A Non-Uniform Hexahedral Mesh Generation Method Based on Regional Density Distribution

Abstract

This invention discloses a non-uniform hexahedral mesh generation method based on the regional density distribution law, belonging to the field of software development technology, including the following steps: S1: For the solution target, triangular facets are used for mesh generation, and regions are divided according to different regional densities to obtain the maximum and minimum mesh size corresponding to each region; S2: After executing step S1, n regions are obtained. In the Cartesian coordinate system, mesh lines are generated sequentially along the three dimensions of x, y, and z. Optimization starts from the region with the smallest maximum mesh size. The advantages of this invention are: through modules such as the identification and calculation of the density distribution of triangular facet regions, the generation of three-dimensional mesh lines in the Cartesian coordinate system, the reconstruction of ray-intersecting hexahedral mesh, and mesh output, the conversion from triangular facet mesh to non-uniform hexahedral mesh is realized, solving the mesh generation and geometric target modeling problems of the finite-difference time-domain (FDTD) method.

Description

Technical Field

[0001] This invention relates to the field of software development technology, specifically to a non-uniform hexahedral mesh generation method based on the regional density distribution law. Background Technology

[0002] The Finite-Difference Time-Domain (FDTD) method for electromagnetic waves discretizes the computational domain in both space and time, using mesh generation to convert continuous electromagnetic fields into discrete data points for computation. In FDTD, space is typically divided into regular hexahedral meshes, and the time step is selected based on stability conditions. Electric and magnetic fields are stored alternately at different mesh locations and updated through spatiotemporal coupling to simulate electromagnetic wave propagation. To ensure the stability of the FDTD method, the mesh generation needs to meet certain size requirements. First, the ratio of adjacent mesh sizes should not be too large or too small; otherwise, the difference process of the algorithm will become extremely unstable or even diverge, affecting the simulation results. Second, to reduce the error caused by the stepped approximation surface and improve simulation accuracy, the size of the hexahedral mesh needs to be finely controlled, as this error is significantly inversely proportional to the mesh size.

[0003] Currently, converting triangular meshes into hexahedral meshes is the mainstream meshing method, and the uniform hexahedral meshing technique has matured. However, non-uniform hexahedral meshing techniques still face many bottlenecks that need to be overcome. The key challenges lie in: accurately defining the sparse and dense regions of the mesh, ensuring efficient generation of mesh lines with reasonable density while satisfying the size ratio constraints of adjacent meshes, and scientifically handling the issue of discarding redundant meshes. As a fundamental step in FDTD simulation calculations, the quality of hexahedral meshing directly affects the efficiency and accuracy of iterative calculations. Therefore, we propose a non-uniform hexahedral meshing method based on the regional density distribution law. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, at least one technical problem raised in the background art is solved.

[0005] This invention solves the above-mentioned technical problems by adopting the following technical solution: It provides a non-uniform hexahedral mesh generation method based on regional density distribution patterns, comprising the following steps:

[0006] S1: For the objective to be solved, triangular facets are used to mesh the area, and regions are divided according to different density to obtain the maximum and minimum mesh size for each region.

[0007] S2: After executing step S1, n regions will be obtained. In the Cartesian coordinate system, grid lines will be generated sequentially along the three dimensions of x, y, and z. Optimization will start from the region with the smallest maximum grid size. The minimum number of grids and grid size will be calculated based on the region range and the maximum grid size. Then, the grid lines of adjacent regions will be optimized in order, while satisfying the constraint of the ratio of adjacent grids.

[0008] S3: After executing step S2, perform intersection tests between rays parallel to the x, y, and z directions and the triangular mesh of the model. Use the space management container data structure to accelerate the reconstruction of the hexahedral mesh outline.

[0009] S4: After executing step S3, three Boolean three-dimensional matrices will be obtained to represent the hexahedral meshes to be removed and retained, and the non-uniform hexahedral mesh topology will be output according to the format.

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

[0011] Preferably, in step S2, the nth region The range of each region is determined by the vector. The maximum grid size of the region is The minimum grid size is The ratio of the adjacent grids is ,in, .

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

[0013] Assuming the area is Region, calculate minimum number of grid cells ;

[0014] calculate Mesh subdivision size on the region ;

[0015] An increasing sequence of generating grid lines .

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

[0017] like Then press simultaneously and Optimize grid lines in the order of regions in both directions;

[0018] like Then according to The order of regions optimizes the grid lines of the remaining regions;

[0019] like Then according to The order of regions optimizes the grid lines of the remaining regions.

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

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] Wherein, the ratio of adjacent grid step sizes is less than ,but and This indicates the maximum grid size required for the left and right critical points of the current region. This indicates the grid spacing that needs to be optimized for the current region.

[0027] Preferably, in step S2, the sequence after the grid lines of adjacent areas are arranged 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. This reduces the amount of computation required for simulation.

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

[0030] Preferably, in step S3, the space management container is a BVH data structure, where BVH stands for Hierarchical Bounding Box.

