Time domain discontinuous Galerkin electromagnetic simulation method and system based on Robin transmission condition

Abstract

The invention discloses a time domain discontinuous Galerkin electromagnetic simulation method and system based on a Robin transmission condition, and the method comprises the following steps: carrying out the geometric modeling of a to-be-simulated model, setting a boundary condition and an excitation source, and obtaining a to-be-simulated geometric model; performing tetrahedral mesh generation on the geometric model to be simulated to obtain a subdivided model; performing region division on the subdivided model to obtain a plurality of sub-regions; selecting a time step length, and determining the position of a sampling point in the sub-region; and calculating time domain results of all time steps by using a time domain discontinuous Galerkin electromagnetic field simulation method, and completing electromagnetic simulation. Compared with an existing FETD method, the method has the advantages that the model is divided into a plurality of sub-domains for parallel calculation by combining regional decomposition with a Robin transmission condition, the problem that a large-size model is difficult to calculate is solved, and the calculation efficiency is higher while the precision is guaranteed.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic simulation, and in particular relates to a time-domain discontinuous Galerkin electromagnetic simulation method and system based on Robin transmission conditions. Background Art

[0002] Computational electromagnetics is based on electromagnetic field theory and is used to solve complex electromagnetic field theory and practical engineering application problems by solving Maxwell's equations. As for the current electromagnetic field numerical methods, they can generally be divided into two categories according to the different solution domains, namely time domain methods and frequency domain methods. If distinguished by the form of the solution equation, it can be divided into integral equation methods and differential equation methods. Currently, the widely used and representative electromagnetic field calculation methods include finite difference time domain method (FDTD), finite element time domain method (FETD), discontinuous Galerkin method in time domain (DGTD), method of moments (MoM) and finite element frequency domain method (FEFD). Among them, as a frequency domain method, MoM is based on integral equations and is more effective in dealing with conductor and sub-regional dielectric problems, while FEFD based on differential equations has more advantages in dealing with complex structure models. However, for ultra-wideband problems, the frequency domain method needs to solve complex system equations repeatedly, while the time domain method can solve the problem well. Among them, FDTD was developed first because of its simple implementation and fast solution speed, but there is a large error in modeling complex and fine structures. The emergence of traditional FETD solves the shortcomings of FDTD in complex structure modeling and has the advantage of high precision, but its system matrix is ​​too large to solve large-scale electromagnetic problems.

[0003] As the most promising electromagnetic field calculation method in recent years, the time-domain discontinuous Galerkin method not only integrates the concept of numerical flow in the time-domain finite volume method, and has the ability of high-performance parallel computing from the algorithm level, but also integrates the characteristics of the time-domain finite element method that can use any high-order interpolation space basis function, so it has any high-order precision convergence rate in theory. According to the order of the control equation to be solved, the time-domain discontinuous Galerkin method can be roughly divided into two categories: 1) DGTD-ME method based on Maxwell equations, which acts on first-order partial differential equations (PDE); 2) DGTD-WE method based on wave equations, which acts on second-order partial differential equations (PDE). The weak solution form of the equation is obtained by the Galerkin method, and the exchange of field values ​​between adjacent units is realized through numerical flow. It supports various types of meshing, such as triangles, quadrilaterals, tetrahedrons, hexahedrons, etc., and uses node basis functions or edge basis functions to solve the system of equations. The time-domain discontinuous Galerkin method can flexibly analyze electromagnetic field problems of complex targets, complex media, and electrically large or multi-size targets.

[0004] Currently, most simulations are based on the DG method of Maxwell's curl equations, which contain two unknown quantities: the electric field E and the magnetic field H. Therefore, for some specific electromagnetic problems that only focus on the electric field or the magnetic field, such as calculating the scattering of electromagnetic targets, it will cause a waste of computing resources and reduce efficiency. Summary of the invention

[0005] The present invention aims to solve the deficiencies of the prior art and provides the following solutions:

[0006] A time-domain discontinuous Galerkin electromagnetic simulation method based on Robin transmission conditions comprises the following steps:

[0007] Perform geometric modeling on the model to be simulated, set boundary conditions and excitation sources, and obtain the geometric model to be simulated;

[0008] Performing tetrahedral mesh division on the geometric model to be simulated to obtain a meshed model;

[0009] Dividing the segmented model into regions to obtain a plurality of sub-regions;

[0010] Selecting a time step and determining sampling point positions in the sub-area;

[0011] The time domain discontinuous Galerkin electromagnetic field simulation method is used to calculate the time domain results of all time steps to complete the electromagnetic simulation.

