Method for generating a cross-scale large-scale electromagnetic surface mesh with periodic fine features

Abstract

The application discloses a cross-scale large-scale electromagnetic surface grid generation method with periodic fine features, comprising the following steps: reading a cross-scale electromagnetic geometric model with periodic fine features, setting a replication direction and a number; setting a periodic boundary condition of the electromagnetic geometric model, determining a source surface and a target surface of the replication direction, extracting a boundary line, and establishing a mapping relationship between the source surface, the target surface and the boundary line; discretizing the electromagnetic geometric model to generate a discrete background triangular grid; generating a size field of the overall geometry according to the periodic fine features and the cross-scale features of the electromagnetic geometric model; generating and merging surface grids of the source surface, the target surface and the remaining surfaces according to the discrete background triangular grid and the size field and the mapping relationship; and batch replicating and merging the surface grids according to the replication direction and the number to generate a cross-scale large-scale electromagnetic surface grid with periodic fine features.

Description

Technical Field

[0001] This invention relates to the field of modern engineering simulation and numerical simulation, and in particular to a method for generating large-scale electromagnetic surface meshes across scales with periodic fine features. Background Technology

[0002] In the field of modern engineering simulation and numerical simulation, mesh generation technology is a core component for numerically discretizing continuous physical problems. Especially in high-precision computational tasks such as electromagnetic simulation and multiphysics coupling, its quality directly affects the stability, computational accuracy, and simulation efficiency of the solver. In electromagnetic field problems, the solution domain often contains multiple boundary conditions, complex material distributions, and fine structural details, placing extremely high demands on the geometric reconstruction and scale resolution capabilities of the mesh. Improper mesh generation will directly lead to the accumulation of simulation errors, convergence difficulties, and even simulation failure. Therefore, generating high-quality, reusable, and controllable scale resolution meshes has become one of the key bottlenecks in current numerical electromagnetic simulations.

[0003] As simulation models continue to expand in scale and multi-scale features and periodic structures are widely introduced, traditional monolithic mesh generation methods are gradually revealing numerous limitations. On the one hand, large-scale models (such as array antennas, electromagnetic metamaterials, and radar scattering structures) typically contain tens of millions to hundreds of millions of elements, making memory bottlenecks highly likely during monolithic mesh generation, thus preventing the completion of single-step mesh generation. On the other hand, a large number of periodic fine features in the model (such as metal grids, capacitor grids, and microstructure slots) are repeatedly discretized in traditional methods, resulting not only in unstable mesh quality but also redundant computational resource consumption. Furthermore, the increasing complexity of models leads to a decrease in the controllability and repeatability of monolithic mesh generation, making it difficult to reuse existing mesh structures during multiple rounds of design optimization or parameter scanning, severely impacting the automation and efficiency of engineering simulation processes. Summary of the Invention

[0004] Based on this, this paper proposes a method for generating large-scale electromagnetic surface meshes across scales with periodic fine features to address the problems existing in the background technology. This application decomposes the original complex electromagnetic geometry model into unit structures with periodic features, performs fine meshing in local regions, and then uses geometric mapping and boundary fusion strategies to achieve large-scale replication and merging of periodic mesh units. This not only significantly reduces the computational burden of single mesh generation but also ensures the consistency and controllability of local mesh quality, making it particularly suitable for electromagnetic simulation scenarios where fine-scale features and macroscopic structures coexist. Compared with traditional holistic meshing methods, this application has advantages such as high generation efficiency, low memory consumption, strong reusability, and wide adaptability. It is especially suitable for simulation needs with periodic and cross-scale features, such as antenna arrays, metasurface devices, electromagnetic shielding structures, and chip packaging, and has good engineering application prospects and promotional value.

[0005] This invention discloses a method for generating large-scale electromagnetic surface meshes across multiple scales with periodic fine features, comprising:

[0006] Read the multi-scale electromagnetic geometry model with periodic fine features, and set the copy direction and number;

[0007] Set the periodic boundary conditions of the electromagnetic geometric model, determine the source and target surfaces in the replication direction, extract the boundary lines, and establish the mapping relationship between the source and target surfaces and their boundary lines.