[0031] Compared with existing technologies, this invention provides a non-uniform hexahedral mesh generation method based on regional density distribution patterns, which has the following advantages: This non-uniform hexahedral mesh generation method based on regional density distribution patterns realizes the conversion from triangular element meshes to non-uniform hexahedral meshes through modules such as identification and calculation of triangular element regional density distribution, generation of three-dimensional mesh lines in Cartesian coordinate system, reconstruction of ray-intersecting hexahedral meshes, and mesh output. It solves the mesh generation and geometric target modeling problems of the finite-difference time-domain (FDTD) method. Compared with uniform hexahedral mesh generation, this invention can reduce the computational load of the FDTD numerical method for calculating the electromagnetic properties of complex targets to a certain extent. Attached Figure Description

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

[0033] Figure 2 This is a schematic diagram showing the size of the hexahedral mesh in each region of the present invention;

[0034] Figure 3 This is a schematic diagram showing the maximum grid size in each region of the present invention;

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

[0036] Figure 5 This is a schematic diagram of the intersection of the ray and the triangular facet of the present invention;

[0037] Figure 6 This is a schematic diagram of the origin of the rays in this invention (top view, with the ray direction pointing outwards from the paper);

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

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

[0040] Figure 9 This is a schematic diagram of the triangular mesh of the F-22 fighter jet according to the present invention;

[0041] Figure 10 This is a schematic diagram of the non-uniform hexahedral mesh of the F22 fighter jet according to the present invention. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] Please see Figure 1-10 A non-uniform hexahedral mesh generation method based on regional density distribution patterns includes the following steps:

[0044] S1: For the objective to be solved, triangular facets are used to mesh the area, and regions are divided according to different density to obtain the maximum and minimum mesh size for each region.

[0045] S2: After executing step S1, n regions will be obtained. In the Cartesian coordinate system, grid lines will be generated sequentially along the three dimensions of x, y, and z. Optimization will start from the region with the smallest maximum grid size. The minimum number of grids and grid size will be calculated based on the region range and the maximum grid size. Then, the grid lines of adjacent regions will be optimized in order, while satisfying the constraint of the ratio of adjacent grids.

[0046] S3: After executing step S2, perform intersection tests between rays parallel to the x, y, and z directions and the triangular mesh of the model. Use the space management container data structure to accelerate the reconstruction of the hexahedral mesh outline.

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

[0048] Specifically, after executing step S3, three Boolean three-dimensional matrices will be obtained. By combining the relevant grid line data, the topology of the entire non-uniform hexahedral mesh can be obtained, and then it will be output according to the relevant format.

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

[0050] Specifically, by using a density distribution and representation method for triangular facet regions in mesh partitioning, and employing multi-resolution clustering, triangular facets can be divided into several regions with different densities, resulting in different mesh sizes for each region. Figure 2 As shown, the horizontal axis represents the extent of the region, taking the x-direction as an example, and the vertical axis represents the grid size.

[0051] In this embodiment, in step S2, the nth region The range of each region is determined by the vector. 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 between adjacent grids is used to ensure the convergence of the electromagnetic wave time-domain finite difference method.

[0052] Specifically, after executing step S1, n regions will be obtained, and these n regions will be numbered respectively. To indicate, the first The range of each region is determined by vectors. This indicates that in a structured mesh, the grid lines are perpendicular to the Cartesian coordinate system in three dimensions. Parallel, therefore the Cartesian coordinate system can be split into independent... Three dimensions, and in order Dimension Dimension The grid line order in the dimensional dimension is optimized, and to ensure the convergence of the electromagnetic wave FDTD method, the ratio of adjacent grids must satisfy the following condition. ,in, .

[0053] In this embodiment, the optimization scheme for the region with the smallest maximum mesh size in step S2 is as follows:

[0054] Assuming the area is Region, calculate minimum number of grid cells ;

[0055] calculate Mesh subdivision size on the region ;

[0056] An increasing sequence of generating grid lines .

[0057] Specifically, to optimize Taking dimensions as an example, we will start from Optimization begins in the region denoted as '[', ']'. For a given region, to minimize the computational cost of the simulation, the mesh size must be as close as possible to the specified size. The formula for obtaining the minimum number of grids required to partition the region is: The formula for obtaining the mesh size in this region is: The grid lines can be laid out using the steps described above, and then an increasing sequence can be used. Show out.

[0058] In this embodiment, step S2, which involves optimizing the grid lines of adjacent regions in sequence, is as follows:

[0059] like Then press simultaneously and Optimize grid lines in the order of regions in both directions;

[0060] like Then according to The order of regions optimizes the grid lines of the remaining regions;

[0061] like Then according to The order of the regions optimizes the grid lines of the remaining regions. In step S2, the sequence after the grid lines of adjacent regions are arranged is as follows: .

[0062] Specifically, by optimizing the grid lines of adjacent areas sequentially, the grid lines in that area can be arranged completely, which can be achieved by a sequence of numbers. Output the results in a table.

[0063] In this embodiment, during step S2, the constraint condition for optimizing the grid lines of adjacent regions is:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] Wherein, the ratio of adjacent grid step sizes is less than ,but and This indicates the maximum grid size required for the left and right critical points of the current region. This indicates the grid spacing that needs to be optimized for the current region.

