A method for generating a volume grid based on a cylindrical surface grid radial growth

Abstract

The application relates to a method for generating a body grid based on radial growth of a cylindrical surface grid, in the field of electromagnetic engineering, and the method comprises the following steps: reading cylindrical surface grid data, including a point list P containing three-dimensional coordinates of N p points, a triangular element list E containing vertex indexes of E e triangular elements, and an element material list M; screening target elements through material matching; establishing a local coordinate system satisfying the right-hand rule and the orthogonal normalization condition of a vector, and performing coordinate transformation; performing radial mapping on the vertices of the screened elements; inversely transforming the mapped points to a world coordinate system; and generating a body grid, and converting a six-vertex triangular prism into three four-vertex tetrahedron elements by using a topological decomposition method. The electromagnetic calculation precision is improved: in electromagnetic field design calculation, the cylindrical radial grid growth technology makes the grid resolution in a strong field area multiply, and the calculation error of a resonance frequency is less than or equal to 0.3%.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic engineering, and more particularly to a method for generating volume meshes based on radial growth of cylindrical surface meshes. Background Technology

[0002] Currently, cylindrical structures are widely used in various key equipment in the field of electromagnetic engineering. Their unique geometry presents unique challenges to mesh generation technology. These structures not only have basic physical functions but also directly affect the electromagnetic field distribution characteristics and equipment performance. For example, 1. Equipment such as coaxial waveguides and microwave resonant cavities rely on precise cylindrical meshes to describe the propagation characteristics of electromagnetic waves. Taking coaxial cables as an example, the cylindrical structure formed by its inner and outer conductors requires high-fidelity meshing to accurately calculate the cutoff frequency and attenuation constant of the TEM wave. 2. Cylindrical conformal microstrip antennas and soft surface electromagnetic bandgap (EBG) structures rely on curved surfaces to achieve beamforming, and their radiation patterns are extremely sensitive to the deformation of the curved mesh. Studies have shown that when the mesh distortion rate of a cylindrical microstrip antenna exceeds 5%, the sidelobe level increases by 2-4 dB, seriously affecting the performance of the radar system.

[0003] Current mainstream mesh generation techniques in electromagnetic simulation face three major challenges when dealing with cylindrical structures, severely limiting computational accuracy and efficiency: 1. Topological constraints of the sweep mesh method: This method generates hexahedral / triangular prism meshes by stretching a two-dimensional surface mesh. While suitable for simple cylinders, it struggles to handle multi-branch curvature structures (such as waveguide bends and flange connections). 2. Geometric distortion of global parameterization methods: Traditional parameterization mapping uses a uniform scaling strategy on the cylindrical side surface, ignoring local curvature variations. 3. Functional limitations of the inflation layers method: Although it can generate high-quality prismatic meshes in fluid boundary layers, it suffers from insufficient directional adaptability when applied to electromagnetic fields. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for generating volume meshes based on radial growth of cylindrical surface meshes, thus solving the deficiencies of the prior art.

[0005] The objective of this invention is achieved through the following technical solution: a method for generating a volume mesh based on radial growth of a cylindrical surface mesh, the method comprising:

[0006] Step 1: Read the cylindrical mesh data, including data containing N. p A list of points P containing the three-dimensional coordinates of points E.e A list of triangular elements E and a list of element materials M with vertex indices for each triangular element;

[0007] Step 2: Screen target units through material matching;

[0008] Step 3: Establish a local coordinate system that satisfies the right-hand rule and the orthogonality and normalization condition of vectors, and perform coordinate transformation;

[0009] Step 4: Perform radial mapping on the vertices of the filtering unit;

[0010] Step 5: Transform the mapped points to the world coordinate system;

[0011] Step 6: Generate the volume mesh by using topological decomposition to convert the 6-vertex triangular prism into 3 4-vertex tetrahedral elements.

[0012] Step two specifically includes:

[0013] Specify target material number ;

[0014] Filter from the triangular element list E that satisfies the condition if and only if the element material number M [j] The element that is equal to the specified material number M0 is selected into the target element set E', where j represents the element number;

[0015] Record the number of units N obtained from the filtering.

[0016] Step three specifically includes:

[0017] Take point P on the circumference of the base. d Calculate the unit radial vector P c Represents the bottom dot;

[0018] Calculate the tangential vector , with P c With the origin as the point, , and Establish a local coordinate system C for the basis vectors;

[0019] each point Change to local coordinates , x , y and z The coordinates of the axes are respectively represented as , and ,in, , , These are the local coordinates in the x, y, and z directions. , , The radial unit vector consists of x, y, and z components. The x, y, and z components are the tangential unit vectors. , The x, y, and z components are the axial unit vectors. , The x, y, and z coordinates of the origin on the bottom surface. , These represent the coordinates on the x, y, and z axes, respectively.

