FDTD Mesh Generation Method and FDTD Electromagnetic Calculation Method
By using the grid filling method of triangular facet random interpolation in the FDTD electromagnetic calculation method, the problems of low grid segmentation efficiency and complex algorithm in the prior art are solved, and higher calculation accuracy and efficiency are achieved.
Patent Information
- Application Number
- CN202210717279.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-23
- Publication Date
- 2025-05-27
- Estimated Expiration
- 2042-06-23
AI Technical Summary
In the existing FDTD electromagnetic calculation methods, the grid segmentation efficiency is low and the algorithm is complex, which affects the calculation accuracy and efficiency.
The Yee grid of the model surface is filled by random interpolation of triangular face elements. By determining the number of random fill points of each triangular face element and mapping the coordinates of the random scatter points into the problem space, the Yee grid of the model is generated.
It improves the efficiency and accuracy of FDTD calculations, reduces the consumption of computing resources, and significantly improves the speed of meshing compared with traditional ray tracing.
Smart Images
Figure CN115048842B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a FDTD (Finite Difference Time Domain) electromagnetic calculation method. Background Art
[0002] The FDTD method is a common numerical calculation method in the electromagnetic field. Based on Maxwell's equations, the electromagnetic field is discretely sampled in space and time, and the propagation of the electromagnetic field is simulated by iterative equations. When using FDTD to perform numerical calculations on a model, it is first necessary to perform mesh discretization on the model, and the quality of the mesh discretization affects the accuracy and calculation efficiency of the calculation results.
[0003] The traditional ray tracing method is a commonly used mesh discretization method. By means of vector operations, winding number algorithms, odd-even intersection points, etc., it judges the intersection of rays and triangular facets, thereby determining the range of the model and obtaining the Yee grid model. Due to the use of a large number of ray intersection operations on the triangular patches on the target surface, the ray tracing method needs to repeatedly read the triangular facet information many times, with low calculation efficiency and a relatively complex algorithm, which is also difficult to understand. Summary of the Invention
[0004] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a FDTD mesh discretization method with higher calculation accuracy and calculation efficiency.
[0005] The present invention specifically adopts the following technical solutions to solve the above technical problems:
[0006] A FDTD mesh discretization method includes the step of converting the triangular facets of the model into the surface Yee grid of the model, and the specific steps are as follows: First, determine the number of randomly filled points n for each triangular facet area , then fill n area randomly scattered points with uniform distribution in the corresponding triangular facet, and finally map the coordinates of the randomly scattered points into the problem space, thereby obtaining the surface Yee grid of the model; the number of randomly filled points n for each triangular facet area is specifically determined by the following formula:
[0007]
[0008] Wherein, is the maximum filling number, area max is the maximum value of the areas of the triangular facets in the model, dx and dy are the sizes of the Yee grid, and α is a preset parameter ranging from 1 to 20; l 2 = l 1 / l max l 1is the average perimeter of the triangular facets in the model, l max is the maximum perimeter of the triangular facets in the model.
[0009] Preferably, the coordinates of the random scatter points are determined according to the following formula:
[0010]
[0011] In the formula, (x, y, z) are the three-dimensional coordinates of the random scatter point, (x 1 , y 1 , z 1 ), (x 2 , y 2 , z 3 ) and (x 3 , y 3 , z 3 ) are the coordinates of the three vertices of the triangular facet, and u, v are random numbers drawn from between 0 and 1.
[0012] Preferably, the following formula is used to map the coordinates of the random scatter points into the problem space:
[0013]
[0014] where, (x f , y f , z f ) are the coordinates of the random scatter point coordinates (x, y, z) mapped into the problem space, x min , y min , z min are the minimum values of the coordinates in the problem space, and dx, dy, dz are the sizes of the Yee grid.
[0015] Preferably, the value of α is 10.
[0016] Furthermore, this mesh generation method further includes the step of performing volume filling on the model after completing the surface Yee grid conversion, specifically as follows: setting the model space boundary and the model surface as perfect electric conductors; under the illumination of the excitation source, after the cumulative energy distribution in the entire model space tends to be stable, counting the cumulative energy spatial distribution, and taking the region where the cumulative energy is less than the preset energy threshold as the range of the target model, that is, completing the volume filling of the model.
[0017] Preferably, the excitation source is 6 Gaussian wave excitation sources.
[0018] Preferably, the energy threshold is 10 -5 .
[0019] Based on the same inventive concept, the following technical solutions can also be obtained:
[0020] An FDTD electromagnetic calculation method includes a step of performing grid division on a model, and the grid division is performed using the FDTD grid division method described in any of the above technical solutions.
