Complex target electromagnetic scattering characteristic calculation method and system and medium

Abstract

The invention provides a method and a system for calculating electromagnetic scattering characteristics of a complex target and a medium. The method comprises the following steps: dividing regions according to material distribution and splitting open regions into open regions and interfaces; constructing an electromagnetic current joint integral equation based on electric field and magnetic field continuity conditions; the equation is directly adopted in an open area, and a variable coefficient is introduced into an interface to correct a Robin transmission condition; constructing a matrix equation by using a full / semi-RWG primary function and combining a Galerkin method through a triangular surface element discrete grid; and after a generalized minimum margin method is adopted for solving, a scattering field and a radar scattering sectional area are calculated. According to the method, variable coefficient DDM, non-conformal mesh generation and discontinuous Galerkin technologies are fused, the problem of discontinuity of multi-scale adaptation and matrix construction is solved, calculation precision and efficiency are both considered, and the method is suitable for rapid calculation of electromagnetic scattering of complex targets.

Description

Technical Field

[0001] This invention relates to the field of electromagnetics, specifically providing a method, system, and medium for calculating the electromagnetic scattering characteristics of complex targets. Background Technology

[0002] When electromagnetic waves irradiate a complex target region composed of various materials such as metals and dielectrics, induced currents and magnetic currents are generated on the surface and inside the complex target, which in turn produce secondary radiation. To obtain the electromagnetic scattering characteristics of complex targets, efficient and high-precision scattering calculation methods are needed. Domain Decomposition (DDM) is an effective method for calculating the scattering of such complex targets. DDM was initially proposed by American scholars such as Jinfeng Li. This method uses the Robin transport condition to separate regions composed of the same material from other regions and utilizes the continuity condition of current and magnetic current to reflect the coupling between regions. To improve the convergence of traditional domain decomposition methods, a precondition matrix is ​​introduced. While the introduction of the precondition matrix significantly reduces the number of iterations, the construction and inversion of the precondition matrix are time-consuming. As an improvement, an indirect inversion method can be used, that is, embedding an iterative process within the main iteration to indirectly realize the matrix inversion.

[0003] Furthermore, complex target scattering calculations require the construction of matrix equations, which can be achieved using area integral equations. Among various area integral equation methods, the Joint Electromagnetic-Cyclic Integral Equation (JMCFIE) exhibits good convergence characteristics. However, when the object being calculated has multi-scale characteristics, the number of convergence steps increases, making the computation process time-consuming. Additionally, the form of the matrix equations established by traditional domain decomposition methods differs between open and interface regions. These two reasons represent practical problems encountered by traditional DDM methods. Summary of the Invention

[0004] In order to address the problems in the prior art, the present invention is proposed to provide solutions or partial solutions to the aforementioned problems.

[0005] In a first aspect, the present invention provides a method for calculating the electromagnetic scattering characteristics of a complex target, comprising the following steps: S1, dividing the complex target into at least two regions according to the material distribution, using the material contact surface as the interface between each region, splitting the open region of each region into an open region and an interface, and defining the boundary line between the open region and the interface; S2, when the field point is located on the surface of each region, establishing electric field integral equations and magnetic field integral equations respectively based on the continuity conditions of electric and magnetic fields, and combining the electric field integral equations and magnetic field integral equations to form a joint electromagnetic current integral equation; S3, when the field point is located in an open region, directly using the electric field integral equations... The magnetohydrodynamic joint integral equation is constructed. When the field point is located at the interface, a variable coefficient is introduced to correct the Robin transmission condition, and a corrected equation for the interface region is constructed. S4: The open regions and interfaces of each region are discretized using triangular elements. Based on the discretized grid, the current and magnetohydrodynamics on the surface of the complex target are discretized using full RWG basis functions or half RWG basis functions. The full RWG basis functions or half RWG basis functions are used as test functions, and a matrix equation is constructed using the Galerkin method. S5: The matrix equation is solved using the generalized minimum margin method. S6: The scattering field and radar cross section of the complex target are calculated.

