Electromagnetic simulation method based on non-uniform grid technology

Abstract

The invention discloses an electromagnetic simulation method based on a non-uniform grid technology. Establishing an electromagnetic simulation object model, and determining a calculation space range of a simulation object size; constructing an ideal electric conductor boundary suitable for a weak condition stable time domain finite difference method; setting a pre-transition area, a transition area and a post-transition area by using a non-uniform grid technology; and combining a weak condition stable time domain finite difference method with a non-uniform grid technology to obtain a magnetic field value and an electric field value at the next moment. According to the method, an efficient combination method of a weak condition stable time domain finite difference method and a non-uniform grid technology is provided, collaborative optimization of local precision guarantee-global efficiency improvement is achieved through a dynamic grid subdivision strategy, especially for electromagnetic simulation of a device with a fine structure, high calculation precision is guaranteed, and the method is suitable for electromagnetic simulation of the device with the fine structure. Moreover, the number of grids is reduced, and the calculation time is obviously shortened.

Description

Technical Field

[0001] The present 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 grid meshing method has a decisive influence on the calculation efficiency and accuracy. Especially when simulating the propagation of electromagnetic waves in a relatively large area, the number of required grid cells is extremely large. When simulating the propagation of electromagnetic waves in a large area or the structure of complex devices, the traditional uniform grid technology faces significant challenges: using dense uniform grids to ensure calculation accuracy will lead to a sharp increase in the consumption of computing resources, and the memory requirements and calculation time will increase exponentially; conversely, if coarse grids are blindly used to improve efficiency, the simulation accuracy will be severely reduced. How to optimize the calculation efficiency while ensuring accuracy has become the core problem to be solved urgently in the field of electromagnetic simulation.

[0003] With the rapid development of computer hardware technology, the memory and computing speed of computers have been greatly improved, making it efficient and feasible to study electromagnetic problems in complex target environments through numerical methods, and it can solve the cost problems generated by a large number of engineering experiments. Currently, the classical full-wave numerical methods include the Finite-Difference Time-Domain (FDTD) method, the Finite Element Method (FEM), and the Method of Moment (MoM). Among them, the FDTD method is one of the most commonly used numerical methods for studying electromagnetic problems. However, due to the limitation of the time stability condition, the simulation efficiency for fine-structure devices is relatively low. In order to reduce the influence brought by the time stability condition, many improvement schemes have been proposed by scholars. Among them, the Weakly Conditionally Stable (WCS) FDTD method relaxes the time stability condition to increase the time step, but this method is accompanied by an increase in numerical dispersion error, especially obvious accuracy loss in long-term simulations. Summary of the Invention

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

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

[0006] Establish an electromagnetic simulation object model and determine the calculation space; wherein, the electromagnetic simulation object has a fine structure;

[0007] According to the calculation space, an ideal electric conductor boundary PEC suitable for the weak conditional stable time-domain finite difference method is constructed; wherein the ideal electric conductor boundary PEC is set along any direction of the x, y, and z directions by using non-uniform grid technology to set the pre-transition region, transition region, and post-transition region of 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;

[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, z directions of the electromagnetic simulation object model are consistent with the Cartesian coordinate system, wherein the pointing directions of the electric field grid and the magnetic field grid are the same as 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 adopted in the fine structure region of the electromagnetic simulation object is selected to be smaller than the subdivision grid size adopted in the empty or rough 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; therefore, 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), it can be known that the total length of adding one unit of the adjacent transition region in the pre-transition region and the post-transition region respectively to the entire transition region is:

[0021] (4)

[0022] Where ΔU is the total length of the transition region, and further it can be known that R is:

[0023] (5)

[0024] At the same time, substituting formula (5) into formula (3), N is obtained as:

[0025] (6).

[0027] Preferably, the specific implementation process of combining the weakly conditionally stable finite-difference time-domain method with the non-uniform grid technique and obtaining the magnetic field value and electric field value at the next moment is:

[0028] Obtain the electric field components and magnetic field components at the n+1 / 2 and n+1 moments under weak conditions according to the weakly conditionally stable finite-difference time-domain method, where , where η = x, y, z; Δη represents the spatial step of the electromagnetic simulation object model in the η direction;

[0029] To achieve the combination of weak condition stability and non-uniform grid technique, when δ η When solving the electric field, according to the direction of the electric field, Δη is replaced with the spatial step Δη in the η direction of the electric field grid e When δ η When solving the magnetic field, according to the direction of the magnetic field, Δη is replaced with the spatial step Δη in the η direction of the magnetic field grid h for replacement.