[0008] The electromagnetic geometric model is discretized to generate a discrete background triangular mesh.

[0009] Based on the periodic fine features and cross-scale features of the electromagnetic geometric model, the size field of the overall geometry is generated;

[0010] Based on the discrete background triangular mesh and size field, and according to the mapping relationship, the surface mesh of the source surface, the target surface, and the remaining surfaces is generated and merged;

[0011] Based on the generated surface mesh, and according to the replication direction and number, the surface mesh is replicated and merged in batches to generate a large-scale electromagnetic surface mesh with periodic fine features across scales.

[0012] The technical solutions provided by the embodiments of this application may include the following beneficial effects:

[0013] This invention introduces periodic boundary surfaces and boundary lines into the mesh generation process, significantly improving the consistency of boundary stitching. By defining the correspondence between the source and target surfaces of the geometry, each geometric surface has a precise node arrangement and correspondence on the boundary. When generating a single-surface mesh, it can be ensured that its boundary nodes are completely aligned with other periodic surfaces, avoiding topological errors caused by unreasonable geometric segment discretization.

[0014] This method treats periodic sub-blocks as basic units and performs batch replication through transformations such as translation to achieve rapid construction of large-scale meshes. This approach is particularly suitable for applications such as material simulation and modular structure modeling with regular repetitive structures. It can significantly reduce the computational and time costs of mesh generation while ensuring topological consistency. It is naturally adapted to parallel computing environments and can evenly divide tasks among multiple processors, thereby further improving the overall efficiency of mesh generation and numerical simulation.

[0015] This method maintains high-precision stitching and topological correctness even when dealing with structures with extreme scale ratios (such as thickness differences of more than a hundred times), overcoming the limitations of traditional geometric threshold-based methods. Particularly in CAE modeling, local mesh refinement makes global consistency a challenge. The introduction of periodic boundary conditions ensures that the boundaries of the refined regions do not inconsistently stitch with the coarse mesh regions, thus significantly improving the quality and stability of the entire mesh system. Attached Figure Description

[0016] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0017] Figure 1 This is a flowchart illustrating a method for generating large-scale electromagnetic surface meshes across scales with periodic fine features, according to an exemplary embodiment.

[0018] Figure 2 This is a diagram of a multi-scale electromagnetic geometry model with periodic fine features, illustrated according to an exemplary embodiment.

[0019] Figure 3 This is a schematic diagram of the electromagnetic geometry model across scales, according to an exemplary embodiment.

[0020] Figure 4 This is a schematic diagram of periodic fine features of an electromagnetic geometric model according to an exemplary embodiment.

[0021] Figure 5 This is a schematic diagram showing the fine features of an electromagnetic geometric model according to an exemplary embodiment.

[0022] Figure 6 This is a geometric schematic diagram illustrating the target mesh size for replication according to an exemplary embodiment.

[0023] Figure 7 This is a schematic diagram of the periodicity condition of an electromagnetic geometric model according to an exemplary embodiment.

[0024] Figure 8This is a schematic diagram of the boundary line of a periodic surface of an electromagnetic geometric model according to an exemplary embodiment.

[0025] Figure 9 This is a schematic diagram of a discrete background triangular mesh according to an exemplary embodiment.

[0026] Figure 10 This is a schematic diagram illustrating the source boundary line and the target boundary line according to an exemplary embodiment.

[0027] Figure 11 This is a schematic diagram of the source and target surfaces according to an exemplary embodiment.

[0028] Figure 12 This is a schematic diagram of a multi-scale geometric overall surface mesh and details, according to an exemplary embodiment.

[0029] Figure 13 This is a schematic diagram of a surface mesh with periodic fine features, illustrating an exemplary embodiment.

