Conductor ultra wide band electromagnetic scattering simulation method based on time domain discontinuous Galerkin integral equation

Abstract

The invention discloses a conductor ultra wide band electromagnetic scattering simulation method based on a time domain discontinuous Galerkin integral equation. The method allows calculation of target electromagnetic scattering results from ultra-low frequency to extremely high frequency under non-conformal grid conditions while covering near-field and far-field electromagnetic fields. Specifically, the method is suitable for processing a wavelength structure with the electrical size range from 1 time to 10-8 times, and the problem of low-frequency numerical value collapse is effectively solved. Compared with a frequency domain discontinuous Galerkin electric field integral equation numerical method, the method has obvious advantages in ultra-wideband scattering analysis. In addition, the method can be easily integrated into the existing time domain discrete Galerkin electric field integral equation method. Compared with an existing order stepping (MOD) method, the method has remarkable advantages, and a valuable tool is provided for ultra-wideband electromagnetic scattering analysis under the non-conformal grid condition; a plurality of typical examples verify the accuracy and effectiveness of the method at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of numerical calculation of electromagnetic fields, and relates to a method for simulating ultra-wideband electromagnetic scattering of conductors based on the time-domain discontinuous Galerkin integral equation. This method uses the step-by-step order time-domain discontinuous Galerkin integral equation method under non-conformal grid conditions to predict the ultra-wideband electromagnetic scattering of complex conductor structures. Background Art

[0002] Integral equations have been widely used in computational electromagnetics due to their unique properties and have attracted continuous attention in the academic community. Basis functions commonly found in integral equations, such as RWG basis functions, curve RWG basis functions, etc., usually have the characteristic of divergence consistency. However, these functions require the grid to be conformal, which is easily restricted when dealing with cases such as multi-scale targets. Fortunately, the emergence of the latest discontinuous Galerkin (DG) method provides an effective way to solve this problem (Peng Z, Lim K H, Lee J F. A discontinuous Galerkin surface integral equation method for electromagnetic wave scattering from nonpenetrable targets [J]. IEEE Transactions on Antennas and Propagation, 2013, 61(7): 3617-3628.). Due to its high flexibility, the DG method is increasingly widely used in many complex electromagnetic problems (Kong B B, Sheng X Q. A discontinuous Galerkin surface integral equation method for scattering from multiscale homogeneous objects [J]. IEEE Transactions on Antennas and propagation, 2018, 66(4): 1937-1946.), especially in the fields of electromagnetic radiation, scattering of homogeneous dielectric bodies, numerical analysis of electromagnetic fields in half-space, and numerical calculation and analysis of high-order problems.

[0003] However, despite the wide application of the discontinuous Galerkin method in the Electric Filed Integral Equation (EFIE), there are still some challenges. One of the main challenges is the numerical accuracy problem encountered in the low-frequency case. When using conformal space basis functions, techniques such as the quasi-Helmholtz decomposition (Adrian S B, Dely A, Consoli D, et al. Electromagnetic integral equations: Insights in conditioning and preconditioning[J]. IEEE Open Journal of Antennas and Propagation, 2021, 2: 1143-1174.) and the introduction of additional charge unknowns (Roth T E, Chew W C. Stability analysis and discretization of A-Φ time domain integral equations for multiscale electromagnetics[J]. Journal of Computational Physics, 2020, 408: 109102.) can be used for charge and current separation. However, due to the characteristics of the monopole RWG basis functions, the application of these methods in the discontinuous Galerkin integral equation is limited to some extent. Although previous studies (Hou Y, Xiao G, Tian X. A discontinuous Galerkin augmented electric field integral equation for multiscale electromagnetic scattering problems[J]. IEEE Transactions on Antennas and Propagation, 2017, 65(7): 3615-3622.) have adopted the Augmented Electric Filed Integral Equation (AEFIE) and perturbation methods to obtain accurate low-frequency solutions, it is still difficult to develop a unified method that is applicable to the extremely high-frequency, medium-frequency, and ultra-low-frequency ranges simultaneously.