[0006] In one technical solution of the above-mentioned method for calculating the electromagnetic scattering characteristics of complex targets, the expression of the joint electromagnetic flow integral equation is as follows: (1) (2) in, Z 0 represents the wave impedance in free space. k 0 = 2π / l 0 represents the wavenumber in free space. l 0 represents the wavelength of an electromagnetic wave in free space. k i =2π / l i Indicates the first i Wavenumber within a region, l i Indicates the first i The wavelength within each region, J i With M i They represent the first i The current and magnetic current on the surface of a region, where α and β are combination coefficients, satisfying α + β = 1, and 0 ≤ α, β ≤ 1. Ω represents the electric field integral operator for the projected components. i Let r represent the i-th region and r represent the field point. Z i This represents the wave impedance in the i-th region. I 0 represents the unitary operator in a vacuum.I i The unitary operator in the i-th region is represented by the superscript symbol ×, which indicates the curl operation on a vector. T This indicates the operation of taking the double curl of a vector. This represents the principal value integral of the magnetic field integral operator. J j and M j Indicates the first j Current and magnetic current on the surface of a region and Let represent the electric field integral operators for the vacuum and the tangential components in the i-th region, respectively. This represents the principal value integral of the magnetic field integral operator for the projected component. This represents the principal value integral of the tangential component magnetic field integral operator. This indicates projecting a vector. E represents taking the tangential component of the vector. inc H represents the incident electric field. inc This indicates the incident magnetic field.

[0007] In one technical solution of the above-mentioned method for calculating the electromagnetic scattering characteristics of complex targets, in S3, when the field point is located in an open region, the electromagnetic flow joint integral equation is directly used; when the field point is located at the interface, variable coefficients are introduced to correct the Robin transmission condition, and a corrected equation for the interface region is constructed, specifically including: S31, When point r is located in the open area of ​​Ω1 With Ω2 open area When the surface is, the field point condition is satisfied. : (7) (8) S32, When point r is located at the interface Γ of Ω1 12 Interface Γ with Ω2 21 When on the surface: (9) (10) in, k It is a variable coefficient, and its value range is... k ≥1; The above expression is equivalent to: (11) (12) That is, the corrected Robin transmission conditions are obtained.

[0008] In one technical solution of the above-mentioned calculation method for the electromagnetic scattering characteristics of complex targets, the current J in S4 i With magnetic current M i The discrete expression is: (13) (14) in, i Indicates the region. m Indicates the index of the basis function. N i Indicates the first i The number of full edges and half edges in the region, f im As basis functions, Z 0 represents wave impedance in free space; Using the full or semi-RWG basis functions as test functions, the construction of matrix equations in conjunction with the Galerkin method specifically includes: According to Galerkin's method, the basis functions f im Treat as test function λ im Then the first i The test function set λ in each region i Represented as: (15) λ i Substituting equations (7) into (10) and taking the inner product, we obtain the following matrix equation: (16) in, M i Indicates the first i The self-impedance matrix of each region C ij Indicates the first i and j The coupling matrix between the electromagnetic currents of the two regions. D ij Indicates the first i and j The adhesion matrix between the two regions B i Indicates the first i The coupling matrix of each region X i Indicates the first i A column vector of unknown coefficients to be determined for each region. b i Indicates the first i The activation column vectors in each region; submatrix M p The matrix element expression is: (17) in, p and q Indicates the region number. p , q =1 or 2, and p ≠ q ; submatrix C pq The matrix element expression is: (18) in, p , q =1 or 2, and p ≠ q ; submatrix B p The matrix element expression is: (19) in, p =1 or 2; submatrix D pq The matrix element expression is: (20) in, p , q =1 or 2, and p ≠ q .

[0009] In one technical solution of the above-mentioned method for calculating the electromagnetic scattering characteristics of complex targets, the process of constructing the matrix equation also includes: using discontinuous Galerkin technique to handle the discontinuity between open regions and interfaces in each region; using full RWG basis functions for the edges inside the open regions and interfaces, and using semi-RWG basis functions for the boundaries; and consequently, it is necessary to adjust the equations (17) to (19) related to... The relevant inner product is corrected, and the specific expression is as follows: (twenty one) in, β p It is an internal penalty factor.

[0010] In one technical solution of the above-mentioned calculation method for the electromagnetic scattering characteristics of complex targets, when the basis function f p With basis function f q When all are full RWG basis functions, the last three terms on the right side of equation (21) are omitted; when the basis function f p With basis function f qWhen one of the basis functions is a full RWG basis function and the other is a semi-RWG basis function, the second or third term on the right-hand side of equation (21) is retained; when the basis function f p With basis function f q When all are semi-RWG basis functions, all four terms on the right side of equation (21) are retained.

