Non-uniform hexahedral mesh generation method based on regional density distribution rule

Abstract

The invention discloses a non-uniform hexahedral mesh generation method based on a region density distribution rule, and relates to the technical field of software development technologies, and the method comprises the following steps: S1, for a solving target, carrying out mesh generation by adopting triangular surface elements, and dividing regions according to different region densities to obtain the maximum and minimum mesh sizes corresponding to each region; s2, after the step S1 is executed, grid lines are sequentially generated in the Cartesian coordinate system according to the x dimension, the y dimension and the z dimension, optimization is started from the area with the minimum maximum grid size, and the maximum grid size is obtained; the method has the advantages that the conversion from a triangular surface element grid to a non-uniform hexahedral grid is realized through modules for identifying and calculating the density distribution of a triangular surface element region, generating three-dimensional grid lines of a Cartesian coordinate system, reconstructing a ray intersecting hexahedral grid, outputting the grid and the like; the problems of mesh generation and geometric target modeling of a finite difference time domain (FDTD) method are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of software development technology, in particular to a non-uniform hexahedral mesh partitioning method based on regional density distribution law. BACKGROUND

[0002] The finite-difference time-domain (FDTD) method discretizes the spatial and temporal domains of the computational region, converting continuous electromagnetic fields into discrete data points for calculation by using mesh partitioning. In the FDTD method, the space is usually divided into regular hexahedral meshes, and the time step is selected according to the stability condition. The electric and magnetic fields are stored alternately at different mesh positions and updated through time-space coupling to simulate the propagation of electromagnetic waves. To ensure the stability of the FDTD method, the mesh partitioning needs to meet certain size requirements. First, the ratio of the sizes of adjacent meshes should not be too large or too small, otherwise the difference process of the algorithm will become very unstable or even divergent, affecting the simulation results. Second, to reduce the error caused by the stepped approximation surface and improve the simulation accuracy, the size of the hexahedral mesh needs to be finely controlled, because the error is inversely proportional to the mesh size.

[0003] Currently, converting the triangular facet mesh of a model into a hexahedral mesh is the mainstream partitioning method, and the uniform hexahedral mesh partitioning technology has been well developed. However, the non-uniform hexahedral mesh partitioning technology still has many bottlenecks that need to be broken through. The key difficulties focus on accurately defining the sparse and dense regions of the mesh, ensuring efficient generation of reasonable mesh lines under the constraint condition of the ratio of adjacent mesh sizes, and scientifically handling the selection problem of redundant meshes. As a basic link of FDTD simulation calculation, the quality of hexahedral mesh partitioning directly affects the efficiency and accuracy of iterative calculation. Therefore, we propose a non-uniform hexahedral mesh partitioning method based on regional density distribution law. SUMMARY

[0004] To make up for the shortcomings of the prior art and solve at least one technical problem proposed in the background art.

[0005] The present application solves the above technical problems by adopting the following technical solutions: a non-uniform hexahedral mesh partitioning method based on regional density distribution law is provided, comprising the following steps:

[0006] S1: For the solution target, triangular facets are used for mesh partitioning, and regions are divided according to different regional densities to obtain the maximum and minimum mesh sizes corresponding to each region;

[0007] S2: After step S1, n regions are obtained, grid lines are generated in x, y, z three dimensions in turn, starting from the region with the smallest maximum grid size, the minimum number of grids and grid size are calculated according to the region range and the maximum grid size, then the grid lines of adjacent regions are optimized in turn, and the constraint of the ratio of adjacent grids is met;

[0008] S3: After step S2, ray intersection test is performed on the triangular facet grid of the model in parallel to the x, y, z three directions, and a spatial management container data structure is used for acceleration to reconstruct the hexahedral grid profile;

[0009] S4: After step S3, three Boolean three-dimensional matrices for representing the hexahedral grids to be removed and retained are obtained, and the non-uniform hexahedral grid topology structure is output in a format.

[0010] Preferably, in step S1, the method for dividing the region density is a multi-resolution clustering method.

[0011] Preferably, in step S2, the range of the n-th region in the n regions is determined by the vector , wherein the maximum grid size of the region is , the minimum grid size is , and the ratio of adjacent grids is . , wherein .