[0012] Preferably, the boundary conditions include: ABC boundary conditions and lumped port boundary conditions;

[0013] The ABC boundary conditions are:

[0014]

[0015] in, represents the external unit normal vector at the absorbing boundary, μ represents the magnetic permeability, represents the curl operator, E represents the electric field intensity, Y 0 represents the inverse of wave impedance, and t represents time;

[0016] The lumped port boundary conditions are:

[0017]

[0018] η eq =Z 0 w / h

[0019] Among them, H 1 and H 2 represents the magnetic field on both sides of the lumped port, E inc represents the excitation source, η eqrepresents the equivalent surface impedance at the lumped port boundary, Z 0 represents the characteristic impedance, w represents the width of the lumped port, and h represents the height of the lumped port.

[0020] Preferably, the method for calculating the time domain result includes:

[0021] Compute the matrix equation containing only the unknowns at the interfaces of adjacent subregions:

[0022]

[0023] T i =R i A i -1

[0024] Among them, R i represents the operator, u i represents the unknown quantity in each sub-region, represents the unknown quantity at the interface of adjacent subdomains, represents the expansion coefficient of the electric field E at the interface between adjacent subdomains, represents the expansion coefficient of the magnetic field H at the interface of adjacent subdomains, T represents the transposition, and A i represents a block matrix, b i A block vector representing the sum of the product of the matrix vectors of the first two time steps and the excitation source vector, where n represents the nth time step;

[0025] Calculate the unknowns in the sub-region based on the matrix equation:

[0026]

[0027] Among them, C ij represents a block matrix;

[0028] The time domain result is calculated based on the matrix equation and the unknown quantity to complete the electromagnetic simulation.

[0029] The present invention also provides a time-domain discontinuous Galerkin electromagnetic simulation system based on Robin transmission conditions, wherein the simulation system applies any of the above-mentioned simulation methods, including: a model building module, a grid generation module, a region division module, a sampling point determination module and a simulation module;

[0030] The model building module is used to perform geometric modeling on the model to be simulated, set boundary conditions and excitation sources, and obtain the geometric model to be simulated;

[0031] The mesh generation module is used to perform tetrahedral mesh generation on the geometric model to be simulated to obtain a meshed model;

[0032] The region division module is used to divide the segmented model into regions to obtain a plurality of sub-regions;

[0033] The sampling point determination module is used to select a time step and determine the sampling point position in the sub-area;

[0034] The simulation module uses a time-domain discontinuous Galerkin electromagnetic field simulation method to calculate time-domain results of all time steps to complete the electromagnetic simulation.

[0035] Preferably, the boundary conditions include: ABC boundary conditions and lumped port boundary conditions;

[0036] The ABC boundary conditions are:

[0037]

[0038] in, represents the external unit normal vector at the absorbing boundary, μ represents the magnetic permeability, represents the curl operator, E represents the electric field intensity, Y 0 represents the inverse of wave impedance, and t represents time;

[0039] The lumped port boundary conditions are:

[0040]

[0041] η eq =Z 0 w / h

[0042] Among them, H 1 and H 2 represents the magnetic field on both sides of the lumped port, E inc represents the excitation source, η eq represents the equivalent surface impedance at the lumped port boundary, Z 0 represents the characteristic impedance, w represents the width of the lumped port, and h represents the height of the lumped port.

[0043] Preferably, the workflow of the simulation module includes:

[0044] Compute the matrix equation containing only the unknowns at the interfaces of adjacent subregions:

[0045]

[0046] T i =R i A i -1

[0047] Among them, R i represents the operator, u irepresents the unknown quantity in each sub-region, represents the unknown quantity at the interface of adjacent subdomains, represents the expansion coefficient of the electric field E at the interface between adjacent subdomains, represents the expansion coefficient of the magnetic field H at the interface of adjacent subdomains, T represents the transposition, and A i represents a block matrix, b i A block vector representing the sum of the product of the matrix vectors of the first two time steps and the excitation source vector, where n represents the nth time step;

[0048] Calculate the unknowns in the sub-region based on the matrix equation:

[0049]

[0050] Among them, C ij represents a block matrix;