[0020] In step four, the radial mapping satisfies the condition that the axial coordinate remains constant. Radial deformation rate Compared with the original radial distance Inversely proportional;

[0021] For the target unit set E', the first j The k-th vertex of the unit Calculate radial distance Calculate the radial deformation rate The coordinates of the three axes of the calculated mapping point are respectively , and , , and The mapping points of the k-th vertex are respectively in x , y and z The coordinates of the axis. The k-th vertex is located at x , y and z The coordinates of the axis. This indicates the radial growth amount.

[0022] Step five specifically includes: inversely transforming the mapped points to the world coordinate system to obtain the coordinates. According to the mapping point , obtain coordinates The three coordinate points are respectively , and .

[0023] Step six specifically includes:

[0024] For each filter unit Connect its original vertex to the point This forms a triangular prism grid;

[0025] The triangular prism mesh is decomposed into three tetrahedral meshes.

[0026] The present invention has the following advantages:

[0027] 1. Improved accuracy of electromagnetic calculations: In electromagnetic field design calculations, the cylindrical radial mesh growth technology doubles the mesh resolution in strong field regions, and the resonant frequency calculation error is ≤0.3% (compared to ≥1.5% by traditional methods).

[0028] 2. Breakthrough optimization of modeling efficiency: Material numbering Automatic binding with electromagnetic properties. The time for generating cylindrical meshes has been reduced from 8-12 hours to less than 1 hour, and the efficiency of parameterized iteration has been improved by 10 times.

[0029] 3. Multi-scenario adaptability advantage: In electromagnetic field design, the waveguide bend model reduces the mesh distortion rate from >25% to <3%, and the helical slow wave structure achieves decoupling control of axial-radial deformation.

[0030] 4. Field computation resource optimization: In electromagnetic simulation calculations, the memory usage of coaxial transmission line simulation in cylindrical coordinates is reduced by 65%. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the process of the present invention;

[0032] Figure 2 This is a diagram of a cylindrical mesh model.

[0033] Figure 3 Match material number The model diagram afterward;

[0034] Figure 4 This is a schematic diagram of coordinate mapping for a cylindrical surface.

[0035] Figure 5 This is a schematic diagram of a triangular prism mesh. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application provided below with reference to the accompanying drawings is not intended to limit the scope of protection of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The present invention will be further described below with reference to the accompanying drawings.

[0037] This invention specifically relates to a method for generating volumetric meshes using radial growth of cylindrical meshes in the electromagnetic field. It provides a radial growth technique for cylindrical meshes that can be applied to electromagnetic field analysis. By establishing a parametric geometric model of the electromagnetic device and using material-driven radial growth of cylindrical meshes, a three-dimensional volumetric mesh suitable for electromagnetic field calculations can be accurately generated. The radial growth amount can be controlled... It can realize parametric deformation of electromagnetic equipment structures, helping engineers and researchers analyze the coupling effect between electromagnetic fields and structural deformation, such as the effect of conductor corrosion on impedance characteristics and the change of resonant frequency due to thermal expansion, thereby improving equipment performance and efficiency.

[0038] like Figure 1 and Figure 2 As shown, it specifically includes the following:

[0039] S1. Read the cylindrical mesh data, including:

[0040] S101, Point list P, containing N p The three-dimensional coordinates of each point;

[0041] S102, Triangular unit list E, containing E e Vertex indices of each triangular unit;

[0042] S103, Unit Material List M.

[0043] S2, such as Figure 3 As shown, target units are selected through material matching. The material matching adopts an exact number matching method, that is, the matching occurs if and only if the unit material number M... [j] When the value equals the specified material number M0, the element is selected into the target element set E', where j is a variable (0~n) representing the element number.

[0044] S201, Specify the target material number ;

[0045] S202. Select triangular elements from the triangular element list E that meet the requirements for radial growth of the cylindrical surface (M) [j] ==M0 )set E';

[0046] S203, Record the number of filter units N.

[0047] S3. Establish a local coordinate system and perform coordinate transformations. The local coordinate system must satisfy the right-hand rule, and the basis vectors must satisfy the orthogonality normalization condition. , ,in, , , Represents the radial, tangential, and axial unit vectors of the local coordinate system.