[0030] Preferably, the method further includes updating the excitation source of the electric field and the loop time step n; specifically:

[0031] 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 components, and gradually update the excitation source;

[0032] Judge whether the current loop time step n reaches the maximum simulation iteration step 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.

[0033] In a second aspect, the present invention provides a computing device, including a processor and a memory, where an executable code is stored in the memory, and when the processor executes the executable code, the method described above is implemented.

[0034] In a third aspect, the present invention provides a computer-readable storage medium having a complete set of computer programs recorded thereon, which, when run on a computer system, causes the computer to execute the method described.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention adopts a fine grid in a fine structure area and a coarse grid in an open or rough area, and reduces numerical errors by optimizing the transition area design, thereby allowing the time step to be set based on the coarse grid step while ensuring the accuracy of the fine structure.

[0037] The non-uniform grid of the present invention realizes a smooth transition of the grid size through the gradual design of the transition area, avoiding the sudden change of the electric field / magnetic field components caused by the traditional sudden grid division. Combined with the weak stability condition, the relationship between the time step and the numerical dispersion is balanced through the adaptive spatial step adjustment, and finally the coordinated optimization of accuracy and efficiency is achieved.

[0038] 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, and realizes the collaborative optimization of "local accuracy assurance-global efficiency improvement" through a dynamic grid division strategy (i.e., partial encryption and partial thickening). 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

[0039] Figure 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;

[0040] Figure 2 is a comparison curve diagram of the simulation results of the S parameters under different CFLN conditions in Example 1 of the present invention;

[0041] Figure 3 It is a schematic diagram of non-uniform grid technology;

[0042] Figure 4 It is a schematic diagram of the grid distribution of non-uniform grid electric field and magnetic field;

[0043] 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 of Figure 2 (b) is S 21The comparison curve graph, the stability constant (Courant-Friedrichs-Lewy Number, CFLN) represents the ratio of the time step of the non-uniform grid weakly conditionally stable finite-difference time-domain method (i.e., UWCS-FDTD method) involved in the method of the present invention to that of the traditional FDTD method, where the CFLN values are 1, 3, 5, and 7 respectively.

[0044] Table 1 Geometric Dimensions of the Low-Pass Filter in Embodiment 1 of the Present Invention

[0045] Specific Embodiment

[0046] The present invention is applied to the electromagnetic simulation method. The involved recurrence formula can be obtained according to the weakly conditionally stable finite-difference time-domain method. The specific embodiment is described in detail by taking the electromagnetic simulation problem of a low-pass filter as an example, and the actual application scope is not limited thereto.

[0047] The present invention provides an electromagnetic simulation method based on non-uniform grid technology, specifically a weakly conditionally stable finite-difference time-domain method based on manually setting coarse grids and fine grids to divide the calculation region in a Cartesian rectangular coordinate system, realizing the method of non-uniform grids. The specific steps of this method are as follows:

[0048] 1) Establish an electromagnetic simulation object model and determine the calculation space; specifically: (a)

[0049] Establish an electromagnetic simulation object model; establish a three-dimensional Cartesian coordinate system; according to the established model, obtain the range of the calculation space; the calculation space range is (X min , Y min , Z min ) ~ (X max , Y max , Z max ), the size of the space range is (X max – X min ) × (Y max – Y min ) × (Z max – Z min ), and the coordinates of the center position are ((X min + X max ) / 2, (Y min + Y max ) / 2, (Z min + Z max ) / 2). Among them, the minimum and maximum spatial positions of the simulation region in the x, y, and z directions are X min , X max , Y min , Y max , Zmin and Z max ;

[0050] The spatial step sizes of the electromagnetic simulation object model in the x, y, and z directions are Δx, Δy, and Δz respectively, and the spatial step sizes of the electric field grid in the x, y, and z directions are Δx e , Δy e , Δz e respectively, and the spatial step sizes of the magnetic field grid in the x, y, and z directions are Δx h , Δy h , Δz h respectively. J is the excitation source function, n is the time step (ranging from 1 to N); N is the total number of simulation iteration steps.

[0051] The electromagnetic simulation object model has a fine structure direction in at least one direction and a rough structure direction in at least one direction. The fine structure referred to here means having a smaller spatial step size in this direction, while the rough structure means having a larger spatial step size in this direction.