[0030] Figure 14 This is a schematic diagram of the source and target surfaces of a periodic multi-scale geometry, according to an exemplary embodiment.

[0031] Figure 15 This is a schematic diagram of a source surface and target surface boundary mesh that does not require copying, according to an exemplary embodiment.

[0032] Figure 16 This is a schematic diagram of a boundary surface mesh that needs to be replicated, according to an exemplary embodiment.

[0033] Figure 17 This is a schematic diagram of a moving target surface according to an exemplary embodiment.

[0034] Figure 18 This is a schematic diagram illustrating the batch copying of the remaining surfaces according to an exemplary embodiment.

[0035] Figure 19 This is a schematic diagram of a large-scale, multi-scale periodic surface mesh according to an exemplary embodiment. Detailed Implementation

[0036] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0037] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0038] This application uses a cubic multi-scale electromagnetic geometric model with periodic fine features as an example for detailed explanation, supporting efficient mesh processing of complex electromagnetic geometric models with periodic fine features. These electromagnetic geometric models are typically constructed from CAD systems and are widely used in precision electromagnetic engineering scenarios such as array antennas, electromagnetic metamaterials, radar stealth structures, and integrated packaging devices. These models not only contain fine microstructural units (such as fine metal grids, capacitor gaps, and microscale vias), but also often exhibit obvious periodic arrangement characteristics, presenting typical multi-scale distribution features. Traditional meshing methods struggle to simultaneously meet the requirements of geometric fidelity, detail preservation, and splicing consistency for such models, easily leading to problems such as node misalignment, topological discontinuity, and feature degradation at periodic boundaries, severely restricting the feasibility and reliability of subsequent high-precision electromagnetic simulations. This invention, through key technical steps such as periodic structure identification, geometric mapping relationship establishment, size field control, and surface mesh replication, can automatically process complex models containing periodic fine features, generating electromagnetic surface meshes with high topological consistency and scale adaptability. Especially for models with large-scale periodic array structures, the entire structure can be quickly spliced ​​and merged through high-precision construction and batch replication of single-period cell meshes. While ensuring accurate closure of periodic boundaries, it significantly reduces the time and memory resource consumption required for overall mesh generation, and has good versatility and engineering promotion value.

[0039] Figure 1 This is a flowchart illustrating a method for generating large-scale electromagnetic surface meshes across scales with periodic fine features, according to an exemplary embodiment. Figure 1 As shown, the method may include the following steps:

[0040] S1: Read the multi-scale electromagnetic geometry model with periodic fine features, and set the copy direction and number; specifically, it may include the following sub-steps:

[0041] S11: Read the multi-scale electromagnetic geometry model with periodic fine features;

[0042] Specifically, in the modeling and simulation of multi-scale engineering structures, electromagnetic geometric models often contain multiple feature regions of different scales, such as thick support structures and extremely thin connecting layers, or regularly arrayed repeating structures and densely porous material regions. The existence of complex geometry makes direct mesh generation on the overall model extremely difficult, leading to problems such as loss of geometric features, degraded mesh quality, and wasted computational resources. Large-scale periodic multi-scale meshes can be generated by decomposing the geometry into periodic modules, generating meshes, and then replicating and merging them. For example... Figure 2 As shown, this application uses a cubic multi-scale electromagnetic geometric model with periodic fine features as an example for detailed explanation. Figure 3 As shown, this electromagnetic geometric model consists of two cubes, each 10 units high, and a middle layer with a height of 0.1 units, resulting in a scale span of 100 times. Figure 4 As shown, the interlayer surface is 20 mm long and 20 mm wide, and contains 400 periodically and uniformly distributed circular rings. Figure 5 As shown, the periodically distributed rings on the surface of the interlayer are of the same size, with an outer radius of 0.4 and an inner radius of 0.2.

