An electromagnetic simulation method based on non-uniform grid technology

Abstract

The present invention discloses an electromagnetic simulation method based on non-uniform grid technology. An electromagnetic simulation object model is established to determine the calculation space range of the simulation object size; an ideal electric conductor boundary suitable for the weak conditional stable time-domain finite difference method is constructed; using non-uniform grid technology, the pre-transition region, transition region, and post-transition region are set; the weak conditional stable time-domain finite difference method is combined with the non-uniform grid technology to obtain the magnetic field value and electric field value at the next moment. The present invention proposes an efficient combination method of the weak conditional stable time-domain finite difference method and the non-uniform grid technology. Through the dynamic grid division strategy, the collaborative optimization of "local accuracy guarantee-global efficiency improvement" is achieved. Especially for electromagnetic simulation of devices with fine structures, it not only ensures high calculation accuracy, but also reduces the number of grids and significantly shortens the calculation time.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic simulation, and relates to an electromagnetic simulation method based on non-uniform grid technology. Background Art

[0002] In electromagnetic simulation technology, the meshing method has a decisive influence on computational efficiency and accuracy, especially when simulating electromagnetic wave propagation over a wide area, where the number of required mesh elements is extremely large. Traditional uniform meshing technology faces significant challenges when simulating electromagnetic wave propagation over a wide area or in complex device structures: using dense uniform meshes to ensure computational accuracy leads to a sharp increase in computational resource consumption, exponential growth in memory requirements and computational time; conversely, blindly using coarse meshes to improve efficiency can lead to a significant decrease in simulation accuracy. Optimizing computational efficiency while ensuring accuracy has become a core issue that needs to be addressed in the field of electromagnetic simulation.

[0003] With the rapid development of computer hardware technology, computer memory and computing speed have greatly increased, making numerical methods for studying electromagnetic problems in complex target environments efficient and feasible, and thus addressing the cost issues associated with large-scale engineering experiments. Currently, classic full-wave numerical methods include the Finite-Difference Time-Domain (FDTD) method, the Finite Element Method (FEM), and the Method of Moment (MoM). The FDTD method is one of the most commonly used numerical methods for studying electromagnetic problems, but due to limitations in temporal stability, it is less efficient for simulating fine-structured devices. To mitigate the impact of temporal stability, researchers have proposed various improvements. Among them, the Weakly Conditionally Stable (WCS) FDTD method relaxes the temporal stability condition to increase the time step size. However, this method is associated with increased numerical dispersion errors, resulting in a significant loss of accuracy, especially in long simulations. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and provide an electromagnetic simulation method based on non-uniform grid technology. The method effectively ensures a small loss of calculation accuracy through non-uniform grid technology, while significantly improving the calculation efficiency.

[0005] In a first aspect, the present invention provides an electromagnetic simulation method based on non-uniform grid technology, the method comprising:

[0006] Establishing an electromagnetic simulation object model and determining a calculation space; wherein the electromagnetic simulation object has a fine structure;

[0007] According to the computational space, an ideal electric conductor boundary PEC suitable for the weak conditional stability finite-difference time-domain method is constructed; wherein the ideal electric conductor boundary PEC is set along any one of the x, y, and z directions by using a non-uniform grid technique to set a pre-transition region, a transition region, and a post-transition region for the ideal electric conductor boundary PEC; the pre-transition region and the post-transition region are both uniform grid regions, but the grid sizes of the pre-transition region and the post-transition region are different; and the transition region is a non-uniform grid region;

[0008] The weak condition stable finite difference time-domain method is combined with the non-uniform grid technology to obtain the magnetic field value and electric field value at the next moment.

[0009] Preferably, the x, y, and z directions of the electromagnetic simulation object model are consistent with a Cartesian coordinate system, wherein the pointing directions of the electric field grid and the magnetic field grid are the same as those of the Cartesian coordinate system.

[0010] Preferably, the electromagnetic simulation object model has a fine structure direction in at least one direction and a coarse structure direction in at least one direction. More preferably, the spatial step length of the fine structure is smaller than the spatial step length of the coarse structure.