[0051] The time domain result is calculated based on the matrix equation and the unknown quantity to complete the electromagnetic simulation.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] Compared with the existing FETD method, the present invention adopts regional decomposition combined with Robin transmission conditions to divide the model into multiple subdomains for parallel calculation, which solves the problem of difficult calculation of large-size models, ensures accuracy and faster calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0055] Figure 1 A schematic diagram of a method flow of an embodiment of the present invention;

[0056] Figure 2 Schematic diagram of model division and result comparison of Example 2 of the present invention, wherein a is a schematic diagram of mesh division after regional decomposition of the model, and b is a schematic diagram of comparison of the RTC-DGTD method with COMSOL software and the traditional FETD method;

[0057] Figure 3 Schematic diagram of simulation model and model division according to the third embodiment of the present invention, wherein a is a schematic diagram of the simulation model, and b is a schematic diagram of mesh division after the model is regionally decomposed;

[0058] Figure 4Schematic diagram for comparing the results of Example 3 of the present invention, wherein a is a schematic diagram for comparing the time domain curves of the RTC-DGTD method and the traditional FETD method, and b is a schematic diagram for comparing the S parameter curves of the RTC-DGTD method and the traditional FETD method. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] Embodiment 1

[0062] In this embodiment, if Figure 1 As shown, a time-domain discontinuous Galerkin electromagnetic simulation method based on Robin transmission conditions includes the following steps:

[0063] S1. Perform geometric modeling on the model to be simulated, set boundary conditions and excitation sources, and obtain the geometric model to be simulated.

[0064] The boundary conditions include: ABC boundary conditions and lumped port boundary conditions; the ABC boundary conditions are:

[0065]

[0066] in, represents the external unit normal vector at the absorbing boundary, μ represents the magnetic permeability in Henry / meter, represents the curl operator, E represents the electric field strength in volts per meter, and Y 0 represents the inverse of the wave impedance, t represents time; the lumped port boundary conditions are:

[0067]

[0068] η eq =Z 0 w / h (3)

[0069] Among them, H 1 and H 2 represents the magnetic field on both sides of the lumped port, E inc represents the excitation source, η eq represents the equivalent surface impedance at the lumped port boundary, Z 0represents the characteristic impedance, w represents the width of the lumped port, and h represents the height of the lumped port.

[0070] S2. Perform tetrahedral meshing on the geometric model to be simulated to obtain a meshed model.

[0071] Meshing is directly related to the accuracy and speed of simulation, so it is necessary to rationally mesh according to the requirements of the selected algorithm.

[0072] In this embodiment, COMSOL software is directly used to mesh the model. In order to improve the accuracy of the calculation, the fine structure in the model needs to be set to a smaller unit size, and materials with different properties need to be meshed separately.

[0073] S3. Divide the segmented model into regions to obtain a number of sub-regions.

[0074] The number of domain decomposition divisions will affect the speed of solving the matrix in the algorithm, so a certain number of sub-regions should be divided according to the size of different models. In this embodiment, the model is divided into regions using the automatic region division algorithm of METIS. Without loss of generality, the electric field E is assumed to be the working variable, and the calculation space is assumed to be filled with isotropic materials. At this time, the electric field in the i-th subdomain satisfies the following governing equation:

[0075]

[0076] Among them, J im represents the external volume current source in the subdomain, in amperes per square meter, μ i represents the magnetic permeability of the ith subdomain, and ε represents the dielectric constant.

[0077] S4. Select the time step and determine the sampling point locations in the sub-area.

[0078] According to the mesh subdivision file exported by COMSOL, a certain coordinate is selected as the sampling point, and the tetrahedron number and node number of the node are calculated.

[0079] S5. Use the time domain discontinuous Galerkin electromagnetic field simulation method to calculate the time domain results of all time steps and complete the electromagnetic simulation.