[0043] S12: Based on the distribution of periodic fine features and the size of the target grid, set the direction and number of copies;

[0044] Specifically, the direction and number of copies are set according to the target mesh size requirements. First, the multi-scale electromagnetic geometric model with periodic, fine features is preprocessed to identify regularly repeating cell regions within the model. The geometric periodicity direction (e.g., structural repeatability along the X, Y, and Z axes) and the size of the smallest repeating cell are analyzed. Combined with the overall size of the target simulation region and the required mesh coverage, the copy direction and number of copies are set. For example, if the model is periodically arranged in the X direction, with a single period length of Lx, and the target region length is Nx × Lx, then Nx copies are set to be made in the X direction. Figure 6 The image shows an example of the target mesh size, which is expanded three times in the X direction compared to the imported multi-scale geometry. The settings for the copy direction and number ensure that the final stitched mesh can completely cover the target structure range, while making full use of the repeatability of periodic cells to achieve efficient construction of large-scale meshes.

[0045] S2: Set the periodic boundary conditions of the electromagnetic geometric model, determine the source and target surfaces in the replication direction, extract the boundary lines, and establish the mapping relationship between the source and target surfaces and their boundary lines; specifically, this may include the following sub-steps:

[0046] S21: Mark periodic boundary conditions on the boundary surface of the electromagnetic geometric model, including the source surface, the target surface, and the remaining surfaces located in the replication direction;

[0047] Specifically, the three-dimensional electromagnetic geometry model is first subjected to boundary identification, extracting all external boundary surfaces and classifying them. Each boundary surface typically corresponds to a topological surface, which can be used to achieve periodic replication, fixed boundary conditions, or natural boundaries (such as free boundaries, symmetrical boundaries, etc.). To construct periodic boundary conditions, boundary surfaces with repeating geometric features along the periodic replication direction in the model are paired, with one surface designated as the "source surface" and the other as the "target surface." Periodic surfaces need to be paired to ensure that their shape, size, and topological structure are highly consistent. Boundary surfaces that do not participate in periodic mapping are marked as "non-periodic boundary conditions" and treated as natural boundaries in mesh generation. Periodic surfaces are automatically selected by comparing indicators such as geometric similarity and positional symmetry of the boundary surfaces. The marking results are bound to the boundary surfaces of the geometry in the form of a data structure, laying the foundation for subsequent boundary line extraction and mapping. Figure 7 As shown, in the periodic direction (assuming it is the positive x-axis direction), source surfaces and periodic surfaces are set to be paired with each other, and source surfaces 1, 2, and 3 are paired with target surfaces 1, 2, and 3 respectively.

[0048] S22: Based on the source and target surface boundary conditions of the electromagnetic geometric model, locate the source boundary line on the source surface and the target boundary line on the target surface. Establish the mapping relationship between the source surface and the source boundary line, and the mapping relationship between the target surface and the target boundary line.

[0049] Specifically, boundary lines are further identified within periodic boundary surfaces, serving as the basis for periodic mapping. Within each pair of periodic surfaces, source and target boundary lines should be extracted separately. Source boundary lines refer to geometric line segments located on the source surface, while target boundary lines reside on the target surface. During extraction, topological structures from geometric modeling (such as edge-face relationships) can be used to traverse the boundary surface contours, obtaining a continuous set of boundary lines. Subsequently, to ensure topological consistency, the extracted boundary lines need to be mapped and associated with their respective boundary surfaces, establishing "source surface—source boundary line" and "target surface—target boundary line" mapping relationships. This mapping relationship will be used to track the geometric surface structure of each boundary line and maintain boundary information consistency during mesh generation.