[0011] Preferably, in the ideal electric conductor boundary PEC, the subdivision grid size used in the fine structure region of the electromagnetic simulation object is selected to be smaller than the subdivision grid size used in the empty or coarse structure region.

[0012] Preferably, in the transition region of the ideal electric conductor boundary PEC, it is assumed that the length of the first unit is set to:

[0013]

[0014] Where 1 represents the index of the first cell, R represents the rate of change between adjacent cells, and Δs represents the grid size in the pre-transition region; thus, the remaining grids in the transition region are expressed as:

[0015]

[0016] Where P is the index of the cell in the transition region, represents the rate of change of the Pth unit in the transition region;

[0017] In the post-transition region, the grid size Δe in the post-transition region is:

[0018]

[0019] Where N is the number of units in the entire transition region;

[0020] Therefore, according to formulas (1)-(3), the total length of a unit of the adjacent transition area in the pre-transition area and the post-transition area plus the entire transition area is:

[0021] (4)

[0022] Where ΔU is the total length of the transition region, and further we know that R is:

[0023] (5)

[0024] At the same time, substitute formula (5) into formula (3) to obtain N:

[0025] (6).

[0026] Preferably, the specific implementation process of combining the weak conditional stable finite-difference time-domain method with the non-uniform grid technology and obtaining the magnetic field value and the electric field value at the next moment is:

[0027] According to the weak condition stability finite difference time domain method, the electric field component and magnetic field component at time n+1 / 2 and n+1 under weak condition stability are obtained, where , where η = x, y, z; Δη represents the spatial step size of the electromagnetic simulation object model in the η direction;

[0028] In order to achieve the combination of weak conditional stability and non-uniform grid technology, when δ η When solving the electric field, the spatial step size Δη of the electric field grid in the η direction is used for Δη according to the direction of the electric field. e Replace; when δ η When solving the magnetic field, the spatial step size Δη of the magnetic field grid in the η direction is used for Δη according to the direction of the magnetic field. h Make a replacement.

[0029] Preferably, the method further includes updating the excitation source and the cycle time step n of the electric field; specifically:

[0030] Set the electric field excitation source J in the fine structure direction of the calculation space, then assign the excitation source to the electric field component and gradually update the excitation source;

[0031] Determine whether the current cycle time step n reaches the maximum simulation iteration step number N. If so, end and record all magnetic field values and electric field values. If not, update the time step n to n+1 and continue to obtain the magnetic field value and electric field value at the next moment.

[0032] In a second aspect, the present invention provides a computing device comprising a processor and a memory, wherein executable code is stored in the memory, and when the processor executes the executable code, the method described is implemented.

[0033] In a third aspect, the present invention provides a computer-readable storage medium having a complete set of computer programs recorded thereon. When the program is run on a computer system, the computer executes the method described above.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention adopts a fine grid in the fine structure area and a coarse grid in the open or rough area, and reduces the numerical error by optimizing the transition area design, thereby allowing the time step to be set based on the coarse grid step while ensuring the fine structure accuracy.

[0036] The non-uniform grid in this invention achieves a smooth transition in mesh size through a gradual design of the transition region, avoiding the sudden changes in electric and magnetic field components caused by traditional abrupt meshing. Combined with weak stability conditions, adaptive spatial step size adjustment balances the relationship between time step size and numerical dispersion, ultimately achieving a coordinated optimization of accuracy and efficiency.