[0021] Compared with the prior art, the present invention has the following beneficial effects:
[0022] The present invention first proposes to fill the Yee grids on the model surface by means of random interpolation of triangular elements. Compared with the traditional ray tracing method, the grid division method of the present invention can improve the calculation efficiency and reduce the consumption of calculation resources while ensuring the validity of the FDTD calculation results. Description of the Drawings
[0023] Figure 1 It is an implementation algorithm flowchart of the FDTD grid division method of the present invention;
[0024] Figure 2 It is a schematic diagram of random scatter point filling; the left side is a schematic diagram of filling several scatter points, and the right side is a schematic diagram of the completion of scatter point filling;
[0025] Figure 3 It is a schematic diagram of the result of grid division of a dielectric sphere using the grid division method of the present invention;
[0026] Figure 4 It is a comparison diagram of the calculation simulation result and the analytical result obtained by the FDTD electromagnetic calculation method of the present invention. Detailed Embodiments
[0027] Aiming at the deficiencies of the prior art, the solution idea of the present invention is to introduce the random filling idea into the filling of the Yee grids on the model surface. Through random interpolation of triangular elements, the number of random filling points is selected according to the area and perimeter of the triangular elements, and uniformly distributed random scatter points are generated on the triangular elements, and then the coordinates of the random scatter points are mapped into the problem space, so as to quickly and accurately complete the surface filling of the Yee grids.
[0028] Specifically, the technical solution proposed by the present invention is as follows:
[0029] An FDTD grid division method includes a step of converting the triangular elements of a model into the surface Yee grids of the model, and this step is specifically as follows: First, determine the number of random filling points n for each triangular element area , then fill n area uniformly distributed random scatter points in the corresponding triangular element, and finally map the coordinates of the random scatter points into the problem space, so as to obtain the surface Yee grids of the model; the number of random filling points n for each triangular element area is specifically determined by the following formula:
[0030]
[0031] Among them, is the maximum filling number, area max is the maximum value of the triangular element area in the model, dx and dy are the sizes of the Yee grid, and α is a preset parameter ranging from 1 to 20; l 2 = l 1 / l max where l 1 is the average perimeter of the triangular elements in the model, and l max is the maximum value of the perimeters of the triangular elements in the model.
[0032] Preferably, the coordinates of the random scatter points are determined according to the following formula:
[0033]
[0034] In the formula, (x, y, z) are the three-dimensional coordinates of the random scatter points, (x 1 , y 1 , z 1 ), (x 2 , y 2 , z 3 ) and (x 3 , y 3 , z 3 ) are the coordinates of the three vertices of the triangular element, and u and v are random numbers drawn from 0 to 1.
[0035] Preferably, the following formula is used to map the coordinates of the random scatter points into the problem space:
[0036]
[0037] Among them, (x f , y f , z f ) are the coordinates of the random scatter point coordinates (x, y, z) mapped into the problem space, x min , y min , z min are the minimum values of the coordinates in the problem space, and dx, dy, and dz are the sizes of the Yee grid.
[0038] Preferably, the value of α is 10.
[0039] Furthermore, this grid meshing method further includes the step of performing volume filling on the model that has completed the surface Yee grid conversion, specifically as follows: Set the model space boundary and the model surface as perfect electric conductors; Under the illumination of the excitation source, count the cumulative energy space distribution after the cumulative energy distribution of the entire model space tends to be stable, and use the area where the cumulative energy is less than the preset energy threshold as the range of the target model, that is, complete the volume filling of the model.
[0040] Preferably, the excitation source is six Gaussian wave excitation sources.
[0041] Preferably, the energy threshold is 10 -5 .
[0042] Based on the same inventive concept, the following technical solutions can also be obtained:
[0043] An FDTD electromagnetic calculation method includes a step of performing grid meshing on a model, and using the FDTD grid meshing method described in any of the above technical solutions to perform the grid meshing.
[0044] For the convenience of public understanding, the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings:
[0045] Figure 1 shows an algorithm implementation process of surface Yee grid filling in the FDTD grid meshing method of the present invention, and the algorithm input is the triangular patch information obtained by reading an STL file. In Figure 1 , j represents the j-th model in the STL file, i represents the i-th triangular element in the model, and a double loop is controlled by i and j to achieve the purpose of traversing the model and triangular elements. k is the k-th random scatter point generated on the triangular element. By comparing the random scatter point with the Yee grid, the surface Yee grid can be obtained. The specific steps of this algorithm are as follows:
[0046] Step 1: Read the STL file and calculate the number of independent models and the number of triangular elements included in each independent model;
[0047] Step 2: Determine whether all models have been traversed. If so, go to Step 7;
[0048] Step 3: Determine whether all triangular elements of the model have been traversed. If so, increment the model number j by 1 and repeat Step 2;
[0049] Step 4: Calculate the area perimeter of the element, calculate the filling number of the triangular element scatter points, and initialize k to 1;
[0050] Step 5: Determine whether the k value of the k-th random scatter point generated on the triangular element reaches the filling number. If so, repeat Step 3;
[0051] Step 6: Generate random scatter point coordinates according to the random filling formula, convert the scatter point coordinates to the coordinates in the problem space, increment k by 1, and repeat Step 5;
[0052] Step 7: End.