[0052] 2) Construct an ideal electric conductor boundary (Perfect Electric Conductor, PEC) suitable for the weakly conditionally stable finite-difference time-domain method; based on the non-uniform grid technology, set the pre-transition region, transition region, and post-transition region in sequence; both the pre-transition region and the post-transition region are 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; the pre-transition region and the post-transition region are the uniform fine grid region and the uniform coarse grid region respectively;

[0053] At the PEC boundary, all incident waves will be completely reflected and there is no transmitted wave. Since the simulation space is large and the number of iteration steps is large, the PEC boundary can simplify the calculation process and has little influence on the calculation results.

[0054] As Figure 3 shown, it shows that a non-uniform grid region is used as the transition region between two uniform regions for the uniform fine grid region and the uniform coarse grid region. In any one of the x, y, and z directions, from the pre-transition region to the post-transition region, the size of the unit gradually changes. The pre-transition region can be a fine grid or a coarse grid. In the transition region, it is assumed that the length of the first unit is set to:

[0055] (1)

[0056] where 1 represents the first unit, R represents the change rate between adjacent units, and Δs represents the grid size of the pre-transition region. Therefore, the remaining grids in the transition region can be expressed as:

[0057] (2)

[0058] Where P is the index of the unit in the transition region, representing the change rate of the P-th unit in the transition region.

[0059] In the next uniform region after the end of the transition region (i.e., the region after transition), the size of the first unit in the region after transition is:

[0060] (3)

[0061] Where Δe is the size of the next uniform grid after the transition region, i.e., the grid size of the region after transition; N is the number of units in the complete transition region.

[0062] Therefore, the total length of the intermediate transition region and the total length of one unit each in the two uniform regions at both ends (i.e., the region before transition and the region after transition) are:

[0063]

[0064] Where ΔU is the total length of the transition region, and from this equation, R can be obtained as:

[0065]

[0066] At the same time, substituting formula (5) into formula (3), N can be obtained as:

[0067] (6)

[0068] Through formulas (1)-(6), the transition process from a uniform grid of one size to a uniform grid of another size can be completed. In the grid of the finite-difference time-domain method, since the components of the electric field and magnetic field are placed at 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, thus better approximating the continuity and dynamic characteristics of Maxwell's equations. Therefore, as Figure 4 shown, when 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 should be noted that the magnetic field is located in the middle of the electric field grid and the electric field is located in the middle of the magnetic field grid, but the sizes of the units of these two grids are different in the non-uniform region. Let the original Δx, Δy, Δz in the uniform grid be replaced by Δx e , Δy e , Δz e , Δx h , Δy h and Δz hIt suffices to represent, that is, the distance between adjacent electric and magnetic fields. During the simulation of specific instances, a uniform fine grid is used in the fine structure region to ensure accuracy. For other regions outside the fine structure, the above transition method is used to transform them into uniform coarse grids to improve the calculation efficiency, and finally, the effect of efficiency improvement is achieved within an acceptable error range.

[0069] Through the non-uniform grid technology, during the simulation process, finer meshes are selected for the fine structure positions of the device, while coarser meshes are used for calculation at positions where the device distribution is relatively rough or blank. Through this non-uniform grid technology, while ensuring accuracy, it can significantly reduce the calculation time.

[0070] 3) Combine the weak-condition stable finite-difference time-domain method with the non-uniform grid technology, and obtain the magnetic field value and electric field value at the next moment; specifically:

[0071] First, obtain the electric and magnetic field expressions according to the weak-condition stable finite-difference time-domain method. In this embodiment, the electromagnetic simulation object can have fine structures in two directions and a rough structure in one direction. For example, it has fine structures in the x and z directions and a rough structure in the y direction. The update equations are expressed as:

[0072]

[0073]

[0074]

[0075] where ε and μ represent the permittivity and permeability respectively, represent the partial derivatives with respect to the x, y, and z directions respectively.

[0076] According to the weak-condition stable finite-difference time-domain method, the Δt 2 term is omitted in the differential equation, and the electromagnetic iteration process is divided into two sub-steps:

[0077] Sub-step ①:

[0078]

[0079] (11)

[0080]

[0081] In the formula, Δt represents the time step size, n, n+1 / 2, and n+1 represent time indices, I represents the identity matrix (6×6), E x 、E y and E z represent the electric field quantities in the x, y, and z directions respectively, and H x 、H y and H z represent the magnetic field quantities in the x, y, and z directions respectively.