[0037] In summary, the present invention adopts an efficient combination of the weak conditional stable time-domain finite difference method and the non-uniform grid technology. Through the dynamic grid division strategy (i.e., partial encryption and partial thickening), it realizes the collaborative optimization of "local accuracy assurance-global efficiency improvement". Especially for the simulation of devices with fine structures, it not only ensures the calculation accuracy but also significantly improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 1. It is a schematic diagram of the geometric model and grid setting of a low-pass filter structure of an embodiment of the implementation method of the present invention;

[0039] Figure 2 1 is a comparison curve diagram of the simulation results of the S parameters under different CFLN conditions in Example 1 of the present invention;

[0040] Figure 3 It is a schematic diagram of non-uniform grid technology;

[0041] Figure 4 It is a schematic diagram of the grid distribution of non-uniform grid electric field and magnetic field;

[0042] Among them, all simulation results are derived from the implementation method of the present invention; Figure 1 P1 is the low-pass filter port 1 in Example 1 of the present invention, P2 is the low-pass filter port 2, and other geometric dimension parameters are detailed in Table 1; Figure 2 (a) is S 11 The comparison curve chart, Figure 2 (b) is S 21The comparison curve diagram shows the stability constant (Courant-Friedrichs-Lewy Number, CFLN) which represents the ratio of the time step between the non-uniform grid weak conditional stability finite-difference time-domain method (i.e., UWCS-FDTD method) involved in the method of the present invention and the traditional FDTD method, where the CFLN values are 1, 3, 5, and 7 respectively.

[0043] Table 1 Geometric dimensions of the low-pass filter in Example 1 of the present invention

[0044] DETAILED DESCRIPTION

[0045] The present invention is applied to electromagnetic simulation methods. The recursive formula involved can be obtained according to the weak conditional stable finite difference time-domain method. The specific implementation method is specifically described by taking the electromagnetic simulation problem of a low-pass filter as an example, and the actual application scope is not limited to this.

[0046] The present invention provides an electromagnetic simulation method based on non-uniform grid technology, specifically a method for achieving non-uniform grids in a Cartesian coordinate system by using a weak conditional stable finite-difference time-domain method based on manually setting coarse and fine grids to divide the calculation area. The specific steps of this method are:

[0047] 1) Establish a three-dimensional electromagnetic simulation object model and determine the calculation space; specifically: (a)

[0048] Establish an electromagnetic simulation object model; establish a three-dimensional Cartesian coordinate system; obtain the range of the calculation space based on the established model; the calculation space range is (X min , Y min , Z min )~(X max , Y max , Z max ), the size of the spatial range is (X max –X min )× (Y max –Y min ) × (Z max –Z min ), the coordinates of the center position are ( (X min +X max ) / 2, (Y min +Y max ) / 2, (Z min +Z max ) / 2 ). The minimum spatial position and maximum spatial position of the simulation area in the x, y, and z directions are X and Y, respectively. min 、X max 、Y min 、Y max 、Zmin and Z max ;

[0049] The spatial steps of the electromagnetic simulation object model in the x, y, and z directions are Δx, Δy, and Δz respectively, and the spatial steps of the electric field grid in the x, y, and z directions are Δx, respectively. e , Δy e , Δz e , the spatial step sizes of the magnetic field grid in the x, y, and z directions are Δx h , Δy h , Δz h , J is the excitation source function, n is the time step (range is 1~N); N is the total number of simulation iterations.

[0050] The electromagnetic simulation object model has a fine structure direction in at least one direction and a coarse structure direction in at least one direction. The fine structure referred to here means having a smaller spatial step in the direction, while the coarse structure means having a larger spatial step in the direction.

[0051] 2) Constructing a perfect electric conductor boundary (PEC) suitable for the weak conditional stability finite-difference time-domain method; based on the non-uniform grid technology, sequentially setting the pre-transition region, transition region, and post-transition region; the pre-transition region and post-transition region are both uniform grid regions, but the grid sizes of the pre-transition region and post-transition region are different; the transition region is a non-uniform grid region; the pre-transition region and post-transition region are uniform fine grid regions and uniform coarse grid regions;

[0052] At the PEC boundary, all incident waves are completely reflected, with no transmitted waves. Since the simulation space is large and the number of iterations is high, the PEC boundary can simplify the calculation process and have little impact on the calculation results.