[0053] The selection of the number of filling points is one of the key points in the random filling of triangular elements. Selecting too many filling points will slow down the running speed of the algorithm and reduce the efficiency. Selecting too few points will make the subsequent generated Yee grid less uniform, unable to fully cover the triangular element, and reduce the algorithm accuracy. The selection of the number of filling points should be related to the perimeter and area of the triangular element. Among them, the area of the triangular element determines the maximum number of fillings. During the process of random interpolation of triangular elements, the actual number of filling points should be less than or equal to the maximum number of fillings. The maximum number of fillings depends on the area of the triangular element, and the actual selected number of filling points also needs to refer to the perimeter of the triangular element. Since each triangular element needs to be filled, the number of filling points should be no less than 1. Using the perimeter value actually plays a role in improving efficiency. Filling all elements with the maximum number of fillings can also obtain the surface Yee grid, but it will increase the meshing time due to too many points.
[0054] The formula for randomly selecting the number of filling points according to the area and perimeter of the triangular element is as follows:
[0055]
[0056] l 2 =l 1 / l max
[0057]
[0058] Among them, n max is the maximum number of fillings, area max is the maximum value of the area of the triangular element in this model, dx, dy are the sizes of the Yee grid, and the range of α is 1 to 20. After multiple experimental verifications, when α is set to 10, the model grid filling program is relatively efficient and accurate. n area is the actual number of fillings, l 1 is the average perimeter of this triangular element, l max is the maximum value of the average perimeter of the triangular element in this model, l 2 is the ratio of the two perimeters, that is, the coefficient determining the actual number of filling points. What is obtained is the area ratio between the area of the triangular element and the area of the Yee grid. Assuming that the area of each Yee grid is fixed at 1, the area of the triangular element is S, and the actual required number of Yee grids is T. T is always greater than S. This is because incomplete Yee grids are needed to fill the edge of the triangular element, so the actual required number of Yee grids must be greater than the obtained area ratio. And since the scattered points are randomly generated, a larger number of filling points than the theoretical value needs to be selected to ensure full coverage of the Yee grid.
[0059] After determining the number of randomly filled points, it is necessary to determine the distribution of randomly scattered points in the triangular facets, and the scattered points should be distributed as evenly as possible in the triangular facets. The present invention uses the following random filling formula to calculate the three-dimensional coordinates of each scattered point:
[0060]
[0061] In the formula, (x, y, z) are the three-dimensional coordinates of the randomly scattered points, (x 1 , y 1 , z 1 ), (x 2 , y 2 , z 3 ) and (x 3 , y 3 , z 3 ) are the coordinates of the three vertices of the triangular facet, and u and v are random numbers drawn from 0 to 1.
[0062] After completing the scattered point filling, the Yee grid filling of the triangular facets is carried out, and the Yee grid is compared point by point. That is, the coordinates of the randomly scattered points are mapped to the problem space using the following formula to obtain the surface Yee grid of the model:
[0063]
[0064] Among them, (x f , y f , z f ) are the coordinates obtained by mapping the randomly scattered point coordinates (x, y, z) to the problem space, x min , y min , z min are the minimum values of the coordinates in the problem space, and dx, dy, and dz are the sizes of the Yee grid.
[0065] After completing the surface filling of the model, it is necessary to perform spatial region segmentation, that is, to perform material filling on the region to complete the volume filling of the model. Specifically: Set the model space boundary and the model surface as perfect electric conductors; Under the illumination of the excitation source, count the cumulative energy space distribution after the cumulative energy distribution in the entire model space tends to be stable, and use the region where the cumulative energy is less than the preset energy threshold as the range of the target model, that is, complete the volume filling of the model. The following is a specific implementation process of volume filling:
[0066] First, both the surface of the model and the boundaries of the three-dimensional space are set as PEC (Perfect Electric Conductor). Six uniform excitation sources are respectively set on the six internal faces of the region. The excitation sources use Gaussian waves. After several time steps, the energy released by the excitation sources cannot be transmitted and accumulates in the space. Eventually, the energy distribution in the entire space will tend to be stable. Thus, the entire space region can be divided into two parts according to energy. The region where the accumulated energy is greater than Ed (Ed is set to 10 -5 is relatively accurate and conforms to the actual theoretical value) is regarded as the region with energy, and this region is marked with 1; the region where the accumulated energy is less than Ed is regarded as the region without energy, and this region is marked with 0. Finally, the region marked with 0 is the range of the target model, and filling the material in this region completes the volume filling of the model.