[0012] Preferably, in step S2, the optimization scheme of the region with the smallest maximum grid size is as follows:

[0013] Assuming that the region is region , the minimum number of grids is calculated as .

[0014] The grid subdivision size on the region is calculated as .

[0015] An increasing sequence of grid lines is generated. .

[0016] Preferably, in step S2, the step of optimizing the grid lines of adjacent regions in turn is as follows:

[0017] If , the grid lines of the regions in the x and y directions are optimized at the same time; .

[0018] If , the grid lines of the remaining regions are optimized in the order of the regions in the x direction; . ​

[0019] like , then press The order of the regions optimizes the grid lines of the remaining regions.

[0020] Preferably, in step S2, when optimizing the grid lines of adjacent regions, the constraint conditions are:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] In which, suppose the ratio of adjacent grid steps is less than ,but and Indicates the maximum grid size required by the critical points on the left and right sides of the current area. Indicates the grid spacing that needs to be optimized in the current area.

[0027] Preferably, in step S2, the sequence of grid lines in adjacent areas after arrangement is as follows: .

[0028] Preferably, in step S2, when generating the grid lines, the grid size is made as close as possible to the maximum grid size of the region. , in order to reduce the amount of simulation calculations.

[0029] Preferably, in step S2, the ratio constraint between adjacent grids is used to ensure the convergence of the electromagnetic wave finite-difference time-domain method.

[0030] Preferably, in step S3, the space management container is a BVH data structure, wherein BVH is a hierarchical bounding box.

[0031] Compared with the existing technology, the present invention provides a non-uniform hexahedral mesh generation method based on the regional density distribution law, which has the following beneficial effects: this non-uniform hexahedral mesh generation method based on the regional density distribution law realizes the conversion from triangular facet mesh to non-uniform hexahedral mesh through modules such as identification and calculation of regional density distribution of triangular facets, generation of three-dimensional grid lines in Cartesian coordinate system, reconstruction of ray intersection hexahedral mesh, and mesh output, thereby solving the mesh generation and geometric target modeling problems of the finite difference time domain (FDTD) method. Compared with uniform hexahedral mesh generation, the present invention can reduce the computational complexity of the FDTD numerical method in calculating the electromagnetic properties of complex targets to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the program flow structure of the present invention;

[0033] Figure 2 Schematic diagram of the hexahedral mesh size of each region of the present invention;

[0034] Figure 3 Schematic diagram of the maximum grid size of each area of ​​the present invention;

[0035] Figure 4 This is a schematic diagram of the actual grid size of each area after optimization of the present invention;

[0036] Figure 5 Schematic diagram of the intersection of rays and triangular surface elements of the present invention;

[0037] Figure 6 Schematic diagram of the ray origin of the present invention (top view, ray direction facing outward from the paper);

[0038] Figure 7 A schematic diagram of a triangular mesh of a glider according to the present invention;

[0039] Figure 8 is a schematic diagram of a hexahedral mesh of a glider of the present invention;

[0040] Figure 9 This is a schematic diagram of the triangular mesh of an F22 fighter jet of the present invention;

[0041] Figure 10 This is a schematic diagram of the non-uniform hexahedral grid of the F22 fighter jet of the present invention. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0043] See also Figure 1-10 , a non-uniform hexahedral meshing method based on regional density distribution law, comprising the following steps:

[0044] S1: For the solution target, triangular surface elements are used for mesh generation, and regions are divided according to different regional densities to obtain the maximum and minimum mesh sizes corresponding to each region;

[0045] S2: After executing step S1, n regions are obtained. In the Cartesian coordinate system, grid lines are generated in sequence according to the x, y, and z dimensions. The optimization starts from the region with the smallest maximum grid size. The minimum number of grids and grid size are calculated based on the region range and the maximum grid size. The grid lines of adjacent regions are then optimized in sequence, and the ratio constraint of adjacent grids is satisfied.

