Volume integral equation grid adaptive encryption electromagnetic simulation method based on discontinuity error estimator

Abstract

The invention discloses a volume integral equation grid adaptive encryption electromagnetic simulation method based on a discontinuity error estimator, and belongs to the technical field of electromagnetic simulation. The method is used for completing electromagnetic characteristic calculation of a complex multi-scale target, provides five kinds of volume integral equation discontinuity error estimators, can accurately perform error estimation on the grid, and can be realized by cooperating with an encryption strategy adaptive encryption method, so that a small amount of unknown quantity of calculation is increased, the grid quality is greatly improved, and the calculation efficiency is improved. The calculation precision is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic simulation, and in particular relates to a volume integral equation grid adaptive encryption electromagnetic simulation method based on a discontinuity error estimator. Background Art

[0002] In recent years, complex multi-scale targets, including electrically large-scale targets such as aircraft, fleet targets, and warship models, and fine targets such as antennas, filters, and chips, have gradually become the focus of modern computational electromagnetics. The structures of these targets are becoming increasingly complex, and their materials are non-uniform, which puts higher requirements on the efficiency and accuracy of electromagnetic simulation and calculation. In order to solve such problems, on the one hand, different calculation methods have their scope of application, so it is necessary to select a calculation method suitable for the target; on the other hand, the calculation grid of the target is also an important influencing factor. The quality of the grid directly affects the efficiency and accuracy of the calculation. How to obtain high-quality electromagnetic calculation grids has become a research hotspot in the current field of computational electromagnetics.

[0003] The prior art “Evaluation of Local Error Estimators for the RWG-Based EFIE” discloses mesh error estimators for surface integrals. These error estimators are very efficient and do not consume computing resources, with a time complexity of (O). However, these error estimators can only analyze triangular meshes, not tetrahedral meshes. The prior art “A Posterior h / p Adaptive Refinement Algorithm for 3-D Goal-Oriented Electromagnetic Problems” discloses an adaptive refinement method for tetrahedral meshes, but the error estimator used is a goal-oriented error estimator (Goal-Oriented error estimator). Although this error estimator is accurate, it is very resource-intensive. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a volume integral equation grid adaptive encryption electromagnetic simulation method based on a discontinuity error estimator, which is used to complete the electromagnetic characteristics calculation of complex multi-scale targets. By accurately estimating the error of the grid and reasonably encrypting it to increase a small amount of unknown quantities for calculation, the grid quality is greatly improved and the calculation accuracy is improved.

[0005] The technical problem proposed by the present invention is solved in this way:

[0006] A volume integral equation grid adaptive encryption electromagnetic simulation method based on a discontinuity error estimator comprises the following steps:

[0007] Step 1. Discretize the target to be calculated into tetrahedral meshes in the physical modeling software, set the initial segmentation length of the tetrahedron to 0.2 to 0.4 wavelengths, and derive the sequence number and vertex coordinates of each tetrahedral mesh;

[0008] Step 2. Use the volume equivalence principle to construct a volume integral equation in the target area; record the center coordinates and volume of each tetrahedral mesh, group adjacent tetrahedral meshes into a tetrahedral pair, number and record the number N of tetrahedral pairs, and record the area of ​​the common face; establish a SWG basis function on each tetrahedral pair;

[0009] Step 3. Expand the electric displacement vector in the target area with the SWG basis function and substitute it into the volume integral equation to obtain the discretized volume integral equation; use the Galerkin test method to perform inner product on both ends of the volume integral equation with N SWG basis functions at the same time, expand the number of volume integral equations to N, and form a linear equation system containing N equations;

[0010] The coefficient term on the left side of the linear equation group is defined as the impedance matrix Z, which is an N-dimensional square matrix; all basis function expansion coefficients are taken as coefficients to be solved, forming the electric displacement vector coefficient vector I to be solved, which is an N×1-dimensional column vector; the coefficient term on the right side of the linear equation group is defined as the excitation term b, which is an N×1-dimensional column vector; the linear equation group is expressed as ZI=b;