[0011] In one technical solution of the above-mentioned calculation method for the electromagnetic scattering characteristics of complex targets, the matrix equation (16) and formulas (17)-(20) are... β =0.7, α =0.3, k =10, β p =0.

[0012] In one technical solution of the above-mentioned method for calculating the electromagnetic scattering characteristics of complex targets, the calculation of the scattering field and radar cross-section of complex targets specifically includes: Substituting the coefficient matrix obtained in step S6 into equations (13) and (14) yields the current J on the complex target surface. i With magnetic current M i ; The surface current J of complex targets i With magnetic current M i Substituting into the following formula, we obtain the surface current J. i With magnetic current M i The resulting scattered field E s : (twenty two) The radar cross section is calculated using the following formula: (twenty three).

[0013] Secondly, the present invention provides a calculation system for the electromagnetic scattering characteristics of complex targets, comprising: a region and surface division module, used to divide at least two regions according to the material distribution of the complex target, using the material contact surface as the interface between each region, splitting the open region of each region into an open region and an interface, and defining the boundary line between the open region and the interface; an integral equation construction module, used to establish electric field integral equations and magnetic field integral equations respectively based on the continuity conditions of electric field and magnetic field when the field point is located on the surface of each region, and combining the electric field integral equations and magnetic field integral equations to form a joint electromagnetic flow integral equation; and an equation adaptation module, used to directly use the joint electromagnetic flow integral when the field point is located in an open region. The system comprises the following equations: Equation 1: When the field point is located at the interface, a variable coefficient is introduced to correct the Robin transmission condition, constructing a corrected equation for the interface region; Matrix equation construction module: This module discretizes the open regions and interfaces of each region using triangular elements. Based on the discretized mesh, the current and magnetic current on the complex target surface are discretized using full RWG basis functions or half RWG basis functions. The full RWG basis functions or half RWG basis functions are used as test functions, combined with the Galerkin method to construct the matrix equation; Matrix solution module: This module solves the matrix equation using the generalized minimum margin method; Scattering characteristic calculation module: This module calculates the scattering field and radar cross-section of the complex target based on the matrix solution results.

[0014] Thirdly, the present invention provides a computer-readable storage medium storing a plurality of program codes adapted to be loaded and run by a processor to perform the method for calculating the electromagnetic scattering characteristics of the complex target.

[0015] The beneficial effects of the calculation method for the electromagnetic scattering characteristics of complex targets provided by this invention are as follows: This invention introduces a variable coefficient to modify the traditional Robin transmission condition, thus forming a variable coefficient DDM method. Furthermore, complex target structures exhibit multi-scale characteristics, and the construction methods for matrix elements in open and interface regions differ in each region. To address this, a non-conformal mesh partitioning technique is introduced to adapt to the needs of multi-scale and independent partitioning. To address the problem of discontinuous matrix construction under non-conformal mesh partitioning, this invention incorporates a discontinuous Galerkin technique. This constitutes an improved ImJMCFIE-DDM calculation method. This method involves key technologies such as non-conformal mesh partitioning, the adoption of the discontinuous Galerkin method, the adoption and numerical selection of the internal penalty factor, the construction of the variable coefficient Robin transmission condition, and the selection of the variable coefficient value. Attached Figure Description

[0016] The disclosure of this invention will become more readily understood with reference to the accompanying drawings. It will be readily understood by those skilled in the art that these drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Furthermore, similar numbers in the drawings are used to denote similar components, wherein: Figure 1 This is a schematic diagram of a complex target partitioning according to an embodiment of the present invention; Figure 2 This is a schematic diagram of surface non-uniform mesh partitioning according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a complex target composed of two cubes according to an embodiment of the present invention; Figure 4 The present invention provides scattering curves of a complex bicubic target under different penalty factors according to an embodiment of the present invention. Figure 5 This is a scattering curve diagram of a complex double-cube target under different variable coefficient conditions according to an embodiment of the present invention. Detailed Implementation

[0017] Some embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0018] like Figure 1-5 As shown, this invention provides a method for calculating the electromagnetic scattering characteristics of complex targets, including: Step S1: First, divide the complex target into regions according to the distribution of materials, using the actual contact surface between the two materials as the interface between the two regions. Taking a complex target composed of two materials as an example, such as... Figure 1 As shown, it contains two regions, Ω1 and Ω2, and Ω1 is divided into an open region. With the interface Γ 12 Two regions, with C1 as their boundary, divide Ω2 into open regions. With the interface Γ 21 There are two regions, and the boundary between the two regions is C2.