[0080] In this embodiment, the method for calculating the time domain result includes:

[0081] Applying the Galerkin test to the governing equation yields the following formula:

[0082]

[0083] in, represents the introduced test basis function for the electric field E, represents the ABC boundary, represents the boundary at the lumped port, Indicates the current sub-region Ω i The corresponding adjacent sub-region Ω j The interface between is a unit vector perpendicular to the element face. It is called numerical flux. In the time-domain discontinuous Galerkin method, numerical flux is used to ensure the continuity of the field between adjacent sub-regions. In this embodiment, upwind flux is used, and its expression is:

[0084]

[0085] Among them, Z i =(μ i / ε i ) 1 / 2 and Z j =(μ j / ε j ) 1 / 2 Represent the current sub-region Ω i and its adjacent subregion Ω j The wave impedance in the sub-domain is ε, and the dielectric constant is Faraday / meter. Substituting (6) into (5), it is not difficult to see that in addition to the electric field E, the magnetic field H is introduced as a new variable at the interface between adjacent sub-domains, so another set of additional auxiliary equations needs to be established to solve E and H at the same time. Therefore, a pair of Robin transmission conditions (RTCs) are introduced to ensure the tangential continuity of the electromagnetic field at the interface between adjacent sub-domains, and the Galerkin test is applied to obtain:

[0086]

[0087]

[0088] Among them, τ is the proportional factor of the equilibrium system matrix, which is -1 in this method, and Ψ k i is the test basis function for the magnetic field H. It can be seen that equation (7) is similar to equation (6), so we combine equation (7) with equation (6) and substitute them into equation (5) to obtain the equation:

[0089]

[0090] Among them, Z 1 =1-Z i / (Z i +Z j ), Z 2 =-1-Z j / (Z i +Z j ), Z3 =1 / (Z i +Z j )+1,Z 4 =-1-Z i / (Z i +Z j ), combined with equations (8) and (9), the electric field E and magnetic field H can be calculated. Different from the traditional DGTD-ME method, the magnetic field H in the time-domain discontinuous Galerkin method is only used as a surface variable at the interface of the subdomains. Compared with the DGTD-ME method, the time-domain discontinuous Galerkin method has greatly reduced the number of unknowns to be solved.

[0091] In this embodiment, E i / j and H i / j Expand using vector stacking basis functions respectively:

[0092]

[0093] Among them, E i / j represents the electric field in the current sub-region i or the adjacent sub-region j, H i / j represents the magnetic field in the current sub-region i or the adjacent sub-region j, Φ i / j Indicates E i / j The vector basis function, e i / j Denotes the corresponding basis function Φ i / j The expansion coefficient of Indicates that in the sub-region Ω i / j Medium E i / j The number of all basis functions of . Similarly, Ψ i / j Indicates H i / j The vector basis function, h i / j Denotes the corresponding basis function Ψ i / j The expansion coefficient of Indicates that in the sub-region Ω i / j Medium H i / j The number of all basis functions, Y i The value is the inverse of the wave impedance, so that e i / j and h i / j At the same scale. Next, substitute equations (10)-(11) into equations (8)-(9) to obtain two sets of equations including E and H as follows:

[0094]

[0095] in:

[0096]

[0097]

[0098] For the partial derivatives of the electric field and magnetic field in equations (12)-(13), this method adopts the Newmark-β difference approximation, that is,

[0099]

[0100] Where β represents a parameter that affects the accuracy and stability of numerical calculations, and R represents a partial differential term, which is replaced by the electric field E and the magnetic field H in the equation. When β ≥ 0.25, the equation has the characteristic of unconditional stability. In this embodiment, β is taken as 0.25. Substituting equation (27) into equations (12)-(13), we can obtain the compact matrix equation shown below:

[0101]

[0102] Among them, at time n+1, there are:

[0103]

[0104] At time n, we have:

[0105]

[0106] At time n-1, we have:

[0107]

[0108]

[0109] Among them, f inc represents the excitation source. In order to avoid directly solving the large matrix in equation (28), this embodiment uses a matrix preprocessing technique similar to FETI for the matrix on the left side of the equation, and divides the overall matrix into two parts: (1) a matrix equation containing only unknown quantities at the interface of adjacent subdomains, and (2) a small matrix equation containing only unknown quantities inside the corresponding subdomain. In order to facilitate the derivation of the formula, the right side of the equation is simplified to a vector representation:

[0110]

[0111] Among them, b i A block vector representing the product of the matrix vectors at n and n-1 time steps and the sum of the excitation source vectors; first, the i-th row on both sides of the equation is multiplied by the diagonal block matrix A i The inverse of , we can get:

[0112]

[0113] Then divide the unknown quantity of each subdomain into three parts: (1) is expressed as the expansion coefficient of the electric field E in the i-th subdomain, (2) is expressed as the expansion coefficient of the electric field E at the interface between adjacent subdomains, (3) It is expressed as the expansion coefficient of the magnetic field H at the interface of adjacent subdomains and is expressed as:

[0114]

[0115] In order to extract the matrix equation containing only the unknown quantities at the interface of adjacent subdomains, it is necessary to introduce the operator R i :

[0116]

[0117] Each row of the matrix equation in (40) is transformed into i Processing, we can obtain a matrix equation containing only the unknown quantities at the interface of adjacent subdomains, as shown below:

[0118]

[0119] T i =R i A i -1 (49)

[0120] Among them, R i represents the operator, u i represents the unknown quantity in each sub-region, represents the unknown quantity at the interface of adjacent subdomains, represents the expansion coefficient of the electric field E at the interface between adjacent subdomains, represents the expansion coefficient of the magnetic field H at the interface of adjacent subdomains, T represents the transposition, and A i represents a block matrix, n represents the nth time step; the unknown quantity in the sub-region is calculated based on the matrix equation (46):

[0121]

[0122] Among them, C ij represents a block matrix; the matrix equations in equations (46) and (50) after preprocessing have smaller dimensions than the matrix equation in the original equation (39). The electromagnetic simulation is completed by calculating the time domain results based on the matrix equations and the unknown quantities. In this embodiment, equation (46) is calculated using the DFGMRES solver in INTEL onemkl, while equation (50) is calculated in parallel using the PARDISO direct solver.

[0123] Embodiment 2

[0124] In this example, a planar waveguide with a height and width of 0.1 mm and a length of 0.4 mm is considered, with a dielectric constant of 1, and its upper and lower sides are PEC surfaces, and its left and right sides are PMC surfaces. Both ends are truncated by ABC. The incident plane wave uses a Gaussian modulated pulse with a center frequency of 50 GHz and a time step of 1 ps. The mesh division of the model after regional decomposition is as follows Figure 2 As shown in (a), the entire area is divided into 4 regions, and a total of 23,889 tetrahedrons are generated. Figure 2 It can be seen from (b) that the result curve of the RTC-DGTD method at the sampling point is consistent with the result curve of the COMSOL software and the traditional FETD method, indicating that the accuracy of the method proposed in this paper is good enough.

[0125] Table 1

[0126] RTC-DGTD FETD Calculation time 12s 15s

[0127] At the same time, it can be seen from Table 1 that the RTC-DGTD method has an advantage in computational efficiency over the traditional FETD method. Each time step of RTC-DGTD takes about 12 seconds, while each time step of FETD takes about 15 seconds, with a comparison gain of 1.25.

[0128] Embodiment 3

[0129] In this embodiment, a typical substrate integrated waveguide filter (SIW) is selected as a model for analysis. Figure 3 As shown in (a), the metal through hole is replaced by the PEC surface, the relative dielectric constant of the substrate is 2.65, a Gaussian modulated pulse with a center frequency of 6 GHz is used as the source input, and the time step is set to 4 ps. The mesh division of the model after regional decomposition is as follows Figure 3 As shown in (b), the entire area is divided into 60 regions, and a total of 70,600 tetrahedrons are generated. The sampling points Port1 and Port2 are taken at the two ports of the model, and their time domain waveforms and S parameter waveforms are calculated and compared with the traditional FETD method, as shown in Figure 4 As shown, Figure 4 (a) is the time domain curve comparison between the RTC-DGTD method and the traditional FETD method. Figure 4 (b) is the comparison of the S-parameter curves of the RTC-DGTD method and the traditional FETD method. It can be seen that the time domain and frequency domain results are very consistent with FETD.

[0130] Table 2

[0131] RTC-DGTD FETD Calculation time 55s 128.7s

[0132] At the same time, it can be seen from Table 2 that the computational efficiency of the RTC-DGTD method is significantly superior to that of the traditional FETD method in large-size models. Each time step of RTC-DGTD takes about 55 seconds, and each time step of FETD takes about 128.7 seconds, with a comparison gain of 2.34.

[0133] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A time-domain discontinuous Galerkin electromagnetic simulation method based on Robin transmission conditions, characterized in that: The following steps are involved: Perform geometric modeling on the model to be simulated, set boundary conditions and excitation sources, and obtain the geometric model to be simulated; Performing tetrahedral mesh division on the geometric model to be simulated to obtain a meshed model; Dividing the segmented model into regions to obtain a plurality of sub-regions; Selecting a time step and determining sampling point positions in the sub-area; The time domain results of all time steps are calculated using the time domain discontinuous Galerkin electromagnetic field simulation method to complete the electromagnetic simulation.