[0070] Specifically, it is necessary to determine a scheme to optimize adjacent grid lines in order to optimize... Taking dimensions as an example, let the grid size in this region be . The area is The maximum value of the grid is If the adjacent left region has been optimized, then it is known If the adjacent right region has been optimized, then it is known that... When the ratio condition between adjacent grids is met, the optimization of grid lines in adjacent regions should follow the above formula constraints, thereby making... Take the smallest value.

[0071] More specifically, after all region grid sizes have been optimized, the following can be obtained: Figure 4 The chart shown has the horizontal axis representing the interval and the vertical axis representing the grid size within that interval. The grid lines are now 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. This reduces the amount of computation required for simulation.

[0073] Specifically, to reduce the computational load of simulations, when generating mesh lines for the corresponding dimensions, it is necessary to get as close as possible to the maximum mesh size of each region, thereby reducing the number of hexahedral meshes. Figure 3 The maximum grid size of each region is presented as a piecewise function, excluding points marked with hollow circles.

[0074] In this embodiment, in step S3, the space management container is a BVH data structure, where BVH stands for Hierarchical Bounding Box.

[0075] Specifically, after executing S2, the constructed mesh outline will inevitably be a cuboid. At this point, ray intersection must be performed to reconstruct the model mesh outline. When reconstructing the entire 3D model mesh outline, parallel to... Rays in three directions are intersected with the model's triangular mesh to reconstruct the hexahedral mesh profile. This process can be accelerated using a space management container, which can accelerate the BVH data structure. Intersection of each ray can also be accelerated in parallel to speed up mesh generation.

[0076] More specifically, in the Cartesian coordinate system, the rays are respectively along... axis, axis, Axial emission is performed, calculating the intersection points where the ray enters and exits the triangle. All hexahedral cells within the intersection points are marked as preserved, such as... Figure 5 As shown, the origin of the ray is taken as the center point of the cell, and the ray is parallel to... Taking the shaft as an example, Figure 6 The lines represent grid lines generated on the plane, and the points represent the origin of ray emission.

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

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

Claims

1. A method for non-uniform hexahedral mesh generation based on regional density distribution patterns, characterized in that, It includes the following steps: S1: For the solution target, triangular facets are used for mesh discretization, and regions are divided according to different regional densities to obtain the maximum and minimum mesh sizes corresponding to each region; S2: After performing step S1, n regions are obtained. In the Cartesian coordinate system, grid lines are generated successively in the three dimensions of x, y, and z; starting from the region with the smallest maximum mesh size for optimization, calculate the minimum number of grids and the mesh discretization size of this region to generate an increasing sequence of grid lines; then optimize the grid lines of adjacent regions in the following order: if the starting optimization region is the t-th region, when 1 < t < n, optimize in the two directions of t - 1, t - 2...1 and t + 1, t + 2...n simultaneously; when t = 1, optimize in the order of t + 1, t + 2...n; when t = n, optimize in the order of t - 1, t - 2...1; during the optimization process, the constraint that the ratio of adjacent grids does not exceed the preset maximum value Rmax is satisfied, and the mesh size is as close as possible to the maximum mesh size of the region; S3: After performing step S2, ray intersection tests between the rays parallel to the three directions of x, y, and z and the triangular facet mesh of the model are respectively carried out, and the spatial management container data structure is used for acceleration to reconstruct the hexahedral mesh contour; S4: After performing step S3, three boolean three-dimensional matrices for representing the hexahedral meshes to be removed and retained are obtained, and the non-uniform hexahedral mesh topology structure is output in a format; In step S2, the range of the i-th region among the n regions is represented by the vector, where the maximum mesh size of the region is, the minimum mesh size is, and the ratio of adjacent grids is, where Rmax > 1; In step S2, the steps for optimizing the grid lines of adjacent regions in order are: If 1 < t < n, then optimize the grid lines in the order of the regions in the two directions of t - 1, t - 2,...1 and t + 1, t + 2,...n simultaneously; If t = 1, then optimize the grid lines of the remaining regions in the order of the regions of t + ​ ​ 2. The non-uniform hexahedral mesh generation method based on regional density distribution law according to claim 1, characterized in that: ​ 3. The non-uniform hexahedral mesh generation method based on regional density distribution law according to claim 1, characterized in that: ​ Assuming the area is Region, calculate minimum number of grid cells ; calculate Mesh size on the region ; An increasing sequence of generating grid lines .

4. The non-uniform hexahedral mesh generation method based on regional density distribution law according to claim 1, characterized in that: ​ ； ； ； ； ； Wherein, the ratio of adjacent grid step sizes is less than ,but and This indicates the maximum grid size required for the left and right critical points of the current region, and D1, D2, ..., DW represent the grid spacing that needs to be optimized for the current region.

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 sequence after the grid lines of adjacent areas are arranged is as follows: .

6. The non-uniform hexahedral mesh generation method based on regional density distribution law according to claim 1, characterized in that: ​

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