[0011] Step 4. Use the Krylov subspace iteration method to solve the linear equation system ZI=b to solve the electric displacement vector coefficient vector I; the electric displacement vector coefficient vector I is combined with the SWG basis function to solve the electric displacement vector distribution of the target area, and then calculate the far-field;

[0012] Step 5. According to the solved electric displacement vector coefficient vector I, select and construct an error estimator for the calculation target, perform error analysis on each tetrahedral mesh of the calculation target, and calculate the global prediction error G err ;

[0013] Step 6. Set the threshold, when the global prediction error G err If it is greater than the threshold, go to step 7, otherwise end;

[0014] Step 7. Set the encryption strategy; perform volume weighting on the error estimate of each tetrahedral mesh and correct the mesh error value at the boundary; set the coefficient a, 0<a<1, and then sort the meshes from large to small according to the error estimate to form a set C; mark the meshes in set C in order, and the number of marked meshes is a×N; use the refined edge method to conformally encrypt the marked meshes, and return to execute step 2.

[0015] Furthermore, the error estimator in step 5 is an electric displacement vector discontinuity error estimator:

[0016] The electric displacement vector obtained based on the vector I and the SWG basis function has a jump discontinuity between two adjacent tetrahedral meshes. For any tetrahedral mesh, the error estimate LE Dtan for:

[0017]

[0018] Among them, 1≤p≤4, and are the tangential electric displacement vector and relative dielectric constant of the pth face of the current tetrahedral mesh, and are the tangential electric displacement vector and relative dielectric constant of the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh, is the unit tangent vector of the pth face of the current tetrahedral mesh, and Dtmax represents the maximum value of the ratio of the tangent point displacement vector at the midpoint of the four faces of all tetrahedral meshes to the relative dielectric constant.

[0019] Furthermore, the error estimator in step 5 is a charge discontinuity error estimator:

[0020] For any tetrahedral mesh, the error estimate LE ρ for:

[0021]

[0022] Where ρ represents the volume charge density of the current tetrahedral mesh, ρ q，p Represents the volume charge density of the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh, ρ max Represents the maximum volume charge density of all tetrahedral meshes.

[0023] Furthermore, the error estimator in step 5 is a combined discontinuity error estimator:

[0024] For any tetrahedral mesh, the error estimate LE Comb for:

[0025] LE Comb =max{LE Dtan , L.E. ρ}

[0026] Among them, max means taking the maximum value.

[0027] Furthermore, the error estimator in step 5 is an electric displacement vector weighted charge discontinuity error estimator:

[0028] For any tetrahedral mesh, the error estimate LE FWC for:

[0029]

[0030] Among them, V and V q，p They represent the volume of the current tetrahedral mesh and the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh respectively. FWCmax represents the maximum value of the sum of the inner product of the electric displacement vector of the four faces of all tetrahedral meshes and the unit tangent vector and the volume charge.

[0031] Furthermore, the error estimator in step 5 is a charge recovery error estimator:

[0032] For vertex K, there are T tetrahedron common vertices, so the charge density at vertex K is ρ K is the average charge density of T tetrahedral mesh centers, expressed as:

[0033]

[0034] Among them, 1≤t≤T, ρ t represents the volume charge density of the t-th tetrahedral mesh adjacent to vertex K;

[0035] Use the Lagrange interpolation method to solve the charge density ρ at any location in the grid Recovery :

[0036]

[0037] Among them, θ t (r) is the t-th order Lagrangian interpolation function consisting of known charge density at known positions;

[0038] For any tetrahedral mesh, the error estimate LE recovery for:

[0039]

[0040] Where ρVmax represents the maximum volume charge of all tetrahedral meshes.

[0041] Furthermore, the specific process of constructing the global prediction error in step 5 is:

[0042] The local discontinuity error estimator can be used to calculate the global error, which is defined as:

[0043]

[0044] Where, 1≤s≤Ncells, Ncells is the total number of tetrahedral meshes of the current calculation target; LEs is the error calculated by the error estimator on the sth tetrahedral mesh, A s is the volume of the sth tetrahedral mesh, A tot To calculate the total volume of the target.