[0053] like Figure 3 The figure shows a non-uniform mesh region between two uniform regions, used as a transition between a uniform fine mesh region and a uniform coarse mesh region. In any of the x, y, and z directions, the cell size gradually changes from the region before the transition to the region after the transition. The region before the transition can be either fine or coarse. In the transition region, assume the length of the first cell is set to:

[0054] (1)

[0055] Where 1 represents the first unit, R represents the rate of change between adjacent units, and Δs represents the grid size in the region before the transition. Therefore, the remaining grids in the transition region can be expressed as:

[0056] (2)

[0057] Where P is the index of the cell in the transition region, represents the rate of change of the Pth unit in the transition region.

[0058] In the next uniform region after the transition region (i.e., the post-transition region), the size of the first unit in the post-transition region is:

[0059] (3)

[0060] Where Δe is the size of the next uniform grid after the transition region, that is, the grid size of the post-transition region; N is the number of cells in the complete transition region.

[0061] Therefore, the total length of the middle transition area and the total length of one unit in the uniform areas at both ends (i.e., the area before the transition and the area after the transition) is:

[0062]

[0063] Where ΔU is the total length of the transition region, and from this formula we can get R as:

[0064]

[0065] At the same time, substituting formula (5) into formula (3) yields N as:

[0066] (6)

[0067] The transition process from a uniform grid of one size to a uniform grid of another size can be completed by formulas (1)-(6). In the grid of the finite-difference time-domain method, since the components of the electric field and the magnetic field are placed in different spatial positions, two separate grids can be defined accordingly: the electric field component grid and the magnetic field component grid. This layout makes the numerical simulation of the electromagnetic field more accurate, thereby better approximating the continuity and dynamic characteristics of Maxwell's equations. Therefore, Figure 4 As shown in the figure, once the position of the electric field is determined, the magnetic field can be placed at the center of the electric field grid. At the same time, it is noted that the magnetic field is located in the center of the electric field grid and the electric field is located in the center of the magnetic field grid, but the size of the cells of the two grids is different in the non-uniform area. Replace the Δx, Δy, and Δz in the original uniform grid with Δx e , Δy e , Δz e , Δx h , Δy h and Δz h, which is the distance between adjacent electric and magnetic fields. In the simulation of a specific example, a uniform fine grid is used in the fine structure area to ensure accuracy. In other areas outside the fine structure, a uniform coarse grid is used through the above transition method to improve computational efficiency, ultimately achieving efficiency improvements within an acceptable error range.

[0068] This paper uses non-uniform grid technology to select finer grids for locations with finer device structures during simulation, while using a coarser grid for locations with relatively coarse or blank device distribution. This non-uniform grid technology significantly reduces calculation time while maintaining accuracy.

[0069] 3) Combine the weak conditional stable finite-difference time-domain method with the non-uniform grid technology to obtain the magnetic field and electric field values at the next moment; specifically:

[0070] First, the electric and magnetic field expressions are obtained using the weak conditional stable finite-difference time-domain method. In this embodiment, the electromagnetic simulation object can have fine structures in two directions and coarse structures in one direction, for example, fine structures in the x and z directions and coarse structures in the y direction. The update equation is expressed as:

[0071]

[0072]

[0073]

[0074] where ε and μ represent the dielectric constant and magnetic permeability, respectively. They represent partial derivatives in the x, y, and z directions, respectively.

[0075] According to the weak conditional stable finite-difference time-domain method, Δt is neglected in the differential equation 2 The electromagnetic iteration process is divided into two sub-steps:

[0076] Sub-step ①:

[0077]

[0078] (11)

[0079]

[0080] Where Δt represents the time step size, n, n+1 / 2 and n+1 represent the time index, I represents the identity matrix (6×6), and E x 、E y and E z Represent the electric field in the x, y and z directions respectively, H x 、H y and H z Represents the magnetic field in the x, y and z directions respectively.

[0081] Expanding formula (10) and formula (11) yields the component expressions of the electric and magnetic fields at time n+1 / 2.