[0019] Step S2: When the field point r is located on the surfaces of Ω1 and Ω2 respectively, establish the electric field integral equation and the magnetic field integral equation on the surfaces of Ω1 and Ω2 respectively, based on the continuity conditions of the electric field and magnetic field: (1) (2) Generally, equation (1) represents the electric field integral equation, and equation (2) represents the magnetic field integral equation. Combining these two equations constitutes the Joint Electromagnetic-Cyclic Integral Equation (JMCFIE). Among them, Z0 represents the wave impedance in free space, which is equal to 370Ω; k 0 = 2π / l 0 represents the wavenumber in free space, while l 0 represents the wavelength of an electromagnetic wave in free space; k i = 2π / l i Indicates the first i The wave number within each region, and Indicates the first i Wavelength within a region; Z i This represents the wave impedance in the i-th region. I 0 represents the unitary operator in a vacuum. I i The unitary operator in the i-th region is represented by the superscript symbol ×, which indicates the curl operation on a vector. T This indicates the operation of taking the double curl of a vector. This represents the principal value integral of the magnetic field integral operator. J j and M j Indicates the first j Current and magnetic current on the surface of a region and Let J represent the electric field integral operators for the vacuum and the tangential components in the i-th region, respectively. i With M i They represent the first i Current and magnetic current on the surface of a region; α and β are combination coefficients, which satisfy α+β=1, and 0≤α, β≤1; The electric field integral operator for the projected component is expressed as: (3) in, Indicates the first i The Green's function within a region, where r represents the field point. Indicates the source point. (Superscript symbol) T This indicates the operation of taking the double curl of a vector: a T =n×a×n.

[0020] The tangential component electric field integral operator is expressed as: (4) The superscript symbol × indicates the curl operation on a vector: a × =n×a.

[0021] The principal value integral of the magnetic field integral operator for the projected component is expressed as: (5) Where PV represents the principal value integral.

[0022] The principal value integral of the tangential component magnetic field integral operator is expressed as: (6) This indicates projecting a vector. This indicates taking the tangential component of the vector. E inc H represents the incident electric field. inc Indicates the incident magnetic field, indicated by the superscript. T Still representing the double curl operation: a T =n×a×n, where the superscript × still indicates the curl operation on a vector: a × =n×a.

[0023] Step S3: When point r is located in the open region between Ω1 and Ω2, i.e. and On the surface, the equations are exactly the same as those in equations (1) and (2), except that the field point conditions are satisfied. Write in the following format: (7) (8) When the field point r is located in the interface region between Ω1 and Ω2, i.e. Γ 12 With Γ 21 When on the surface, such as Figure 1 As shown, the equation is slightly different in form from equations (1) and (2), and can be expressed as: (9) (10) in, k It is a variable coefficient, and its value range is... k ≥ 1. Equation (9) and Equation (10) are equivalent to: (11) (12) The two equations above are actually variations of the Robin transmission condition, the difference being the addition of a variable coefficient. k .

[0024] Step S4: Open region of Ω1 With Γ 12The mesh is discretized using triangular facets for the open region of Ω2. With Γ 21 Discretize the mesh using triangular facets, such as... Figure 2 As shown.