[0048] S301, Take point P on the circumference of the bottom surface. d Calculate the unit radial vector P c Represents the bottom dot;

[0049] S302, Calculate the tangential vector ; with P c With the origin as the point, , and Establish a local coordinate system C for the basis vectors;

[0050] S303, each point Change to local coordinates The three coordinate points are represented as follows:

[0051] ,

[0052] ,

[0053] .

[0054] in, , , These are the local coordinates in the x, y, and z directions. , , The radial unit vector consists of x, y, and z components. The x, y, and z components are the tangential unit vectors. , The x, y, and z components are the axial unit vectors. , The x, y, and z coordinates of the origin on the bottom surface. , These represent the coordinates on the x, y, and z axes, respectively.

[0055] S4, such as Figure 4 As shown, radial mapping is performed on the vertices of the filtering unit, where the radial mapping satisfies the following condition: the axial coordinates remain constant. Radial deformation rate radial distance Inversely proportional to the first term in E' j The k-th vertex of the unit ; Calculate radial distance Calculate the radial deformation rate The coordinates of the three axes of the calculated mapping point are respectively , and , , and The mapping points of the k-th vertex are respectively in x , y and z The coordinates of the axis. The k-th vertex is located at x , y and z The coordinates of the axis. This indicates the radial growth amount.

[0056] S5. Inversely transform the mapped points to world coordinates. According to the mapping point The three coordinate points are as follows:

[0057] ,

[0058] ,

[0059] .

[0060] S6, such as Figure 5 As shown, when generating a volume mesh, the triangular prism mesh is decomposed into a tetrahedral mesh. The topological decomposition method is used to convert the 6-vertex triangular prism into 3 4-vertex tetrahedral elements to maintain geometric continuity.

[0061] S601, For each filtering unit Connect its original vertex to the point This forms a triangular prism grid;

[0062] S602. Decompose the triangular prism mesh into 3 tetrahedral meshes.

[0063] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and improvements, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for generating volume meshes based on radial growth of cylindrical surface meshes, characterized in that: The method includes: Step 1: Read the cylindrical mesh data, including data containing N. p A list of points P containing the three-dimensional coordinates of points E. e A list of triangular elements E and a list of element materials M with vertex indices for each triangular element; Step 2: Screen target units through material matching; Step 3: Establish a local coordinate system that satisfies the right-hand rule and the orthogonality and normalization condition of vectors, and perform coordinate transformation; Step 4: Perform radial mapping on the vertices of the filtering unit; Step 5: Transform the mapped points to the world coordinate system; Step 6: Generate the volume mesh by using topological decomposition to convert the 6-vertex triangular prism into 3 four-vertex tetrahedral elements; Specify target material number ; Filter from the triangular element list E that satisfies the condition if and only if the element material number M [j] The element that is equal to the specified material number M0 is selected into the target element set E', where j represents the element number; Record the number of units N obtained from the filtering process; In step four, the radial mapping satisfies the condition that the axial coordinate remains constant. Radial deformation rate Compared with the original radial distance Inversely proportional; For the k-th vertex of the j-th element in the target element set E' Calculate radial distance Calculate the radial deformation rate The coordinates of the three axes of the calculated mapping point are respectively , and , , and Let be the coordinates of the mapping point of the k-th vertex on the x, y, and z axes, respectively. Let x, y, and z be the coordinates of the k-th vertex on the x, y, and z axes, respectively. This indicates the radial growth amount.

2. The method for generating a volume mesh based on radial growth of a cylindrical surface mesh according to claim 1, characterized in that: Step three specifically includes: Take point P on the circumference of the base. d Calculate the unit radial vector P c Represents the bottom dot; Calculate the tangential vector , with P c With the origin as the point, , and Establish a local coordinate system C for the basis vectors; each point Change to local coordinates The coordinates of the x, y, and z axes are respectively represented as , and ,in, , , These are the local coordinates in the x, y, and z directions. , , The radial unit vector consists of x, y, and z components. The x, y, and z components are the tangential unit vectors. , The x, y, and z components are the axial unit vectors. , The x, y, and z coordinates of the origin on the base surface. , These represent the coordinates on the x, y, and z axes, respectively.

3. The method for generating a volume mesh based on radial growth of a cylindrical surface mesh according to claim 1, characterized in that: Step five specifically includes: inversely transforming the mapped points to the world coordinate system to obtain the coordinates. According to the mapping point , obtain coordinates The three coordinate points are respectively , and .

4. The method for generating a volume mesh based on radial growth of a cylindrical surface mesh according to claim 3, characterized in that: Step six specifically includes: For each filter unit Connect its original vertex to the point This forms a triangular prism grid; The triangular prism mesh is decomposed into three tetrahedral meshes.

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