[0082] (13)

[0083] (14)

[0084]

[0085]

[0086]

[0087]

[0088] According to the components of the electric field and magnetic field at time n, the components of the electric field and magnetic field at time n+1 / 2 can be obtained by formula (13)-formula (18), but in E x 、E y In the solution process, it is necessary to use H at the same time y and H z The value of cannot be solved directly, so we can substitute formula (17) and formula (18) into formula (15) and formula (16) respectively to obtain:

[0089]

[0090] (20)

[0091] in, represents Γ at time T0 η , Γ = E, H, T0= n, n+1 / 2, n+1, η = x, y, z; ε x , ε y , ε z Represents the dielectric constant in the x, y, and z directions, μ x 、μy 、μ z Represents the magnetic permeability in the x, y, and z directions respectively. η = Δη∂ / ∂ η , where η = x, y, z;

[0092] According to formula (19) and formula (20), the electric field component and magnetic field component at time n+1 under weak condition stability are obtained.

[0093] Sub-step ②:

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] (26)

[0100] According to the components of the electric field and magnetic field at time n+1 / 2, the components of the electric field and magnetic field at time n+1 can be obtained by formula (21)-formula (26). Similarly, in E y and E z The solution process requires the use of H at the same time x and H y , so we substitute formula (24) and formula (26) into formula (23) and formula (25) respectively to obtain:

[0101]

[0102]

[0103] According to the above formulas (13) to (28), the electric field and magnetic field components at time n+1 under weak condition stability can be calculated.

[0104] Next, in order to realize the combination of weak conditional stability and non-uniform grid technology, in formula (13)-formula (28), when δ η When solving the electric field, the spatial step size Δx of the electric field grid is used according to the direction of the electric field. e , Δy e and Δze Replace Δx, Δy, Δz in the original formula. When δ η When solving the magnetic field, the spatial step size Δx of the magnetic field grid is used according to the direction of the magnetic field. h , Δy h and Δz h Replace Δx, Δy, and Δz in the original formula. After replacement, the non-uniform grid division of this method can be realized. In the model simulation area, the uniform fine grid, uniform coarse grid, and the length and position of the non-uniform transition area are set, and the transition can be performed according to formulas (1) to (6), completing the effective combination of non-uniform grid technology and weak conditional stable finite difference time-domain method.

[0105] 4) Update the excitation source of the electric field and the loop time step n; specifically:

[0106] In this embodiment, an electric field excitation source J can be set in the z direction of the fine structure of the calculation space and the value of J can be gradually updated. Then, the excitation source is assigned to the electric field component, and the excitation source is updated immediately. The formula is as follows:

[0107]

[0108] in Represents the electric field excitation source in the z direction.

[0109] After adding the excitation source, determine whether the current cycle time step n reaches the maximum simulation iteration number N. If so, end and record all magnetic field values and electric field values in step 3). If not, update time step n to n+1, and return to step 3) to continue obtaining the magnetic field value and electric field value at the next moment.

[0110] This embodiment can verify the electromagnetic simulation problem of the low-pass filter. The geometric structure model of the device is as follows: Figure 1 As shown, it specifically includes a dielectric substrate, and a patch antenna configured on the dielectric substrate. The patch antenna includes a first metal patch 1, a second metal patch 2, and two third metal patches 3; the first metal patch 1 and the second metal patch 2 form a T-shaped structure, and the center position of the second metal patch 2 is connected to one end of the first metal patch 1; the two third metal patches 3 are respectively arranged at both ends of the second metal patch 2. The width of the second metal patch 2 in the x direction is much smaller than the length in the y direction. The width of the first metal patch 1 in the y direction is much smaller than the length in the x direction. From the attached Figure 1It can be seen that the device of this embodiment has a fine structure along the x-direction, which is the width l1 portion of the second metal patch 2 in the figure, and a coarse structure along the y-direction, which is the width w4 portion of the first metal patch 1 in the figure. Furthermore, the method of the present invention is also applicable to devices with fine structures in two directions, such as the x and z directions, but it is not required to have fine structures in both directions.

