two and four.

[0065] Figure 4 This is a flowchart of step three. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0067] like Figure 1 As shown, a method for analyzing electromagnetic scattering of metallic scatterers based on the electric field integral equation is proposed. This method utilizes a preconditioning matrix derived from the inverse square root of the Gram matrix to effectively precondition the electric field integral equation, enabling efficient solution of the equation and obtaining the spatial scattering field of the metallic scatterer. The method includes the following steps:

[0068] The first step, for a metallic scatterer target, is to discretize the target surface using triangular patch elements. Based on this, RWG basis functions are defined, and an expansion approximation is performed on the surface current; for example... Figure 2 As shown, the specific steps include:

[0069] (1) The surface S of the metal scatterer target is geometrically discretized using triangular patch elements. Based on this mesh, the RWG basis function f is defined. n (r), its expression is

[0070]

[0071] Where r is a point on surface S, and For two triangular units connected to the nth side, and Triangular units and The free vertex, and Triangular units and The area;

[0072] (2) Using RWG basis functions f n (r), n = 1, 2, ..., N E The surface current J(r) is approximated by expansion, and its expansion is as follows:

[0073]

[0074] Where, N E denoted as the number of discrete grid edges, and j as the vector containing the expansion coefficients of the unknown current to be solved.

[0075] The second step involves substituting the approximate expansion of the surface current into the electric field integral equation, and then using a test function based on RWG to test the equation, obtaining the discretized electric field integral equation matrix system; such as Figure 3 As shown, the specific steps include:

[0076] (1) Calculate the scattered electric field E generated by the target surface current J(r) in the background medium. sca (r), its expression is:

[0077]

[0078] Where g(r,r′)=e -jkR / (4πR) is the Green's function. Let ω be the wavenumber, ε be the angular frequency, μ be the permittivity and permeability of the background medium, r be the field point and r′ be the source point, and r′ ∈ S, and R = |rr′| be the Eulerian distance between the field and source points. For surface divergence operators;

[0079] (2) Based on the electric field boundary conditions of the target surface of the metal scatterer The electric field integral equation is established as follows:

[0080]

[0081] Among them, E inc (r) represents the incident electric field on the surface of the metal scatterer target. Let r be the unit outward normal vector at point r;

[0082] (3) Substitute the approximate expansion of the surface current into the above electric field integral equation, and use the test function based on RWG. The equation was tested, and the discretized electric field integral equation matrix system was obtained, which has the following form:

[0083] Tj = v

[0084] Where T is the dimension N E ×N E The boundary element matrix, where v is of dimension N. E The right-hand side of the ×1 vector, and the matrix and vector elements of both are as follows:

[0085]

[0086]

[0087] in, S a Let a(r) be the supporting domain.

[0088] The third step involves constructing the Gram matrix corresponding to the RWG basis functions. Based on matrix function theory, the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar is extended to an approximation expansion applicable to the inverse square root of a matrix, thus enabling the numerical calculation of the inverse square root of the Gram matrix. Figure 4 As shown, the specific steps include:

[0089] (1) Define the inverse square root function of a matrix. Based on this, its scalar dual form is defined, namely the scalar inverse square root function. Where X is a symmetric positive definite matrix with dimension N. E ×N E x is a positive real scalar;

[0090] (2) Construct the Gram matrix G corresponding to the RWG basis functions. f,f Its matrix dimension is N E ×N E Its matrix elements are:

[0091] {G f,f} mn = <f m (r),f n (r)>.

[0092] (3) Calculate the Gram matrix G f,f condition number cond(G) f,f Based on this, the Chebyshev polynomial approximation interval [n0,1] for the scalar inverse square root is determined, where n0=1 / cond(G f,f );

[0093] (4) The inverse square root of the scalar is approximately expanded using Chebyshev polynomials in the interval [n0,1] as follows:

[0094]

[0095] Where, N C Let T be the order of the Chebyshev polynomial expansion. n (x) is a Chebyshev polynomial defined in the interval [n0,1], and its recursive expression is:

[0096]

[0097] also, Let n be the nth expansion coefficient of the Chebyshev polynomial approximation expansion of the inverse square root of the scalar, and its specific form is:

[0098]

[0099] (5) Based on matrix function theory, the Chebyshev polynomial T applicable to scalars is... n (x) extends to the Chebyshev polynomial T applicable to matrices. n (X):

[0100]

[0101] Where I represents a dimension of N E ×N E The identity matrix;

[0102] (6) Based on this, the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar is extended to the Chebyshev polynomial approximation expansion applicable to the inverse square root of a matrix:

[0103]

[0104] (7) Let X = G in the above formula f,f / ||G f,f ||2, calculated based on the above Chebyshev polynomial approximation expansion. Based on this, the Gram matrix G is calculated according to the following formula. f,f Find the inverse square root and calculate its numerical value:

[0105]

[0106] Among them, ||G f,f ||2 is G f,f The matrix norm 2.