[0045] The beneficial effects of the present invention are:

[0046] The electromagnetic simulation method described in the present invention is used to complete the calculation of the electromagnetic characteristics of complex multi-scale targets. It provides five volume integral equation error estimators, which can accurately estimate the error of the grid and is implemented in conjunction with the encryption strategy adaptive encryption method to increase a small amount of calculated unknowns, greatly improve the grid quality, and improve the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A schematic diagram of a computational target grid division for the electromagnetic simulation method described in the embodiment;

[0048] Figure 2 The RCS curve diagram obtained by the last adaptive calculation under five different error estimators in the electromagnetic simulation method described in the embodiment;

[0049] Figure 3 is an error distribution diagram of an initial grid of an electric displacement vector discontinuity error estimator in the electromagnetic simulation method described in the embodiment;

[0050] Figure 4 is an error distribution diagram of an initial grid of a charge discontinuity error estimator in the electromagnetic simulation method described in the embodiment;

[0051] Figure 5 is an error distribution diagram of an initial grid of a combined discontinuous error estimator in the electromagnetic simulation method described in the embodiment;

[0052] Figure 6 is an error distribution diagram of an initial grid of an electric displacement vector weighted charge discontinuity error estimator in the electromagnetic simulation method described in the embodiment;

[0053] Figure 7 is an error distribution diagram of an initial grid of a charge recovery error estimator in the electromagnetic simulation method described in the embodiment;

[0054] Figure 8 This is a curve chart showing how the root mean square error of RCS changes with the number of encryption times under five different error estimators in the electromagnetic simulation method described in the embodiment. DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0056] This embodiment provides a grid adaptive encryption electromagnetic simulation method based on volume integral equation, such as Figure 1 As shown, the following steps are included:

[0057] Step 1. In the physical modeling software, discretize the target to be calculated using tetrahedral meshes, and set the initial mesh length of the tetrahedron to 0.4-0.2 wavelengths. The initial mesh must ensure the geometric characteristics of the target. Finally, export the serial number and vertex coordinates of each tetrahedron.

[0058] The calculation target of the method described in this embodiment is a dielectric plate, the length and width of the dielectric plate are 1m, and the height is 0.1m. Figure 1 As shown, the relative dielectric constant is 2.6, the incident wave frequency is 30 MHz, the incident direction is along the x direction, the electric field polarization direction is along the y direction, and the initial segmentation length of the grid is 0.2 m.

[0059] Step 2. Use the volume equivalence principle to construct a volume integral equation in the target area. Record the center coordinates and volume of each tetrahedral mesh, group adjacent tetrahedral meshes into a tetrahedral pair, number and record the number N, and record the area of ​​the common face. Establish a SWG basis function on each tetrahedral pair.

[0060] Step 3. Expand the electric displacement vector in the target area using the SWG basis function and express it as 1≤n≤N,I n represents the basis function expansion coefficient of the nth tetrahedron pair; substitute the above formula into the volume integral equation to obtain the discretized volume integral equation. Using the Galerkin test method, that is, using N SWG basis functions to perform inner products on both ends of the volume integral equation, the number of equations is expanded to N, forming a linear equation system containing N equations.

[0061] Define the coefficients on the left side of the linear equation system as the impedance matrix Z, where Z is an N-dimensional square matrix; n As the coefficients to be solved, the electric displacement vector coefficient vector I to be solved is formed, where I is an N×1 dimensional column vector; the coefficient term on the right side of the equal sign of the linear equation group is defined as the excitation term b, where b is an N×1 dimensional column vector; the linear equation group is expressed as ZI=b.

[0062] Step 4. Use the Krylov subspace iteration method to solve the linear equation system ZI=b and solve the electric displacement vector coefficient vector I. The electric displacement vector coefficient vector I combined with the SWG basis function can be used to obtain the electric displacement vector distribution of the target area, and then the far-field can be calculated.

[0063] Furthermore, in step 4, the specific process of solving the linear equations using the Krylov subspace iteration method is as follows:

[0064] The linear equations to be solved are ZI = b. Set the initial vector I (0) , calculate the initial residual r 0=b-ZI (0) , v (1) =r 0 / ||r 0 ||,v (1) represents the basis vector of the Krylov subspace. And find the best approximate solution in the Krylov subspace I (1) , that is: I (1) ∈I (0) +K 1 =I (0) +span{v (1)}, span{a, b, c} represents any linear combination of vectors a, b, c.