[0004] In summary, existing methods often require additional unknowns or cannot achieve a unified high-precision electromagnetic numerical solution across the entire frequency band, which limits their application in specific ultra-wideband frequency ranges. Therefore, there is an urgent need to develop a method for calculating ultra-wideband electromagnetic scattering that can effectively solve problems under multi-scale models and non-conformal grids, ensuring accurate and reliable electromagnetic solutions. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the object of the present invention is to provide a simulation method for ultra-wideband electromagnetic scattering of conductors based on the time-domain discontinuous Galerkin integral equation for numerical calculation of electromagnetic fields.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A simulation method for ultra-wideband electromagnetic scattering of conductors based on the time-domain discontinuous Galerkin integral equation, comprising the following steps:

[0008] In the first step, a geometric model of a complex structure, i.e., the conductor structure to be solved, is established, and it is initially meshed to obtain the grid topology of the electromagnetic calculation structure, i.e., the basis function information and the element adjacency relationship, and the grid level is topologically divided to generate non-conformal grid elements, and the time-domain electric field integral equation of the electromagnetic field is established.

[0009] In the second step: Load the electromagnetic calculation grid topology obtained by preprocessing, discretize the time-domain electric field integral equation of the electromagnetic field using the monopole RWG basis function, and expand and test it using the Galerkin method to obtain the discontinuous Galerkin electric field integral equation.

[0010] In the third step: Pre-calculate the generalized Laguerre polynomials required for the excitation source and the impedance matrix part. The preprocessing is to pre-calculate the values of the generalized Laguerre polynomials from the zero order to the required order to solve the numerical integration part of the excitation source and the impedance matrix;

[0011] In the fourth step: Using the discontinuous Galerkin electric field integral equation obtained by discretization in step two, calculate its vector potential and scalar potential respectively, judge the relative positions of the discontinuous edges and determine the penalty term constraint conditions, and add penalty term constraint conditions by confirming the overlapping situation of different basis function edges, so as to satisfy no charge accumulation on the non-conformal edges.

[0012] In the fifth step: Use the singular value cancellation or Gaussian area integration method to obtain the influence of the impedance matrix and the right-hand side term history to solve the equivalent source.

[0013] In the sixth step: For the excitation source part, use Gaussian Legendre integration to solve the one-dimensional excitation matrix part obtained after the Laguerre polynomial test; and adopt an adaptive truncation algorithm to obtain the order that meets the accuracy requirements.

[0014] Step 7: Perform impedance matrix and right-hand side assembly, accelerate the summation part of the right-hand side Toeplitz matrix using FFT, and perform efficient matrix solution using LU decomposition.

[0015] Step 8: Repeat Steps 4 to 8 until the adaptive truncation condition is met and the loop is exited, and observe the coefficient distribution of the normalized Laguerre polynomials.

[0016] In the above technical solution, the electromagnetic field time-domain electric field integral equation established in the first step is:

[0017]

[0018] The operator is:

[0019]

[0020] where n is the unit normal vector pointing outward from the object, E i (r,t) is the incident electric field as the excitation source, J(r,t) is the equivalent surface current on the object surface using the equivalence principle, r is the position of the observation point, r′ is the position of the source point, c is the light propagation speed in free space, S′ represents the surface of the scattering target, R is the distance between the source point and the observation point, and τ = t - R / c is the time delay.

[0021] Furthermore, in Step 2, the electric field integral equation method is discretized using the spatial boundary element monopole RWG basis function. The electromagnetic time-domain electric field integral equation is spatially discretized using the spatial boundary element monopole RWG basis function, and the generalized Laguerre polynomial is used as the time basis function for time discretization.

[0022] Furthermore, during the discretization process, the following constraints are imposed on the current continuity between adjacent elements:

[0023]

[0024] where N S is the number of spatial monopole RWG basis functions, is the unit normal vector of the nth monopole RWG basis function pointing outside the common edge, is the surface current density of the nth monopole RWG basis function.

[0025] Furthermore, according to the electric field integral equation operator, the discrete Galerkin matrix form is derived and expanded and verified for itself, and the following expression can be obtained:

[0026]

[0027] where, For the interaction part between the impedance matrix and the equivalent source coefficients expanded and tested using the spatial monopole RWG basis functions, e n,i is the current expansion coefficient corresponding to the i-th order Laguerre polynomial on the n-th basis function, which is the quantity to be solved is the excitation term expansion coefficient corresponding to the i-th order on the m-th basis function The specific expression of is:

[0028]

[0029] where, Ξ 1,ij , Ξ 2,ij and Ξ 3,ij are respectively:

[0030]

[0031] Furthermore, the penalty term constraint condition can be expressed as:

[0032]

[0033] where, is the monopole RWG basis function is the unit normal vector of the monopole RWG basis function pointing outside the common edge, γ represents the expression sR / c, and R is the distance between the source point r′ and the observation point r is the i-th order weighted Laguerre polynomial, specifically expressed as where represents the i-th order Laguerre polynomial, and α represents an arbitrary real number

[0034] Furthermore, the physical objectives are various parameters such as scattered low-frequency near field, scattered high-frequency near field, scattered high-frequency far field, scattered low-frequency far field, surface current distribution, etc.