[0107] The fourth step involves using the inverse square root of the Gram matrix to precondition the discretized electric field integral equation matrix system, and establishing the correlation between the solution vectors of the preconditioned matrix equation system and the solution vectors of the original matrix equation system, ultimately obtaining the spatial scattering field of the metal scatterer; for example... Figure 3 As shown, the specific steps include:

[0108] (1) Using G f,f Applying the inverse square root as a precondition to the discretized matrix system of electric field integral equations, we obtain the preconditioned matrix equation system as follows:

[0109]

[0110] in, The solution vector of the matrix equation system after preconditioning;

[0111] (2) Solve the matrix equation system under the above preconditions to obtain the solution vector. Based on this, the solution vector j of the original electric field integral equation system is calculated, and its correlation is:

[0112]

[0113] (3) Substitute the solution vector j obtained above into the surface current approximate expansion in step 1-2 to calculate J(r), and then substitute the calculated J(r) into step 2-1 to calculate the background spatial scattering electric field E of the metallic scattering target. sca (r).

[0114] This invention also proposes a metal scattering electromagnetic scattering analysis system based on the electric field integral equation, which implements the aforementioned metal scattering electromagnetic scattering analysis method based on the electric field integral equation to achieve electromagnetic scattering analysis of metal scattering bodies.

[0115] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the electromagnetic scattering analysis method for metal scatterers based on the electric field integral equation, thereby realizing the electromagnetic scattering analysis of metal scatterers.

[0116] A computer-readable storage medium storing a computer program thereon, wherein when the computer program is executed by a processor, the method for electromagnetic scattering analysis of metal scatterers based on the electric field integral equation is implemented to realize electromagnetic scattering analysis of metal scatterers.

[0117] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0118] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for analyzing electromagnetic scattering of metallic scatterers based on the electric field integral equation, characterized in that, Based on the precondition matrix of the inverse square root of the Gram matrix, effective preconditions are applied to the electric field integral equation, enabling efficient solution of the electric field integral equation and obtaining the spatial scattering field of the metallic scatterer. The steps are as follows: Step 1: For the metal scatterer target, the target surface is discretized using triangular patch elements. Based on this, RWG basis functions are defined, and the surface current is expanded to approximate the surface current. Step 2: Substitute the surface current approximate expansion into the electric field integral equation, and use the RWG-based test function to test the equation to obtain the discretized electric field integral equation matrix system. Step 3: Construct the Gram matrix corresponding to the RWG basis functions. Based on matrix function theory, extend the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar to the Chebyshev polynomial approximation expansion applicable to the inverse square root of a matrix, thereby realizing the numerical calculation of the inverse square root of the Gram matrix. Step 4: Use the inverse square root of the Gram matrix to precondition the discretized electric field integral equation matrix system, and establish the correlation between the solution vector of the matrix equation system after preconditioning and the solution vector of the original matrix equation system, and finally obtain the spatial scattering field of the metal scatterer.

2. The method for electromagnetic scattering analysis of metallic scatterers according to claim 1, characterized in that, Step 1: For the metallic scatterer target, the target surface is discretized using triangular patch elements. Based on this, RWG basis functions are defined, and the surface current is approximated by expansion. The specific method is as follows: Step 1-1: Use triangular facet units to target the surface of the metal scatterer. Perform geometric discretization, and define RWG basis functions based on this mesh. Its expression is ； in, For surface The point on, and In order to be with the first Two triangular units connected by a strip edge, and Triangular units and The free vertex, and Triangular units and The area; Steps 1-2: Use RWG base functions , Current on the opposite side By expansion approximation, its expansion is: ； in, The number of discrete grid edges. It is a vector containing the expansion coefficients of the unknown current to be solved.