[0065] Call the Arnoldi or Lanczos procedure on the matrix Z to calculate the vector v m , find the best approximate solution in the Krylov subspace I (m) That is: I (m) ∈I (0) +K m =I (0) +span{v (1) , …, v (m)}, and calculate the residual r 0 =b-ZI (m) If the residual is less than the set threshold, I (m) The electric displacement vector coefficient is substituted, otherwise the step is repeated until the residual is less than the set threshold.

[0066] In the method described in this embodiment, the radar cross section (RCS) is as follows: Figure 2 As shown, the RCS calculated by the last adaptive calculation and the RCS calculated by the last global encryption are shown under five different error estimators.

[0067] Step 5. According to the solved electric displacement vector coefficient vector I, select and construct the corresponding error estimator for the calculation target, perform error analysis on each tetrahedral mesh of the calculation target, and then calculate the global prediction error G err .

[0068] Furthermore, the specific process of constructing the error estimator in step 5 is:

[0069] Electric displacement vector discontinuity error estimator:

[0070] The electric displacement vector obtained by the vector I and the SWG basis function will have a jump discontinuity between two adjacent tetrahedral meshes. Based on this discontinuity, an electric displacement vector discontinuity estimator can be constructed. For any tetrahedral mesh, the error estimate LE DtanIt is: the average value of the tangential discontinuity of the electric displacement vector to the relative permittivity at the midpoints of the four surfaces, normalized and divided by the global maximum electric displacement vector to the relative permittivity value.

[0071]

[0072] Among them, 1≤p≤4, and are the tangential electric displacement vector and relative dielectric constant of the pth face of the current tetrahedral mesh, and are the tangential electric displacement vector and relative dielectric constant of the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh, is the unit tangent vector of the pth face of the current tetrahedral mesh, and Dtmax represents the maximum value of the ratio of the tangent point displacement vector at the midpoint of the four faces of all tetrahedral meshes to the relative dielectric constant.

[0073] Charge discontinuity error estimator:

[0074] Since the SWG basis function is a first-order basis function, the free charge density in the grid is a constant and does not change with position. The smaller the regional error, the smoother the distribution of free charge density between grids and the smaller the difference. Often, the greater the difference in free charge density between grids, the greater the regional error, and a denser grid is required to calculate the area. For any tetrahedral grid, the error estimate LE p is: the average value of the difference between the charge density at the current grid and the charge density at the four adjacent grids, expressed as:

[0075]

[0076] Where ρ represents the volume charge density of the current tetrahedral mesh, p q，p Represents the volume charge density of the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh, ρ max Represents the maximum volume charge density of all tetrahedral meshes.

[0077] Combined discontinuity error estimator:

[0078] Using the electric displacement vector discontinuity error estimator or the charge discontinuity error estimator alone may ignore some areas where the error is too large. The combined discontinuity estimator is obtained by the maximum value of the electric displacement vector discontinuity estimator and the charge discontinuity estimator at the grid:

[0079] LE Comb =max{LE Dtan , L.E. ρ}

[0080] Electric displacement vector weighted charge discontinuity error estimator:

[0081] Discontinuous estimators may fail under certain conditions, when the quantities they process are forced to cancel due to geometric symmetry or the symmetry of the source. However, the two estimators fail under different conditions. This suggests that the estimator based on these two quantities may be more robust. For the error estimate LE at any grid FWC for:

[0082]

[0083] Among them, V and V q，p Respectively represent the volume of the current tetrahedral mesh and the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh. FWCmax represents the maximum value of the sum of the inner product of the electric displacement vector and the unit tangent vector of the four faces of all tetrahedral meshes and the volume charge. The overall dimension is kept as Coulomb C (electric displacement vector is integrated over the face, and charge density is weighted by volume).