[0067] To verify the effectiveness of the present invention, the dielectric sphere was meshed using the above method. After the meshing was completed, the FDTD algorithm was used for electromagnetic simulation calculation, and Figure 3 the meshing diagram and Figure 4 the RCS result diagram of the model were obtained. Figure 3 The FDTD space where the dielectric sphere is located and its model diagram are given. The external solid line is the CPML boundary, and the dashed line is the air layer boundary. The dielectric sphere in the space is irradiated by a plane wave (polarized in the z direction and propagating in the x direction). The waveform of the incident plane wave is a Gaussian wave. This problem space is composed of grid cells with a side length of 0.75 cm. The radius of the dielectric sphere is 10 cm, the relative permittivity is 3, the relative permeability is 2, and the number of simulation time steps is 2000. The output of this FDTD simulation is the far-field calculation at 1 GHz, and the RCS is calculated. Figure 4 The simulation results of the method of the present invention are compared with the analytical results. From Figure 4 it can be seen that the results of calculating the RCS by the method of the present invention are in good agreement with the analytical solution results, and thus the effectiveness of the method of the present invention can be obtained.
[0068] To verify whether there is progress in the efficiency of the meshing method of the present invention, the meshing method of the present invention is compared with the traditional ray tracing method in terms of meshing time. The surface of a sphere model with a radius of 50 m is meshed using the two methods. The comparison of the meshing times of the two methods is shown in Table 1. It can be seen from Table 1 that the method of the present invention is several times faster than the original ray tracing method in terms of time, improving the calculation efficiency.
[0069] Table 1 Comparison of computing resources
[0070] Yee grid size / m Ray tracing method meshing time / s Meshing time of the method of the present invention / s 1×1×1 31.17 0.91 0.9×0.9×0.9 44.84 0.96 0.8×0.8×0.8 46.91 1.18 0.7×0.7×0.7 57.62 1.48 0.6×0.6×0.6 74.18 2.10 0.5×0.5×0.5 101.66 2.91 0.4×0.4×0.4 151.70 4.58 0.3×0.3×0.3 257.15 10.02 0.2×0.2×0.2 272.35 7.04
Claims
1. An FDTD grid meshing method, comprising the step of converting the triangular facets of a model into the surface Yee grid of the model, characterized in that, The specific steps are as follows: First, determine the random filling points number n for each triangular element area , then fill n area randomly distributed scatter points in the corresponding triangular element, and finally map the coordinates of the random scatter points into the problem space to obtain the surface Yee grid of the model; the random filling points number n for each triangular element area is specifically determined by the following formula: Among them, is the maximum filling number, area max is the maximum value of the triangular facet area in the model, dx and dy are the sizes of the Yee grid, and α is a preset parameter ranging from 1 to 20; l 2 = l 1 / l max where l 1 is the average perimeter of the triangular facets in the model, and l max is the maximum value of the perimeters of the triangular facets in the model; the coordinates of the random scatter points are determined according to the following formula: where (x, y, z) are the three-dimensional coordinates of the random scatter points, (x 1 , y 1 , z 1 ), (x 2 , y 2 , z 3 ) and (x 3 , y 3 , z 3 ) are the three vertex coordinates of the triangular facet, and u, v are random numbers drawn from between 0 and 1; the following formula is used to map the coordinates of the random scatter points into the problem space: Among them, (x f , y f , z f ) are the coordinates obtained by mapping the random scatter point coordinates (x, y, z) into the problem space. x min , y min , z min are the minimum values of the coordinates in the problem space, and dx, dy, and dz are the sizes of the Yee grid.
2. The FDTD grid meshing method according to claim 1, characterized in that, The value of α is 10.
3. The FDTD grid meshing method according to claim 1 or 2, characterized in that, The grid meshing method further comprises the step of performing volume filling on the model after the conversion of the surface Yee grid is completed, specifically as follows: setting the model space boundary and the model surface as perfect electric conductors; under the illumination of an excitation source, statistically analyzing the cumulative energy space distribution after the cumulative energy distribution of the entire model space tends to be stable, and taking the region where the cumulative energy is less than a preset energy threshold as the range of the target model, that is, completing the volume filling of the model.
4. The FDTD grid meshing method according to claim 3, characterized in that, The excitation source is 6 Gaussian wave excitation sources.
5. The FDTD grid meshing method according to claim 3, characterized in that, The energy threshold is 10 -5 .
6. An FDTD electromagnetic calculation method, comprising the step of performing grid meshing on a model, characterized in that, The grid meshing is performed using the FDTD grid meshing method according to any one of claims 1 to 5.