[0035] The beneficial effects of the present invention are as follows: The present invention proposes a new method for solving ultra-wideband electromagnetic scattering using the time-domain discontinuous Galerkin electric field integral equation. This method can calculate scattering results from ultra-low frequencies to extremely high frequencies under non-conformal grid conditions, covering near-field and far-field electromagnetic fields. Specifically, this method is applicable to processing electrical sizes ranging from 1 to as low as 10 -8 times the wavelength, effectively solving the low-frequency numerical collapse problem. Due to the easy implementation of the algorithm, it has obvious advantages compared with the frequency-domain discontinuous Galerkin electric field integral equation in the numerical analysis of ultra-wideband electromagnetic scattering. In addition, this method is easy to integrate into the existing time-domain discontinuous Galerkin electric field integral equation code. Compared with the existing method of order stepping (MOD), this method has significant advantages and provides an important tool for the numerical analysis of ultra-wideband electromagnetic scattering under non-conformal grid conditions. Multiple typical examples verify the accuracy and effectiveness of this method. Description of the Drawings

[0036] Figure 1 It is the flow chart of the time-domain discontinuous Galerkin integral equation method of the present invention.

[0037] Figure 2 It is a schematic diagram of a non-conformal mesh for sphere subdivision, where (a) is non-conformal mesh division, (b) is the monopole RWG basis function, and (c) is the conformal RWG basis function.

[0038] Figure 3 It is a comparison diagram of the far-field RCS sweep points of different methods and the Mie analytical solution.

[0039] Figure 4 It is the near electric field sweep situation of different methods at the position (0.0, 0.0, 1.0) [m].

[0040] Figure 5 It is the near magnetic field sweep situation of different methods at the position (0.0, 0.0, 1.0) [m].

[0041] Figure 6 It is a schematic diagram of a submarine model and its mesh subdivision.

[0042] Figure 7 It is the transient current response of the submarine model corresponding to the 30th edge, 80th edge, and 110th edge.

[0043] Figure 8 It is a logarithmic form diagram of the transient current response of the submarine model corresponding to the 30th edge, 80th edge, and 110th edge.

[0044] Figure 9 It is a schematic diagram of the near electric field of the submarine at 100 MHz. The left is the commercial software FEKO, and the right is the time-domain discontinuous Galerkin method.

[0045] Figure 10 It is a schematic diagram of the near electric field of the submarine at 1 Hz. The left is the commercial software FEKO, and the right is the time-domain discontinuous Galerkin method.

[0046] Figure 11 It is a schematic diagram of the near magnetic field of the submarine at 100 MHz. The left is the commercial software FEKO, and the right is the time-domain discontinuous Galerkin method.

[0047] Figure 12 It is a schematic diagram of the near magnetic field of the submarine at 1 Hz. The left is the commercial software FEKO, and the right is the time-domain discontinuous Galerkin method. Specific implementation manners

[0048] The following further elaborates on the technical solution of the present invention in detail in conjunction with the accompanying drawings and specific examples.

[0049] The present invention proposes a new method for solving ultra-wideband electromagnetic scattering using the time-domain discontinuous Galerkin electric field integral equation. This method allows the calculation of scattering results from ultra-low frequencies to extremely high frequencies under non-conformal grid conditions, covering near-field and far-field electromagnetic fields. The monopole RWG basis function is used as the spatial basis function, which allows flexible mesh discretization without strict conformality. In time, the generalized Laguerre polynomial is selected as the time basis function, combined with the order-stepping time-domain method, effectively avoiding the late-time instability problem of the conventional time-domain integral equation method. The content of the invention has significant advantages compared with the existing order-stepping, providing an important tool for the numerical calculation and analysis of ultra-wideband electromagnetic scattering under non-conformal grid conditions.