[0082] After expanding formulas (10) and (11), the component expressions of the electric and magnetic fields at the n+1 / 2 moment are obtained.

[0083] (13)

[0084] (14)

[0085]

[0086]

[0087]

[0088]

[0089] According to the components of the electric and magnetic fields at the n moment, the components of the electric and magnetic fields at the n+1 / 2 moment can be obtained through formulas (13)-(18), but in the process of solving E x 、E y , the values of H y and H z at the same moment are required and cannot be directly solved. Therefore, substituting formulas (17) and (18) into formulas (15) and (16) respectively can obtain:

[0090]

[0091] (20)

[0092] Among them, represents Γ 0 at the T η moment, Γ = E, H, T 0 = n, n+1 / 2, n+1, η = x, y, z; ε x 、ε y 、ε zrepresent the permittivities in the x, y, and z directions, respectively, μ x , μ y , μ z represent the permeabilities in the x, y, and z directions, respectively. δ η = Δη∂ / ∂ η , where η = x, y, z;

[0093] According to equations (19) and (20), the electric and magnetic field components at the (n + 1)-th time step under the weak condition stability are obtained.

[0094] Sub-step ②:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] (26)

[0101] Based on the electric and magnetic field components at the (n + 1 / 2)-th time step, the electric and magnetic field components at the (n + 1)-th time step can be obtained through equations (21) - (26). Similarly, during the solution process of E y and E z , the H x and H y at the same time step are required. Therefore, substituting equations (24) and (26) into equations (23) and (25) respectively, we get:

[0102]

[0103]

[0104] According to the above equations (13) - (28), the electric and magnetic field components at the (n + 1)-th time step under the weak condition stability can be obtained.

[0105] Next, to achieve the combination of weak condition stability and non-uniform grid technology, in equations (13) - (28), when δ η solving for the electric field, according to the direction of the electric field, the spatial step Δx of the electric field grid is respectively adoptede , Δy e and Δz e are used to replace Δx, Δy, and Δz in the original formula. When δ η solving for the magnetic field, according to the direction of the magnetic field, the spatial step sizes Δx h , Δy h and Δz h of the magnetic field grid are respectively used to replace Δx, Δy, and Δz in the original formula. After replacement, the non-uniform grid division of this method can be realized. By selecting and setting the length and position of the uniform fine grid, uniform coarse grid, and non-uniform transition region in the model simulation area, the transition can be carried out according to formulas (1)-(6), and the effective combination of the non-uniform grid technology and the weakly conditional stable finite-difference time-domain method can be completed.

[0106] 4) Update the excitation source of the electric field and the loop time step n; specifically:

[0107] In this embodiment, an electric field excitation source J can be set in the fine structure z direction of the calculation space, and the value of J is gradually updated. Subsequently, the excitation source is assigned to the electric field component, and then the update of the excitation source is completed. The formula is expressed as follows:

[0108]

[0109] where represents the electric field excitation source in the z direction.

[0110] After adding the excitation source, it is judged whether the current loop time step n reaches the maximum simulation iteration step N. If so, the process ends and all magnetic field values and electric field values in step 3) are recorded. If not, the time step n is updated to n + 1, and then return to step 3) to continue obtaining the magnetic field values and electric field values at the next moment.

[0111] This embodiment can verify the electromagnetic simulation problem of a low-pass filter. The geometric structure model of the device is as Figure 1 shown, specifically including a dielectric substrate and a patch antenna disposed 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 disposed 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 its length in the y direction. The width of the first metal patch 1 in the y direction is much smaller than its length in the x direction. From the attached Figure 1 it can be seen that the device in this embodiment has a fine structure along the x direction, that is, the width l 1 of the second metal patch 2 in the figure, and has a rough structure along the y direction, that is, the width w4 In addition, 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 the x and z directions.

[0112] The implementation process of the embodiment is the same as that of the electromagnetic simulation method based on the non-uniform grid technology; in the uniform fine grid region, the space step is 20Δx = 7.87Δy = Δz = 1 mm, and in the uniform coarse grid region, the space step is 10Δx = 7.87Δy = Δz = 1 mm. The CFLN values are 1, 3, 5, and 7 respectively. A Gaussian excitation source J is added at the center position of the calculation space. In this example, as Figure 1 shown in the gray area, in the fine structure region from 2.6 mm to 4.6 mm in the x direction, a uniform fine grid is used for meshing. After passing through a transition region with a width of 2 mm outside the gray area, it transitions to a uniform coarse grid for meshing.