[0025] Based on these discrete grids, the surface current J i With magnetic current M i You can use full RWG basis functions or semi-RWG basis functions f im Discretize, where i Indicates the region. m Indicates the index of the basis function. Finally, the discrete expressions for current and magnetic current are: (13) (14) in, N i Indicates the first i The number of full edges and half edges in the region is determined by substituting equations (13) and (14) into equations (7) to (10), and then the basis functions f are calculated according to the Galerkin method. im Treat as test function λ im Thus the first i The test function set λ in each region i This can be represented as: (15) λ i Substituting equations (7) into (10) and taking the inner product, we obtain the following matrix equation: (16) in, M i Indicates the first i The self-impedance matrix of each region C ij Indicates the first i and j The coupling matrix between the electromagnetic currents of the two regions. D ij Indicates the first i and j The adhesion matrix between the two regions B i Indicates the first i The coupling matrix of each region X i Indicates the first i A column vector of unknown coefficients to be determined for each region. b i Indicates the first i The activation column vectors in each region; submatrix M p Matrix elements in p and q Indicates the region number. p , q =1 or 2, and p ≠ q The expression is: (17) submatrix C pq Matrix elements in p , q =1 or 2, and p ≠ q The expression is: (18) submatrix B p Matrix elements in p The expression for (=1 or 2) is: (19) submatrix D pq Matrix elements in p , q =1 or 2, and p ≠ q The expression is: (20) Furthermore, the discontinuous Galerkin technique addresses the discontinuity between open regions and interface regions in each region. Full RWG basis functions are used for the edges within the open regions and interfaces, while semi-RWG basis functions are used at the boundaries. Consequently, equations (17) to (19) involving... The relevant inner product is corrected, and the specific expression is as follows: (twenty one) in, β p It is the internal penalty factor. When the basis function f p With basis function f q When all are full RWG basis functions, the last three terms on the right side of equation (21) are omitted; when the basis function f p With basis function f q When one of the basis functions is a full RWG basis function and the other is a semi-RWG basis function, the second or third term on the right-hand side of equation (21) is retained; when the basis function f p With basis function f q When all are semi-RWG basis functions, all four terms on the right side of equation (21) are retained.

[0026] Matrix equation (16) and formulas (17) to (20) β =0.7, α =0.3, k =10, β p =0.

[0027] Step S5: Solve the matrix equation (16) using the generalized minimum residual method (GMRES).

[0028] Step S6: Solve for the radar cross-section σ of the complex target. Substitute the coefficient matrix obtained in the previous step into equations (13) and (14) to obtain the current J on the surface of the complex target. i With magnetic current M i The surface current J can be obtained using the following formula. i With magnetic current M i The resulting scattered field E s .

[0029] (twenty two) The final radar cross section can be calculated using the following formula: (twenty three).

[0030] To verify the feasibility of the present invention, Figure 3 A calculation example is given, where the scatterer is a cuboid composed of two cubes. A portion of it... e 1 equals 8, and the side length equals 0.4. l The average side length of the partition is l / 12. And the other part e 2 equals 2, the average side length of the partition is l / 8. The incident wave is still i Polarization, incident direction is θ= 180° and =0°. The operating frequency is 300MHz. The convergence condition of GMRES is 1e-6. Figure 4 Different penalty factors are given β p The calculation results under the given values, where β =0.7, α =0.3, k =8, which shows β p The calculation accuracy is not affected by different values. Table 1 shows the different values. β p The number of iteration steps under the given value can be seen. β pWhen the value is 0, the number of iterations is minimized. Figure 5 Different variable coefficients are given k The number of iteration steps at time, where β =0.7, α =0.3, β p =0, as can be seen from the graph, the coefficient is variable. k It only affects the number of iterations and does not affect the calculation accuracy. Table 2 shows the different... k The number of iteration steps under the given value can be seen. k When the value is 20, the number of iterations is minimized.

[0031] Table 1

[0032] Table 2

[0033] Example 2 This invention discloses a calculation system for the electromagnetic scattering characteristics of complex targets. The calculation system for the electromagnetic scattering characteristics of complex targets in this embodiment mainly includes a region and surface partitioning module, an integral equation construction module, an equation adaptation module, a matrix equation construction module, a matrix solving module, and a scattering characteristic calculation module. In some embodiments, one or more of these modules can be combined into a single module. In some embodiments, the region and surface partitioning module can be configured to execute step S1. The integral equation construction module can be configured to execute step S2. The equation adaptation module can be configured to execute step S3. The matrix equation construction module executes step S4. The matrix solving module executes step S5. The scattering characteristic calculation module executes step S6. In one embodiment, a description of the specific functions can be found in steps S1-S6.