[0050] According to a specific embodiment of the present invention, as Figure 1 shown, the method may specifically include the following steps:

[0051] First step, establish a geometric model of a complex structure, perform initial mesh discretization on it to obtain the mesh topology of the computational electromagnetic structure, that is, the basis function information and the element adjacency relationship, and perform topological division on the mesh level to generate non-conformal mesh elements.

[0052] Second step: Load the computational electromagnetic mesh topology obtained by preprocessing, discretize the time-domain electric field integral equation of the electromagnetic field using the monopole RWG basis function, and perform expansion and testing using the Galerkin method.

[0053] Third step: Perform pre-computation on the generalized Laguerre polynomials required for the excitation source and the impedance matrix part.

[0054] Fourth step: Use the discontinuous Galerkin electric field integral equation discretized in the second step to calculate its vector potential and scalar potential respectively, judge the relative position of the discontinuous edges, and determine the penalty term constraint conditions.

[0055] Fifth step: Use the singular value cancellation or Gaussian quadrature method to obtain the influence of the impedance matrix and the right-hand side history to solve the equivalent source.

[0056] Sixth step: For the excitation source part, use Gaussian-Legendre quadrature to solve the one-dimensional excitation matrix part obtained after testing with the Laguerre polynomial; and adopt an adaptive truncation algorithm to obtain the order that meets the accuracy requirements.

[0057] Seventh step: Perform impedance matrix and right-hand side assembly, use FFT to accelerate the summation part of the right-hand side Toeplitz matrix, and use LU decomposition for efficient matrix solution.

[0058] Eighth step: Repeat the fourth step to the eighth step until the adaptive truncation condition is met and jump out of the loop, and observe the distribution of the normalized Laguerre polynomial coefficients.

[0059] The key operations in the solution of the present invention are described in detail as follows. Steps and methods well-known in other fields used in the solution will not be elaborated further:

[0060] The initial mesh of the complex structure can be generated using various boundary element mesh generation software. Its basis function information, element (point, edge, face) adjacency relationship, and boundary conditions are determined and read in.

[0061] The electromagnetic field is described by the time-domain electric field integral equation:

[0062]

[0063] where the operators can be expressed respectively as:

[0064]

[0065] The descriptions of each symbol are as follows:

[0066] r′ Position of the source point

[0067] τ = t - R / c Time delay

[0068] r Position of the observation point

[0069] c Speed of light propagation in free space

[0070] R Distance between the source point and the observation point

[0071] The above formulas jointly describe the forward problem of the time-domain electric field integral equation. The equivalent source in the above formulas is expanded and tested using the spatial monopole RWG basis function and the time-domain Laguerre polynomial, and the discretized Galerkin electric field integral equation expression of the equation is obtained.

[0072] Among them, the matrix form is expressed as:

[0073]

[0074] The surface current density is expressed as:

[0075]

[0076] Among them, is the weighted Laguerre polynomial.

[0077] The far-field expression form of the scattered electric field can be expressed as:

[0078]

[0079] The near-field expression form of the scattered electric field can be expressed as:

[0080]

[0081] The near - field expression of the scattered magnetic field can be expressed as:

[0082]

[0083] Different from the RWG basis functions, each monopole RWG spatial basis function is independently defined on a single triangle, rather than on a pair of triangular patches. If no additional treatment is performed on the current continuity condition between adjacent elements, direct calculation of line - line integrals is required to solve the above equation. However, when the field point and the source point coincide, the line - line integral will become infinite, making the calculation very complex. Therefore, to avoid this situation, additional constraint conditions are introduced to ensure current continuity:

[0084]

[0085] To match the magnitude of the impedance matrix, the above formula needs to be scaled. A constant coefficient can be multiplied on both sides. First, a Galerkin test in the spatial domain is performed on the equation, and the following can be obtained:

[0086]

[0087] After testing the Laguerre polynomials and using the inherent properties of the weighted Laguerre polynomials, the following is obtained:

[0088]

[0089] By setting the error charge part caused by the scalar potential to 0 and keeping the entire object electrically neutral, the charge convention condition can be obtained as:

[0090]

[0091] By eliminating the infinite line - line integral of the partial scalar potential in the original impedance matrix and applying the constraint of the object's electrical neutrality condition, the dimensionality reduction of the singular part can be performed. By introducing a penalty coefficient χ and associating the constraint condition with the original matrix equation, the final form of the matrix equation is:

[0092]

[0093] Among them, is the interaction part between the impedance matrix expanded and tested using the spatial monopole RWG basis functions and the equivalent source coefficients, e n,i is the current expansion coefficient corresponding to the i - th order Laguerre polynomial on the n - th basis function, is the excitation term expansion coefficient corresponding to the i - th order on the m - th basis function. The left - hand side term of the impedance matrix and the excitation source matrix part can be expressed as:

[0094]

[0095]

[0096] μ is the magnetic permeability of free space, is the test monopole RWG basis function, is the source monopole RWG basis function, ε is the permittivity of free space, t m is the unit normal vector of the m-th triangle's edge pointing from the inside to the outside, t n is the unit normal vector of the n-th triangle's edge pointing from the inside to the outside, χ is the penalty factor, l m is the length of the edge opposite the free vertex of the m-th triangle, l n is the length of the edge opposite the free vertex of the n-th triangle; Ξ 1,ij , Ξ 2,ij and Ξ 3,ij are respectively:

[0097]

[0098] s is the Laguerre polynomial time-domain scaling coefficient, γ represents the expression sR / c, is the i-th order weighted Laguerre polynomial, specifically expressed as where represents the i-th order Laguerre polynomial, α represents an arbitrary real number.

[0099] Several typical examples are used to verify the method of the present invention:

[0100] Figure 2 is a schematic diagram of a non-conformal mesh of a sphere dissection. Among them, (a) is the non-conformal mesh division, (b) is the monopole RWG basis function, and (c) is the conformal RWG basis function; Figure 3 is for different methods at θ = 0, Comparison diagram of far-field RCS sweep points and MIE analytical solutions; Figure 4 is the near electric field sweep situation of different methods at the position (0.0, 0.0, 1.0) [m]; Figure 5 is the calculation result of the near magnetic field sweep of different methods at the position (0.0, 0.0, 1.0) [m].

[0101] Figure 6 is a schematic diagram of a submarine model and its mesh dissection; Figure 7 is the transient current response of the submarine model corresponding to the 30th edge, 80th edge, and 110th edge; Figure 8 is the logarithmic form diagram of the transient current response of the submarine model corresponding to the above edges; Figure 9 is the calculation result of the near electric field distribution of the submarine at 100 MHz. On the left is the commercial software FEKO, and on the right is the time-domain discontinuous Galerkin method proposed by the present invention; Figure 10It is the calculation result of the near electric field distribution of the submarine at 1 Hz; Figure 11 It is the calculation result of the near magnetic field of the submarine at 100 MHz; Figure 12 It is the calculation result of the near magnetic field of the submarine at 1 Hz.

[0102] It can be seen that the method proposed in the present invention has good consistency with the commercial software FEKO in both the low-frequency and high-frequency parts on the premise of satisfying non-conformal meshes, and the method of the present invention has accuracy and effectiveness.

Claims

1. A conductor ultra-wideband electromagnetic scattering simulation method based on the time-domain discontinuous Galerkin integral equation, characterized in that: It includes the following steps: In the first step, a geometric model of the conductor structure to be solved is established, and initial mesh division is performed on it to obtain the electromagnetic mesh topology of the calculation structure, that is, basis function information and element adjacency relationship. And the mesh layer is topologically divided to generate non-conformal mesh elements, and the time-domain electric field integral equation of the electromagnetic field is established; In the second step: Based on the electromagnetic mesh topology obtained from the first-step preprocessing, the time-domain electric field integral equation of the electromagnetic field is discretized, and the Galerkin method is used for expansion and verification to obtain the discontinuous Galerkin electric field integral equation; In the third step: The generalized Laguerre polynomials required for the excitation source and the impedance matrix part are pre-calculated, and the values of the generalized Laguerre polynomials from the zero order to the required order are processed in advance to solve the numerical integration part of the excitation source and the impedance matrix; In the fourth step: The discontinuous Galerkin electric field integral equation obtained by the second-step discretization is used to calculate its vector potential and scalar potential respectively; further judge the relative positions of the discontinuous edges, and add penalty term constraint conditions by confirming the overlapping situation of different basis function edges, so as to satisfy that there is no charge accumulation on the non-conformal edges; In the fifth step: The singular value cancellation or Gaussian quadrature method is used to obtain the impedance matrix and the right-hand side term; In the sixth step: For the excitation source part, the Gaussian-Legendre integration is used to solve the Laguerre polynomial, and the one-dimensional excitation matrix part obtained after verification is obtained; and the adaptive truncation is used to obtain the order that meets the accuracy requirements; In the seventh step: The impedance matrix and the right-hand side term are assembled, the FFT is used to accelerate the summation part of the Toeplitz matrix of the right-hand side term, and the LU decomposition is used to complete the efficient solution of the matrix; In the eighth step: Repeat steps four to eight until the condition of the adaptive truncation is met, that is, jump out of the loop, observe the distribution of the normalized Laguerre polynomial coefficients, and realize the simulation of the target physical parameters of the electromagnetic scattering of the conductor structure.