[0084] Charge recovery error estimator:

[0085] The charge recovery method adopted is superconvergent patch recovery (SPR), and the specific process is to restore the charge at each tetrahedron vertex. For vertex K, there are T tetrahedron common vertices, so the charge density at vertex K is ρ K is the average charge density of the center of mass of T tetrahedral grids, that is:

[0086]

[0087] Among them, 1≤t≤T, ρ t represents the volume charge density of the t-th tetrahedral mesh adjacent to vertex K;

[0088] After using SPR to recover the charge of each vertex, the charge density at each mesh vertex and the center of mass is known, and the Lagrange interpolation method is used to solve the charge density at any point in the mesh:

[0089]

[0090] Among them, θ t (r) is the t-th order Lagrangian interpolation function consisting of known charge density at known positions.

[0091] For the error estimate LE at the current tetrahedral mesh recovery for:

[0092]

[0093] Where ρVmax represents the maximum volume charge of all tetrahedral meshes.

[0094] These five error estimators are very efficient and do not consume computing resources, with a time complexity of (L). Different error estimators can be selected for different computing problems to improve the efficiency of the adaptive encryption program.

[0095] Furthermore, the specific process of constructing the global prediction error in step 5 is:

[0096] The local discontinuity error estimator can be used to calculate the global error, which is defined as:

[0097]

[0098] Where, 1≤s≤Ncells, Ncells is the total number of tetrahedral meshes of the current calculation target; LE s is the error calculated by 5 different error estimators on the sth tetrahedral mesh, A s is the volume of the sth tetrahedral mesh, A tot To calculate the total volume of the target.

[0099] In the method described in this embodiment, five error estimators are used in turn to perform error analysis on each tetrahedral mesh. Figure 3 The error distribution of the initial grid of the electric displacement vector discontinuity error estimator is shown. Figure 4 The error distribution of the initial grid of the charge discontinuity error estimator is shown. Figure 5 The error distribution of the initial grid of the combined discontinuous error estimator is shown. Figure 6 The error distribution of the initial grid of the electric displacement vector weighted charge discontinuity error estimator is shown. Figure 7 The error distribution of the initial grid of the charge recovery error estimator is shown.

[0100] Step 6. Set the threshold, when the global prediction error G err If it is greater than the threshold, go to step 7, otherwise end;

[0101] Step 7. Set the encryption strategy. Perform volume weighting on the error estimate of each tetrahedral mesh and correct the mesh error value at the boundary. Set the coefficient a (in the range of 0-1), and then sort the meshes from large to small according to the error estimate to form a set C. Mark the meshes in set C in order, and the number of marked meshes is a×N. Use the refinement edge method to conformally encrypt the marked meshes, and return to step 2;

[0102] Furthermore, the specific setting process of the encryption policy in step 7 is as follows:

[0103] Volume Weighted:

[0104] Due to the singularity of the target edge, the edge will be over-encrypted after using the discontinuity error estimator. Therefore, in order to make the errors calculated for each grid more suitable for adaptive encryption, the grid is volume-weighted. The volume-weighted error Error of the s-th tetrahedral grid is s It is expressed as:

[0105]

[0106] Among them, A ave Represents the average volume of all tetrahedral meshes.

[0107] Correction of error estimates at boundaries:

[0108] When the tetrahedral mesh is on the boundary of the computational target, the number of meshes adjacent to the mesh is not 4, but a number smaller than 4. The error estimator is modified, and it is assumed that the tetrahedral mesh on the boundary is adjacent to k meshes. At this time, the mesh can obtain k discontinuous values ​​with the adjacent meshes, that is, the error estimate of the mesh. The error estimate is multiplied by k / 4 to keep the error of the mesh in the same dimension as that of all meshes.

[0109] In this embodiment, the coefficient a is set to 0.2.

[0110] In this embodiment, the grid adaptive encryption electromagnetic scattering simulation method based on volume integral equation is compared with global encryption, and the RCS value after each grid encryption is recorded in turn. The RCS calculated by the last global encryption is taken as the reference solution. Then, the root mean square error (RMSE) is calculated by comparing the RCS value after each grid encryption with the reference RCS, as shown in Figure 8 As shown in the figure, it can be seen that no matter which error estimator is used, the adaptive mesh encryption always calculates more accurate results with fewer unknowns compared to the global encryption. This proves that the five error estimators are reliable and that the adaptive method is also effective.