[0046] S3: After executing step S2, the intersection test between the rays parallel to the x, y, and z directions and the triangular facet mesh of the model is performed respectively, and the spatial management container data structure is used for acceleration to reconstruct the hexahedral mesh outline;

[0047] S4: After executing step S3, three Boolean three-dimensional matrices representing the hexahedral meshes to be removed and retained are obtained, and the non-uniform hexahedral mesh topology structure is output according to the format.

[0048] Specifically, after executing step S3, three Boolean three-dimensional matrices are obtained. When combined with the grid line related data, the topological structure of the entire non-uniform hexahedral grid can be obtained, and then output according to the relevant format.

[0049] In this embodiment, in step S1 , the method for dividing regional density is a multi-resolution clustering method.

[0050] Specifically, through a density distribution and representation method of the triangular surface area in the mesh subdivision, the multi-resolution clustering method can be used to divide the triangular surface into several areas with different densities, and obtain different mesh sizes corresponding to each area, such as Figure 2 As shown, the horizontal axis represents the range of the area, taking the x direction as an example here, and the vertical axis represents the grid size.

[0051] In this embodiment, in step S2, the first The region is bounded by the vector , where the maximum grid size of the region is , the minimum grid size is , the ratio of adjacent grids is ,in, ,In step S2, the ratio constraint of adjacent grids is used to ensure the convergence of ,the electromagnetic wave finite-difference time-domain method.

[0052] Specifically, after executing step S1, n areas will be obtained, and the n areas are numbered To express, The region is bounded by the vector In structured grids, the grid lines are aligned with the Cartesian coordinate system in three dimensions. Parallel, so the Cartesian coordinate system can be split into independent Three dimensions, and press Dimension, Dimension, The order of grid lines in the dimension is optimized, and in order to ensure the convergence of the electromagnetic wave FDTD method, the ratio of adjacent grids must meet ,in, .

[0053] In this embodiment, in step S2, the optimization scheme for the area with the smallest maximum grid size is:

[0054] Assume that the area is Area, calculate the minimum number of grids ;

[0055] calculate Mesh size on the region ;

[0056] Generate an increasing sequence of grid lines .

[0057] Specifically, to optimize Dimension as an example, we will start from The optimization starts from the area of In order to minimize the amount of simulation calculation, the grid size of this area must be as close as possible to , the formula for obtaining the minimum number of grids for dividing the region is , the formula for obtaining the mesh size in this area is , the grid lines can be arranged through the above steps, and then the grid lines can be arranged by increasing the number of Show out.

[0058] In this embodiment, in step S2, the steps of sequentially optimizing the grid lines of adjacent regions are:

[0059] like , then press and Sequential optimization grid lines for regions in two directions;

[0060] like , then press The order of regions optimizes the grid lines of the remaining regions;

[0061] like , then press The order of the regions is optimized for the grid lines of the remaining regions. In step S2, the sequence of grid lines of adjacent regions after arrangement is completed is: .

[0062] Specifically, by sequentially optimizing the steps of the grid lines of adjacent regions, the grid lines on the region can be arranged, which can be represented by the sequence: Perform the table.

[0063] In this embodiment, in step S2, when optimizing the grid lines of adjacent regions, the constraints are:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] In which, suppose the ratio of adjacent grid steps is less than ,but and Indicates the maximum grid size required by the critical points on the left and right sides of the current area. Indicates the grid spacing that needs to be optimized in the current area.

[0070] Specifically, we need to determine the solution to optimize adjacent grid lines to optimize dimension as an example, let the grid size in this area be , the area range is , the maximum value of the grid is , if the adjacent left area has been optimized, then it is known that , if the adjacent right region has been optimized, then it is known that , when the ratio condition of adjacent grids is met, the optimization of the grid lines in the adjacent areas should follow the above formula constraints, so that The minimum value.

[0071] More specifically, after all the area grid sizes are optimized, we can get the following: Figure 4 In the chart shown, the horizontal axis represents the interval, and the vertical axis represents the grid size on the interval. At this point, the grid lines are generated.

[0072] In this embodiment, in step S2, when generating grid lines, the grid size is made as close as possible to the maximum grid size of the region. , in order to reduce the amount of simulation calculations.