2. The conductor ultra-wideband electromagnetic scattering simulation method based on the time-domain discontinuous Galerkin integral equation according to claim 1, characterized in that: The time-domain electric field integral equation of the electromagnetic field established in the first step is: Operator is as follows: where n is the unit normal vector pointing to the outside of the object, E i (r,t) is the incident electric field as the excitation source, J(r,t) is the equivalent surface current on the object surface using the equivalence principle, r is the position of the observation point, r′ is the position of the source point, c is the light propagation speed in free space, S′ represents the surface of the scattering target, R is the distance between the source point and the observation point, and τ = t - R / c is the time delay.

3. The conductor ultra-wideband electromagnetic scattering simulation method based on the time-domain discontinuous Galerkin integral equation according to claim 2, characterized in that: In the second step, the space boundary element monopole RWG basis function is used to discretize the time-domain electric field integral equation of the electromagnetic field in space, and the generalized Laguerre polynomial is used as the time basis function for time discretization.

4. The conductor ultra-wideband electromagnetic scattering simulation method based on the time-domain discontinuous Galerkin integral equation according to claim 2, wherein During the discretization process, the following constraints are imposed on the current continuity between adjacent elements: where N S is the number of spatial monopole RWG basis functions, is the unit normal vector of the nth monopole RWG basis function pointing outside the common edge, is the surface current density of the nth monopole RWG basis function.

5. The method for simulating conductor ultra-wideband electromagnetic scattering based on the time-domain discontinuous Galerkin integral equation according to claim 4, characterized in that The equivalent source is expanded and verified by using the space monopole RWG basis function and the time-domain Laguerre polynomial to obtain the discrete Galerkin matrix form of the time-domain electric field integral equation of the electromagnetic field: Among them, is the interaction part of the impedance matrix and the equivalent source coefficient expanded and tested using the spatial monopole RWG basis functions. n is the source basis function index, m is the test basis function index, and e n,i is the current expansion coefficient corresponding to the i-th order Laguerre polynomial on the n-th basis function, is the excitation term expansion coefficient corresponding to the i-th order on the m-th basis function. The specific expression is: where μ is the magnetic permeability of free space, is the test monopole RWG basis function, is the source monopole RWG basis function, ε is the permittivity of free space, t m is the unit normal vector of the m-th triangle's edge pointing from inside to outside, t n is the unit normal vector of the n-th triangle's edge pointing from inside to outside, χ is the penalty factor, l m is the length of the edge opposite to the free vertex of the m-th triangle, l n is the length of the edge opposite to the free vertex of the n-th triangle; Ξ 1,ij , Ξ 2,ij and Ξ 3,ij are respectively: s is the Laguerre polynomial time-domain scaling coefficient, and γ represents the expression sR / c. is the i-th order weighted Laguerre polynomial, specifically expressed as where represents the i-th order Laguerre polynomial, and α represents an arbitrary real number.

6. The conductor ultra-wideband electromagnetic scattering simulation method based on the time-domain discontinuous Galerkin integral equation according to claim 5, wherein: The penalty term constraint condition is: wherein, is a monopole RWG basis function, is the unit normal vector of the monopole RWG basis function pointing outside the common edge, and R is the distance between the source point r′ and the observation point r.

7. The conductor ultra-wideband electromagnetic scattering simulation method based on the time-domain discontinuous Galerkin integral equation according to claim 1, characterized in that: The target physical parameters are any of the scattered low-frequency near field, scattered high-frequency near field, scattered high-frequency far field, scattered low-frequency far field, and surface current distribution of the conductor electromagnetism.

Images