[0111] The volume integral equation method is suitable for solving the electromagnetic target characteristic problem of inhomogeneous media, and is also very suitable for analyzing and solving thin medium targets containing a large number of sharp corners and edges. Because the volume integral equation method belongs to the second kind of Fredholm integral equation, its matrix system has good conditional properties and good convergence. Therefore, the volume integral equation method is a suitable method for complex multi-scale targets. Adaptive grid encryption technology is a numerical calculation method widely used in the fields of computational mechanics and computational fluids. Its core idea is to combine the physical characteristics of the problem, the numerical calculation method and the grid distribution, and to continuously adjust the grid distribution according to the characteristics of the numerical solution to obtain a more accurate solution. The application of the method described in the present invention can effectively improve the calculation accuracy, which is of great significance for solving complex engineering problems.

[0112] The method of the present invention constructs five different volume integral equation error estimators. They are: electric displacement vector discontinuity error estimator, charge discontinuity error estimator, combined discontinuity error estimator, electric displacement vector weighted charge discontinuity error estimator and charge recovery error estimator. The electric displacement vector obtained according to the SWG basis function will have a jump discontinuity between two adjacent units. Through this discontinuity, an electric displacement vector discontinuity estimator can be constructed. Since the SWG basis function is a first-order basis function, the free charge density in the grid is a constant and does not change with the position. The greater the difference in free charge density between grids, the greater the regional error, and a denser grid is required to calculate the area. Thus, a charge discontinuity error estimator is constructed. Using the electric displacement vector discontinuity error estimator or the charge discontinuity error estimator alone may ignore some areas with excessive errors. Thus, a combined discontinuity error estimator is constructed. Under certain conditions, the discontinuity estimators may fail, and the quantities they process are forced to offset due to geometric symmetry or source symmetry. However, these two estimators will fail under different conditions. This shows that the estimator based on these two quantities may be more robust. Thus, the electric displacement vector weighted charge discontinuity error estimator is constructed. The SPR method is used to restore the true charge density distribution, and the restored charge density is compared with the numerically calculated charge density, so that the charge recovery error estimator is constructed. These five error estimators are very efficient and do not consume computing resources, with a time complexity of (O). After analyzing the error of each grid through the error estimator, adaptive encryption can be achieved in conjunction with the encryption strategy. Since these five error estimators are very accurate, the adaptive encryption program can greatly improve the grid quality and calculation accuracy by adding a small amount of unknown quantities to the calculation.

Claims

1. A volume integral equation grid adaptive encryption electromagnetic simulation method based on a discontinuity error estimator, characterized in that: The following steps are involved: Step 1. Discretize the target to be calculated into tetrahedral meshes in the physical modeling software, set the initial segmentation length of the tetrahedron to 0.2 to 0.4 wavelengths, and derive the sequence number and vertex coordinates of each tetrahedral mesh; Step 2. Use the volume equivalence principle to construct a volume integral equation in the target area; record the center coordinates and volume of each tetrahedral mesh, group adjacent tetrahedral meshes into a tetrahedral pair, number and record the number N of tetrahedral pairs, and record the area of ​​the common face; establish a SWG basis function on each tetrahedral pair; Step 3. Expand the electric displacement vector in the target area with the SWG basis function and substitute it into the volume integral equation to obtain the discretized volume integral equation; use the Galerkin test method to perform inner product on both ends of the volume integral equation with N SWG basis functions at the same time, expand the number of volume integral equations to N, and form a linear equation system containing N equations; The coefficient terms on the left side of the linear equation system are defined as the impedance matrix Z, where Z is an N-dimensional square matrix; All basis function expansion coefficients are used as coefficients to be solved to form the electric displacement vector coefficient vector I to be solved, where I is an N×1 dimensional column vector; The coefficient term on the right side of the linear equation system is defined as the excitation term b, where b is an N×1 dimensional column vector; The linear equation system is expressed as ZI = b; Step 4. Use the Krylov subspace iteration method to solve the linear equation system ZI=b to solve the electric displacement vector coefficient vector I; the electric displacement vector coefficient vector I is combined with the SWG basis function to solve the electric displacement vector distribution of the target area, and then calculate the far-field; Step 5. According to the solved electric displacement vector coefficient vector I, select and construct an error estimator for the calculation target, perform error analysis on each tetrahedral mesh of the calculation target, and calculate the global prediction error G err ; Step 6. Set the threshold, when the global prediction error G err If it is greater than the threshold, go to step 7, otherwise end; Step 7. Set the encryption strategy; perform volume weighting on the error estimate of each tetrahedral mesh and correct the mesh error value at the boundary; set the coefficient a, 0<a<1, and then sort the meshes from large to small according to the error estimate to form a set C; mark the meshes in set C in order, and the number of marked meshes is a×N; use the refined edge method to conformally encrypt the marked meshes, and return to execute step 2.