3. The method for electromagnetic scattering analysis of metallic scatterers according to claim 2, characterized in that, Step 2: Substitute the approximate expansion of the surface current into the electric field integral equation, and use the RWG-based test function to test the equation to obtain the discretized electric field integral equation matrix system. The specific method is as follows: Step 2-1: Calculate the target surface current Scattered electric field generated in the background medium Its expression is: ； in, For Green's function, For wave number, Angular frequency, and These are the dielectric constant and permeability of the background medium, respectively. and They are the field point and the source point, respectively. , The Eulerian distance between the source points. For surface divergence operators; Step 2-2: Based on the electric field boundary conditions of the target surface of the metal scatterer Establish the electric field integral equation, which is in the form of: ； in, The incident electric field on the surface of the metal scattering target is denoted as . for The unit outward normal vector at that location; Steps 2-3: Substitute the approximate expansion of the surface current into the above electric field integral equation, and use the RWG-based test function. , The equation was tested, and the discretized electric field integral equation matrix system was obtained, which has the following form: ； in, dimension The boundary element matrix, dimension The right-hand vector of both, and their matrix and vector elements are as follows: ； ； in, , for The supporting domain.

4. The method for electromagnetic scattering analysis of metallic scatterers according to claim 3, characterized in that, Step 3: Construct the Gram matrix corresponding to the RWG basis functions. Based on matrix function theory, extend the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar to the Chebyshev polynomial approximation expansion applicable to the inverse square root of a matrix, thus realizing the numerical calculation of the inverse square root of the Gram matrix. The specific method is as follows: Step 3-1: Define the inverse square root function of a matrix. Based on this, its scalar dual form is defined, namely the scalar inverse square root function. ,in It is a symmetric positive definite matrix with dimension . , It is a positive real scalar; Step 3-2: Construct the Gram matrix corresponding to the RWG basis functions. Its matrix dimension is Its matrix elements are: ； Step 3-3: Calculate the Gram matrix condition number Based on this, the Chebyshev polynomial approximation interval for the inverse square root of the scalar is determined. ,in ; Steps 3-4: Find the inverse square root of the scalar in the interval The Chebyshev polynomial expansion is approximately as follows: ； in, Let be the order of the Chebyshev polynomial expansion. To define in the interval The Chebyshev polynomial within the expression is recursively expressed as: ； also, The first digit of the Chebyshev polynomial approximation expansion of the inverse square root of the scalar The expansion coefficients are in the following form: ； Steps 3-5: Based on matrix function theory, apply the Chebyshev polynomials to scalars. Extended to Chebyshev polynomials applicable to matrices : ； in, Indicates dimension as The identity matrix; Steps 3-6: Based on this, the Chebyshev polynomial approximation expansion applicable to the inverse square root of a scalar is extended to the Chebyshev polynomial approximation expansion applicable to the inverse square root of a matrix: ； Steps 3-7: Let the above formula contain... Based on the Chebyshev polynomial approximation expansion mentioned above, the following calculations were performed: Based on this, the Gram matrix is ​​calculated according to the following formula. Find the inverse square root and calculate its numerical value: ； in, for The matrix norm 2.

5. The method for electromagnetic scattering analysis of metallic scatterers according to claim 4, characterized in that, Step 4: Apply preconditions to the discretized electric field integral equation matrix system using the inverse square root of the Gram matrix, and establish the correlation between the solution vectors of the preconditioned matrix equation system and the solution vectors of the original matrix equation system. Finally, obtain the spatial scattering field of the metal scatterer. The specific method is as follows: Step 4-1, using Applying the inverse square root as a precondition to the discretized matrix system of electric field integral equations, we obtain the preconditioned matrix equation system as follows: ； in, The solution vector of the matrix equation system after preconditioning; Step 4-2: Solve the matrix equation system under the above preconditions to obtain the solution vector. Based on this, the solution vector of the original electric field integral equation system is calculated. Its correlation is: ； Step 4-3: Convert the solution vector obtained above... Substituting into the approximate expansion of the surface current in step 1-2, we can calculate... Then calculate Substitute into step 2-1 to calculate the background spatial scattering electric field of the metallic scattering target. .

6. A system for analyzing electromagnetic scattering of metallic scatterers based on an electric field integral equation, characterized in that, Implement the electromagnetic scattering analysis method for metal scatterers based on the electric field integral equation as described in any one of claims 1-5 to realize the electromagnetic scattering analysis of metal scatterers.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the electromagnetic scattering analysis method for metal scatterers based on the electric field integral equation as described in any one of claims 1-5, thereby realizing electromagnetic scattering analysis of metal scatterers.

8. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the electromagnetic scattering analysis method for metal scatterers based on the electric field integral equation as described in any one of claims 1-5, thereby realizing electromagnetic scattering analysis of metal scatterers.

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