[0111] The implementation process of the embodiment is the same as that of the electromagnetic simulation method based on non-uniform grid technology; in the uniform fine grid area, the spatial step size is 20Δx = 7.87Δy = Δz = 1 mm, in the uniform coarse grid area, the spatial step size is 10Δx = 7.87Δy = Δz = 1 mm, CFLN is 1, 3, 5, and 7 respectively, and a Gaussian excitation source J is added at the center of the calculation space. In this example, Figure 1 As shown in the gray area, the fine structure area from 2.6 mm to 4.6 mm in the x-direction is divided by a uniform fine grid. After passing through a transition area with a width of 2 mm outside the gray area, it transitions to a uniform coarse grid for division.

[0112] Figure 2 The S parameters obtained by simulation calculation and experimental results of the present invention are shown in FIG. Figure 2 As shown in the simulation results for the low-pass filter S11 and S21, as CFLN gradually increases to 7, the proposed method exhibits some deviation in the results for S11 and S21, but the deviation is small and the error is within an acceptable range. Overall, the accuracy of the results of the proposed method remains highly consistent with the results of the traditional FDTD method and the traditional WCS-FDTD method, demonstrating the high precision of the proposed method.

[0113] Table 2 shows a comparison of the computational time and memory usage of various electromagnetic algorithms. As CFLN increases from 1 to 7, the computational error increases synchronously. Table 2 shows that the computational time of the proposed method, when CFLN = 7, is improved by 59.35% and 52.43%, respectively, compared to the results of the traditional FDTD method on a uniform fine grid and the traditional WCS-FDTD method on a uniform fine grid, demonstrating the significant computational efficiency improvement of this method. The proposed method combines the traditional FDTD method with a uniform fine grid (i.e., FDTD Fine), the traditional WCS-FDTD method with a uniform fine grid (i.e., WCS-FDTD Fine), and the traditional WCS-FDTD method with a uniform coarse grid (i.e., WCS-FDTD Coarse).

[0114] Table 2 Computation time and memory usage of different methods in Example 1

[0115]

[0116] The proposed method simulates a low-pass filter and demonstrates its accuracy and efficiency in fine structure simulations by comparing scattering parameters, computation time, and memory usage. Furthermore, a comparison with the results of the traditional FDTD method and the traditional WCS-FDTD method on a uniformly fine grid reveals that when the CFLN is increased to 7, the efficiency of the proposed method increases by 59.35% and 52.43%, respectively, while maintaining an acceptable error range. This demonstrates the accuracy and efficiency of the proposed method.