2. The volume integral equation grid adaptive encryption electromagnetic simulation method based on discontinuity error estimator according to claim 1 is characterized in that: The error estimator in step 5 is the electric displacement vector discontinuity error estimator: The electric displacement vector obtained based on the vector I and the SWG basis function has a jump discontinuity between two adjacent tetrahedral meshes. For any tetrahedral mesh, the error estimate LE Dtan for: Among them, 1≤p≤4, and are the tangential electric displacement vector and relative dielectric constant of the pth face of the current tetrahedral mesh, and are the tangential electric displacement vector and relative dielectric constant of the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh, is the unit tangent vector of the pth face of the current tetrahedral mesh, and Dtmax represents the maximum value of the ratio of the tangent point displacement vector at the midpoint of the four faces of all tetrahedral meshes to the relative dielectric constant.

3. The volume integral equation grid adaptive encryption electromagnetic simulation method based on discontinuity error estimator according to claim 2 is characterized in that: The error estimator in step 5 is the charge discontinuity error estimator: For any tetrahedral mesh, the error estimate LE ρ for: Where ρ represents the volume charge density of the current tetrahedral mesh, ρ q，p Represents the volume charge density of the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh, ρ max Represents the maximum volume charge density of all tetrahedral meshes.

4. The volume integral equation grid adaptive encryption electromagnetic simulation method based on discontinuity error estimator according to claim 3 is characterized in that: The error estimator in step 5 is a combined discontinuity error estimator: For any tetrahedral mesh, the error estimate LE Comb for: THE Comb =max{LE Dtan ,THE ρ } Among them, max means taking the maximum value.

5. The volume integral equation grid adaptive encryption electromagnetic simulation method based on discontinuity error estimator according to claim 1 is characterized in that: The error estimator in step 5 is an electric displacement vector weighted charge discontinuity error estimator: For any tetrahedral mesh, the error estimate LE FWC for: Among them, V and V q，p They represent the volume of the current tetrahedral mesh and the tetrahedral mesh adjacent to the pth face of the current tetrahedral mesh respectively. FWCmax represents the maximum value of the sum of the inner product of the electric displacement vector of the four faces of all tetrahedral meshes and the unit tangent vector and the volume charge.

6. The volume integral equation grid adaptive encryption electromagnetic simulation method based on discontinuity error estimator according to claim 1 is characterized in that: The error estimator in step 5 is a charge recovery error estimator: For vertex K, there are T tetrahedron common vertices, so the charge density at vertex K is ρ K is the average charge density of T tetrahedral mesh centers, expressed as: Among them, 1≤t≤T, ρ t represents the volume charge density of the t-th tetrahedral mesh adjacent to vertex K; Use the Lagrange interpolation method to solve the charge density ρ at any location in the grid Recovery : Among them, θ t (r) is the t-th order Lagrangian interpolation function consisting of known charge density at known positions; For any tetrahedral mesh, the error estimate LE recovery for: Where pVmax represents the maximum volume charge of all tetrahedral meshes.

7. The volume integral equation grid adaptive encryption electromagnetic simulation method based on discontinuity error estimator according to claim 1 is characterized in that: The specific process of constructing the global prediction error in step 5 is: The local discontinuity error estimator can be used to calculate the global error, which is defined as: Where, 1≤s≤Ncells, Ncells is the total number of tetrahedral meshes of the current calculation target; LE s is the error calculated by the error estimator on the sth tetrahedral mesh, A s is the volume of the sth tetrahedral mesh, A tot To calculate the total volume of the target.

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