[0073] Specifically, in order to reduce the amount of simulation calculations, when generating grid lines of corresponding dimensions, it is necessary to keep them as close as possible to the maximum grid size of each area to reduce the number of hexahedral grids. Figure 3 The maximum grid size of each region is presented as a piecewise function, where the points marked by hollow circles are excluded.

[0074] In this embodiment, in step S3, the space management container is a BVH data structure, where BVH is a hierarchical bounding box.

[0075] Specifically, after executing S2, the constructed mesh outline must be a cuboid. At this time, ray intersection must be performed to reconstruct the model mesh outline. When reconstructing the entire 3D model mesh outline, it is necessary to perform ray intersections parallel to the mesh outline. The rays in three directions are tested for intersection with the triangular face mesh of the model to reconstruct the hexahedral mesh outline. This process can use a space management container, which can accelerate the BVH data structure. The intersection of each ray can also be accelerated in parallel to speed up the mesh generation time.

[0076] More specifically, in the Cartesian coordinate system, the rays are respectively axis, axis, Axis emission, calculate the intersection of the ray entering and leaving the triangle, all hexahedral cells between the intersections are marked as retained, such as Figure 5 As shown, the origin of the ray is the center of the cell, and the ray is parallel to Take the axis as an example, Figure 6 The lines represent the grid lines generated on the plane, and the dots represent the origins of the ray emission.

[0077] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0078] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A non-uniform hexahedral meshing method based on regional density distribution law, characterized in that: The following steps are involved: S1: For the solution target, triangular surface elements are used for mesh generation, and regions are divided according to different regional densities to obtain the maximum and minimum mesh sizes corresponding to each region; S2: After executing step S1, n regions are obtained. In the Cartesian coordinate system, grid lines are generated in sequence according to the x, y, and z dimensions. The optimization starts from the region with the smallest maximum grid size. The minimum number of grids and grid size are calculated based on the region range and the maximum grid size. The grid lines of adjacent regions are then optimized in sequence, and the ratio constraint of adjacent grids is satisfied. S3: After executing step S2, the intersection test between the rays parallel to the x, y, and z directions and the triangular facet mesh of the model is performed respectively, and the spatial management container data structure is used for acceleration to reconstruct the hexahedral mesh outline; S4: After executing step S3, three Boolean three-dimensional matrices representing the hexahedral meshes to be removed and retained are obtained, and the non-uniform hexahedral mesh topology structure is output according to the format.

2. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 1, characterized in that: In step S1, the method for dividing regional density is a multi-resolution clustering method.

3. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 2, characterized in that: In step S2, the first The region is bounded by the vector , where the maximum grid size of the region is , the minimum grid size is , the ratio of adjacent grids is ,in, .

4. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 3, characterized in that: In step S2, the optimization scheme for the area with the smallest maximum grid size is: Assume that the area is Area, calculate the minimum number of grids ; calculate Mesh size on the region ; Generate an increasing sequence of grid lines .

5. The non-uniform hexahedral mesh generation method based on regional density distribution law according to claim 4, characterized in that: In step S2, the steps of sequentially optimizing the grid lines of adjacent regions are: like , then press and Sequential optimization grid lines for regions in two directions; like , then press The order of regions optimizes the grid lines of the remaining regions; like , then press The order of the regions optimizes the grid lines of the remaining regions.

6. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 5, characterized in that: In step S2, when optimizing the grid lines of adjacent regions, the constraints are: ； ； ； ； ； In which, suppose the ratio of adjacent grid steps is less than ,but and Indicates the maximum grid size required by the critical points on the left and right sides of the current area. Indicates the grid spacing that needs to be optimized in the current area.

7. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 6, characterized in that: In step S2, the sequence after the grid lines of adjacent areas are arranged is: .

8. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 7, characterized in that: In step S2, when generating the grid lines, the grid size is made as close as possible to the maximum grid size of the region. , in order to reduce the amount of simulation calculations.

9. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 1, characterized in that: In step S2, the ratio constraint between adjacent grids is used to ensure the convergence of the electromagnetic wave finite-difference time-domain method.

10. The non-uniform hexahedral meshing method based on regional density distribution law according to claim 1, characterized in that: In step S3, the space management container is a BVH data structure, where BVH is a hierarchical bounding box.

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