[0117] In summary, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they may adjust the technical solutions described in the aforementioned embodiments, or replace some of the technical features. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An electromagnetic simulation method based on non-uniform grid technology, characterized in that: The method comprises: Establish an electromagnetic simulation object model and determine the calculation space; wherein, the electromagnetic simulation object model is x and z There is a fine structure in the direction y There is a rough structure in the direction; According to the calculation space, an ideal electric conductor boundary PEC suitable for the weak conditional stability finite-difference time-domain method is constructed; wherein, the ideal electric conductor boundary PEC is set along any one of the x, y, and z directions by using a non-uniform grid technology to set a pre-transition region, a transition region, and a post-transition region for the ideal electric conductor boundary PEC; the pre-transition region and the post-transition region are both uniform grid regions, but the grid sizes of the pre-transition region and the post-transition region are different; the transition region is a non-uniform grid region; in the ideal electric conductor boundary PEC, the subdivision grid size used in the fine structure region of the electromagnetic simulation object is selected to be smaller than the subdivision grid size used in the open or coarse structure region; Combine the weak conditional stable finite-difference time-domain method with the non-uniform grid technology to obtain the magnetic field and electric field values at the next moment. Specifically: First, the electric field and magnetic field expressions are obtained according to the weak conditional stable finite difference time-domain method, which are expressed as: ； ; ; where ε and μ represent the dielectric constant and magnetic permeability, respectively. Respectively represent the partial derivatives in the x, y, and z directions; According to the weak conditional stable finite-difference time-domain method, Δt is neglected in the differential equation 2 The electromagnetic iteration process is divided into two sub-steps: Sub-step ①: ; （11）; ; Where Δt represents the time step size, n, n+1 / 2 and n+1 represent the time index, I represents the identity matrix, and E x 、E y and E z Represent the electric field in the x, y and z directions respectively, H x 、H y and H z Represent the magnetic field quantities in the x, y and z directions respectively; Expanding formula (10) and formula (11) yields the component expressions of the electric and magnetic fields at time n+1 / 2; （13）; （14）; ; ; ; ; According to the components of the electric field and magnetic field at time n, the components of the electric field and magnetic field at time n+1 / 2 can be obtained by formula (13)-formula (18), but in E x 、E y In the solution process, it is necessary to use H at the same time y and H z The value of cannot be solved directly, so we can substitute formula (17) and formula (18) into formula (15) and formula (16) respectively to obtain: ; （20）; in, represents Γ at time T0 η , Γ = E, H, T0= n, n+1 / 2, n+1, η = x, y, z; ε x , ε y , ε z Represents the dielectric constant in the x, y, and z directions, μ x 、μ y 、μ z Represents the magnetic permeability in the x, y, and z directions, δ η = Δη∂ / ∂ η , where η = x, y, z; According to formula (19) and formula (20), the electric field component and magnetic field component at time n+1 under weak condition stability are obtained; Sub-step ②: ; ; ; ; ; （26）; According to the components of the electric field and magnetic field at time n+1 / 2, the components of the electric field and magnetic field at time n+1 are obtained by formula (21)-formula (26). Similarly, in E y and E z The solution process requires the use of H at the same time x and H y , so we substitute formula (24) and formula (26) into formula (23) and formula (25) respectively to obtain: ; ; According to the above formulas (13)-(28), the electric field and magnetic field components at time n+1 under weak condition stability can be obtained; Next, in order to realize the combination of weak conditional stability and non-uniform grid technology, in formula (13)-formula (28), when δ η When solving the electric field, the spatial step size Δx of the electric field grid is used according to the direction of the electric field. e , Δy e and Δz e Replace Δx, Δy, Δz, when δ η When solving the magnetic field, the spatial step size Δx of the magnetic field grid is used according to the direction of the magnetic field. h , Δy h and Δz h Perform substitutions Δx, Δy, and Δz.

2. The method according to claim 1, characterized in that The electromagnetic simulation object model x, y, z The orientation is consistent with the Cartesian coordinate system, where the electric field grid and the magnetic field grid point in the same direction as the Cartesian coordinate system.

3. The method according to claim 2, characterized in that The spatial step size of the fine structure is smaller than the spatial step size of the coarse structure.

4. The method according to claim 1, characterized in that In the ideal electric conductor boundary PEC, in the transition region, it is assumed that the length of the first unit is set to: (1) Where 1 represents the index of the first cell, R represents the rate of change between adjacent units, Δ s represents the mesh size in the region before the transition; the remaining mesh in the transition region is thus expressed as: (2) Where P is the index of the cell in the transition region, represents the rate of change of the Pth unit in the transition region; In the post-transition region, the grid size Δ e for: (3) in N is the number of units in the entire transition region; Therefore, according to formulas (1)-(3), the total length of a unit of the adjacent transition area in the pre-transition area and the post-transition area plus the entire transition area is: (4) Where ΔU is the total length of the transition region, and further we know that R is: (5) At the same time, substitute formula (5) into formula (3) to obtain N: (6)。 5. The method according to claim 1, characterized in that: The method also includes updating the excitation source of the electric field and the cyclic time step n Specifically: Set the electric field excitation source J in the fine structure direction of the calculation space, then assign the excitation source to the electric field component and gradually update the excitation source; Determine whether the current cycle time step n reaches the maximum simulation iteration step number N. If so, end and record all magnetic field values and electric field values. If not, update the time step n to n+1, and continue to obtain the magnetic field value and electric field value at the next moment.

6. A computer-readable storage medium having a complete computer program recorded thereon, which, when run on a computer system, causes the computer to execute the method according to any one of claims 1 to 5.

7. A computing device comprising a memory and a processor, wherein the memory stores executable code, and when the processor executes the executable code, the method according to any one of claims 1 to 5 is implemented.

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