2. According to claim 1, a time-domain discontinuous Galerkin electromagnetic simulation method based on Robin transmission conditions is characterized in that: The boundary conditions include: ABC boundary conditions and lumped port boundary conditions; The ABC boundary conditions are: in, represents the external unit normal vector at the absorbing boundary, μ represents the magnetic permeability, represents the curl operator, E represents the electric field intensity, Y0 represents the inverse of the wave impedance, and t represents time; The lumped port boundary conditions are: or eq =Z0w / h Where H1 and H2 represent the magnetic field on both sides of the lumped port, and E inc represents the excitation source, η eq represents the equivalent surface impedance at the boundary of the lumped port, Z0 represents the characteristic impedance, w represents the width of the lumped port, and h represents the height of the lumped port.

3. According to claim 1, a time-domain discontinuous Galerkin electromagnetic simulation method based on Robin transmission conditions is characterized in that: The method for calculating the time domain result includes: Compute the matrix equation containing only the unknowns at the interfaces of adjacent subregions: T i =R i A i -1 Among them, R i represents the operator, u i represents the unknown quantity in each sub-region, represents the unknown quantity at the interface of adjacent subdomains, represents the expansion coefficient of the electric field E at the interface between adjacent subdomains, represents the expansion coefficient of the magnetic field H at the interface of adjacent subdomains, T represents the transposition, and A i represents a block matrix, b i A block vector representing the sum of the product of the matrix vectors of the first two time steps and the excitation source vector, where n represents the nth time step; Calculate the unknowns in the sub-region based on the matrix equation: Among them, C ij represents a block matrix; The time domain result is calculated based on the matrix equation and the unknown quantity to complete the electromagnetic simulation.

4. A time-domain discontinuous Galerkin electromagnetic simulation system based on Robin transmission conditions, wherein the simulation system applies the simulation method according to any one of claims 1 to 3, characterized in that: include: Model building module, grid generation module, region division module, sampling point determination module and simulation module; The model building module is used to perform geometric modeling on the model to be simulated, set boundary conditions and excitation sources, and obtain the geometric model to be simulated; The mesh generation module is used to perform tetrahedral mesh generation on the geometric model to be simulated to obtain a meshed model; The region division module is used to divide the segmented model into regions to obtain a plurality of sub-regions; The sampling point determination module is used to select a time step and determine the sampling point position in the sub-area; The simulation module uses a time-domain discontinuous Galerkin electromagnetic field simulation method to calculate time-domain results of all time steps to complete the electromagnetic simulation.

5. The time-domain discontinuous Galerkin electromagnetic simulation system based on Robin transmission condition according to claim 4, characterized in that: The boundary conditions include: ABC boundary conditions and lumped port boundary conditions; The ABC boundary conditions are: in, represents the external unit normal vector at the absorbing boundary, μ represents the magnetic permeability, represents the curl operator, E represents the electric field intensity, Y0 represents the inverse of the wave impedance, and t represents time; The lumped port boundary conditions are: or eq =Z0w / h Where H1 and H2 represent the magnetic field on both sides of the lumped port, and E inc represents the excitation source, η eq represents the equivalent surface impedance at the boundary of the lumped port, Z0 represents the characteristic impedance, w represents the width of the lumped port, and h represents the height of the lumped port.

6. The time-domain discontinuous Galerkin electromagnetic simulation system based on Robin transmission condition according to claim 4, characterized in that: The workflow of the simulation module includes: Compute the matrix equation containing only the unknowns at the interfaces of adjacent subregions: T i =R i A i -1 Among them, R i represents the operator, u i represents the unknown quantity in each sub-region, represents the unknown quantity at the interface of adjacent subdomains, represents the expansion coefficient of the electric field E at the interface between adjacent subdomains, represents the expansion coefficient of the magnetic field H at the interface of adjacent subdomains, T represents the transposition, and A i represents a block matrix, b i A block vector representing the sum of the product of the matrix vectors of the first two time steps and the excitation source vector, where n represents the nth time step; Calculate the unknowns in the sub-region based on the matrix equation: Among them, C ij represents a block matrix; The time domain result is calculated based on the matrix equation and the unknown quantity to complete the electromagnetic simulation.

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