[0113] Figure 2 The S parameters obtained by simulating and calculating the method of the present invention and the experimental results are shown. As Figure 2 shown, in the simulation results of S11 and S21 of the low-pass filter, as CFLN gradually increases to 7, in the results of S11 and S21, the method proposed in the present invention shows a certain deviation, but the deviation is small and the error is within an acceptable range. Generally, the result accuracy of the method proposed in the present invention still maintains a high degree of consistency with the results of the traditional FDTD method and the traditional WCS-FDTD method, demonstrating the high-precision performance of this method.

[0114] The comparison results of the calculation duration and the memory occupation size of various electromagnetic algorithms are shown in Table 2. As CFLN increases from 1 to 7, the calculation error also increases synchronously. From the results in Table 2, when CFLN = 7, the calculation time of the method of the present invention is 59.35% and 52.43% more efficient than the results of the traditional FDTD method with a uniform fine grid and the traditional WCS-FDTD method with a uniform fine grid respectively, demonstrating that this method has a high improvement in calculation efficiency. Among them, the combination method of the traditional FDTD method and the uniform fine grid (i.e., FDTD Fine), the combination method of the traditional WCS-FDTD method and the uniform fine grid (i.e., WCS-FDTD Fine), and the combination method of the traditional WCS-FDTD method and the uniform coarse grid (i.e., WCS-FDTD Coarse).

[0115] Table 2 Calculation duration and memory occupation of different methods in Embodiment 1

[0116]

[0117] The method of the present invention simulates a low-pass filter. By comparing the scattering parameters, calculation duration, and memory occupancy results, it proves the accuracy and efficiency of the method in fine-structure simulation. At the same time, compared with the results of the traditional FDTD method and the traditional WCS-FDTD method under a uniform fine grid, when the CFLN increases to 7, on the premise that the error remains within an acceptable range, the efficiency of this method is improved by 59.35% and 52.43% respectively, proving the accuracy and efficiency of this method.

[0118] In summary, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can adjust the technical solutions recorded in the foregoing embodiments, or replace some technical features; and 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: Establishing an electromagnetic simulation object model and determining a calculation space; wherein the electromagnetic simulation object has a fine structure; According to the calculation space, an ideal electric conductor boundary PEC suitable for the weak conditional stable time-domain finite difference method is constructed; wherein the ideal electric conductor boundary PEC is set along any direction of the x, y, and z directions by using non-uniform grid technology to set the pre-transition region, transition region, and post-transition region of 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; 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.

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 1, characterized in that: 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.

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

5. The method according to claim 1, characterized in that: In the ideal electric conductor boundary PEC, the subdivision grid size used in the fine structure area of ​​the electromagnetic simulation object is selected to be smaller than the subdivision grid size used in the empty or rough structure area.

6. The method according to claim 1, characterized in that: In the ideal 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; therefore the remaining mesh in the transition region is 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 each 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, substituting formula (5) into formula (3), we get N as: (6)。 7. The method according to claim 1, characterized in that: The specific implementation process of combining the weak condition stable finite difference time domain method with the non-uniform grid technology and obtaining the magnetic field value and electric field value at the next moment is: According to the weak conditional stability finite difference time domain method, the weak conditional stability n +1 / 2, n+1 time electric field component and magnetic field component, where ,in η = x, y, z ; Δ η Represents the electromagnetic simulation object model in η The spatial step length in the direction; In order to achieve the combination of weak condition stability and non-uniform grid technology, δ η When solving the electric field, Δ η Using the electric field grid η The spatial step length Δ in the direction η e Replace; when δ η When solving the magnetic field, Δ η Using magnetic field grid η The spatial step length Δ in the direction η h Make a replacement.

8. 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: An electric field excitation source J is set in the fine structure direction of the calculation space, and then the excitation source is assigned to the electric field component, and the excitation source is gradually updated; 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.

9. 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 8.

10. A computing device, comprising a memory and a processor, wherein the memory stores executable codes, and when the processor executes the executable codes, the method according to any one of claims 1 to 8 is implemented.

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