[0034] The above-described calculation system for the electromagnetic scattering characteristics of complex targets is an embodiment of the calculation method for the electromagnetic scattering characteristics of complex targets. The technical principles, the technical problems solved, and the technical effects produced by the two are similar. Those skilled in the art can clearly understand that, for the sake of convenience and brevity, the specific working process and related descriptions of the calculation system for the electromagnetic scattering characteristics of complex targets can be found in the description of the embodiment of the calculation method for the electromagnetic scattering characteristics of complex targets, and will not be repeated here.

[0035] Example 3 The present invention also provides a computer-readable storage medium. In one embodiment of the computer-readable storage medium according to the present invention, the computer-readable storage medium can be configured to store a program for performing a calculation method for the electromagnetic scattering characteristics of a complex target according to the above-described method embodiments. This program can be loaded and run by a processor to implement the calculation method for the electromagnetic scattering characteristics of the complex target. For ease of explanation, only the parts related to the embodiments of the present invention are shown; for specific technical details not disclosed, please refer to the method section of the embodiments of the present invention. The computer-readable storage medium can be a storage device comprising various electronic devices. Optionally, in the embodiments of the present invention, the computer-readable storage medium is a non-transitory computer-readable storage medium.

[0036] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, and the technical solutions resulting from these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for calculating electromagnetic scattering properties of a complex object, characterized in that, The method comprises the following steps: S1, dividing at least two regions according to the material distribution of the complex target, taking the material contact surface as the boundary surface of each region, splitting the open region of each region into an open region and an interface, and defining the interface line of the open region and the interface; S2, when the field point is located on the surface of each region, respectively establishing an electric field integral equation and a magnetic field integral equation according to the continuity conditions of the electric field and the magnetic field, and combining the electric field integral equation and the magnetic field integral equation to form an electromagnetic current joint integral equation; S3, when the field point is located in the open region, directly using the electromagnetic current joint integral equation; when the field point is located on the interface, introducing a variable coefficient to modify the Robin transmission condition, and constructing a modified equation for the interface region; S4, discretely meshing the open region and the interface of each region with triangular face elements, discretely meshing the current and the magnetic current on the surface of the complex target with full RWG basis functions or half RWG basis functions based on the discrete meshes, taking the full RWG basis functions or the half RWG basis functions as test functions, and constructing a matrix equation by combining the Galerkin method; S5, solving the matrix equation by using the generalized least square method; S6, calculating the scattering field and the radar cross section area of the complex target.

2. The method of claim 1, wherein, The expression of the electromagnetic current joint integral equation is: （1） （2） in, Z 0 represents the wave impedance in free space. k 0 = 2π / When the field point is located in the open region in S3, the electromagnetic current joint integral equation is directly used; 0 represents the wavenumber in free space. when the field point is located on the interface, a variable coefficient is introduced to modify the Robin transmission condition, and a modified equation for the interface region is constructed, which specifically comprises: 0 represents the wavelength of an electromagnetic wave in free space. k i =2π / The above formula is equivalent to: i Indicates the first i Wavenumber within each region, That is, the modified Robin transmission condition is obtained. i Indicates the first i The wavelength within each region, J i With M i They represent the first i The current and magnetic current on the surface of a region, where α and β are combination coefficients, satisfying α + β = 1, and 0 ≤ α, β ≤ 1. Ω represents the electric field integral operator for the projected components. i Let r represent the i-th region and r represent the field point. Z i This represents the wave impedance in the i-th region. I 0 represents the unitary operator in a vacuum. I i The unitary operator in the i-th region is represented by the superscript symbol ×, which indicates the curl operation on a vector. T This indicates the operation of taking the double curl of a vector. This represents the principal value integral of the magnetic field integral operator. J j and M j Indicates the first j Current and magnetic current on the surface of a region and Let represent the electric field integral operators for the vacuum and the tangential components in the i-th region, respectively. This represents the principal value integral of the magnetic field integral operator for the projected component. This represents the principal value integral of the tangential component magnetic field integral operator. This indicates projecting a vector. E represents taking the tangential component of the vector. inc H represents the incident electric field. inc This indicates the incident magnetic field.

3. The method of claim 2, wherein, Taking the full RWG basis functions or the half RWG basis functions as test functions, and constructing a matrix equation by combining the Galerkin method specifically comprises: The calculation of the scattering field and the radar cross section area of the complex target specifically comprises: S31, when the field point r is located in the open region of Ω1 with the open region of Ω2 the field point condition is satisfied : (7) (8); S32, when the point r lies on the interface Γ 12 of Ω1 and the interface Γ 21 of Ω2: （9） （10） wherein The radar cross section area is solved by using the following formula: is a variable coefficient, taking a value in the range It comprises: ≥ 1; A region and surface division module is configured to divide at least two regions according to the material distribution of the complex target, take the material contact surface as the boundary surface of each region, split the open region of each region into an open region and an interface, and define the interface line of the open region and the interface; （11） （12） An integral equation construction module is configured to, when the field point is located on the surface of each region, respectively establish an electric field integral equation and a magnetic field integral equation according to the continuity conditions of the electric field and the magnetic field, and combine the electric field integral equation and the magnetic field integral equation to form an electromagnetic current joint integral equation; 4. The method of claim 3, wherein, Current J in S4 i with the magnetic current M i The discrete expression for M is （13） （14） wherein i denotes the region of interest, m denotes the sequence number of the basis function, N i denotes the first i number of full and half edges in the region, f im is the basis function, Z 0 denotes the wave impedance in free space; An equation adaptation module is configured to, when the field point is located in the open region, directly use the electromagnetic current joint integral equation; The basis functions f im When the test function λ im is taken as i The test function set λ i in the first i region is expressed as: (15) Inserting (7) into (10) and taking the inner product gives the following matrix equation: i Inserting (7) into (10) and taking the inner product gives the following matrix equation: (16) in, M i Indicates the first i The self-impedance matrix of each region C ij Indicates the first i and j The coupling matrix between the electromagnetic currents of the two regions. D ij Indicates the first i and j The adhesion matrix between the two regions B i Indicates the first i The coupling matrix of each region X i Indicates the first i A column vector of unknown coefficients to be determined for each region. b i Indicates the first i The activation column vectors in each region; sub-matrix M p The matrix element expression in is (17) wherein p with q denotes the region number in which it is located, p , q = 1 or 2, and p ≠ q ; sub-matrix C pq The matrix element expression in is (18) wherein p , q = 1 or 2, and p ≠ q ; sub-matrix B p The matrix element expression in is (19) wherein p = 1 or 2; sub-matrix D pq The matrix element expression in is (20) wherein p , q = 1 or 2, and p ≠ q .

5. The method of claim 4, wherein, In the process of constructing the matrix equation, the non-continuity between the open region and the interface in each region is handled by using the non-continuous Galerkin technique, the edges inside the open region and the interface are selected by using the full RWG basis function, and the boundary is selected by using the half RWG basis function, and then the inner product related to the formula (17) to (19) needs to be modified, and the specific expression is as follows: ​ (21) wherein, β p is an inner penalty factor.

6. The method of claim 5, wherein, When the basis function f p When the basis function f q When the basis function f p When the basis function f q When the basis function f p When the basis function f q When the basis function f 7. The method of claim 5, wherein, The matrix equation (16) and the formulas (17) - (20) are β = 0.7, α = 0.3, when the field point is located on the interface, introduce a variable coefficient to modify the Robin transmission condition, and construct a modified equation for the interface region; = 10, β p = 0.

8. The method of claim 5, wherein, A matrix equation construction module is configured to discretely mesh the open region and the interface of each region with triangular face elements, discretely mesh the current and the magnetic current on the surface of the complex target with full RWG basis functions or half RWG basis functions based on the discrete meshes, take the full RWG basis functions or the half RWG basis functions as test functions, and construct a matrix equation by combining the Galerkin method. The coefficient matrix solved in step S6 is brought into equations (13) and (14) to obtain the current J of the complex target surface i and the magnetic flow M i ; The complex target surface current J i is related to the magnetic current M i Substituting into the following equation, the surface current J i is related to the magnetic current M i The resulting scattered field E s : (22) ​ (23) 。 9. A system for computing electromagnetic scattering properties of a complex object, the system comprising: ​ ​ ​ ​ ​ ​ a matrix solving module, configured to solve the matrix equation by using a generalized least squares method; a scattering characteristic calculating module, configured to calculate the scattering field and radar cross section of the complex target based on the matrix solving result.

10. A computer readable storage medium having stored therein a plurality of program codes, characterized in that, The program code is adapted to be loaded and run by the processor to execute the method for calculating the electromagnetic scattering characteristic of the complex target according to any one of claims 1 to 8.

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