[0050] S23: Based on the distance between the endpoints of the source boundary line and the target boundary line, find the boundary line whose endpoint distance is equal to the geometric distance between the source surface and the target surface, and establish the mapping relationship between the source boundary line and the target boundary line;

[0051] Specifically, the correspondence between the source and target boundary lines must be clearly defined. The matching process relies not only on the boundary line numbers or their corresponding surfaces but also on metrics such as geometric distance for verification. The distances between the start and end points of the source and target boundary lines are compared sequentially. If the distances are within the allowable error threshold and are proportional to the overall model size, the two boundary lines are considered a matching pair, and a mapping relationship is established between them. This mapping can be expressed using data structures such as bidirectional dictionaries or index tables, recording the boundary line start and end point numbers, direction vectors, and geometric attributes. The selection of the distance threshold should consider the minimum structural scale of the model to ensure the accuracy of the mapping. Figure 8 As shown, boundary lines 1, 2, 3, and 4 belong to source surface 1 and are paired with boundary lines 11, 12, 13, and 14 that make up target surface 1. Boundary lines 4, 5, 6, and 7 belong to source surface 2 and are paired with boundary lines 14, 15, 16, and 17 that make up target surface 2. Boundary lines 7, 8, 9, and 10 belong to source surface 3 and are paired with boundary lines 17, 18, 19, and 20 that make up target surface 3.

[0052] S3: Discretize the electromagnetic geometric model to generate a discrete background triangular mesh; this may include the following sub-steps:

[0053] S31: Based on the input geometry, the continuous surface is parametrically mapped to generate a finite number of local triangular elements, which are then spliced ​​together to form an overall closed discrete background triangular mesh.

[0054] Specifically, the CAD electromagnetic geometry models input into actual engineering models are typically based on B-Rep (Boundary Representation) structures, which include information such as boundary surfaces, edge lines, and vertices. While this geometric data is suitable for design, it is not directly applicable to numerical discretization. Therefore, before discretization, the input electromagnetic geometry model is first geometrically simplified and imperfections are repaired. Subsequently, based on the triangulation method of the BRepMesh module in OpenCASECADE, each smooth surface is parameterized onto a two-dimensional plane, then local triangulation is performed, and finally mapped back to three-dimensional space. To ensure seamless stitching between the triangulated facets, node alignment and topological stitching are performed on the common boundaries between each facet, ultimately constructing a globally closed triangular mesh. This mesh should satisfy conditions such as continuity, non-overlapping, and complete coverage of the three-dimensional outer boundary, serving as a discrete approximation that accurately represents the original geometry.

[0055] S32: Merge duplicate points in the generated discrete background triangle mesh to generate a complete discrete background triangle mesh.

[0056] Specifically, in the aforementioned triangulation and patch stitching process, some faces may share vertices or boundaries. Each triangle typically stores its three vertices separately, potentially leading to a large number of redundant point coordinates and even duplicate points within the accuracy error range, affecting subsequent processing efficiency and mesh quality. By using point coordinate merging technology, all triangle vertices are uniformly numbered and managed, vertices considered identical within a certain tolerance range are merged into a common point. Simultaneously, the vertex indices of the corresponding triangles are updated, effectively reducing mesh data redundancy and ensuring topological consistency and boundary point uniformity. After merging, the mesh data can be reorganized into a "point set + patch index" structure, and the topological validity of the mesh can be further checked, such as single-sided or multi-sided overlap, and normal consistency issues, ensuring that the discrete mesh meets high-quality requirements and can serve as a background structure for subsequent use. Figure 9 As shown, this is the discrete background triangle mesh generated from the input use case geometry.

[0057] S4: Based on the periodic fine features and cross-scale features of the electromagnetic geometric model, generate the size field of the overall geometry; specifically, this may include the following sub-steps:

[0058] S41: Based on the overall structural characteristics of the electromagnetic geometric model, local size constraints are set for the existing scale spanning large and small feature regions.

[0059] Specifically, through geometric analysis and feature recognition, regions with significant scale differences are identified within the model, and specific mesh element size constraints are set for these regions. Typical scale-differentiated regions include: thin-walled regions (e.g., wall thickness much smaller than length), slender structures (such as beams and pipes), micropores or gaps, and regions with abrupt changes in curvature. Extraction methods can combine the geometric size distribution, local minimum feature size at the boundary, curvature information, and gradient change degree as indicators. After identifying key regions, a target mesh size range is manually or automatically set for each type of region based on the required simulation accuracy, physical phenomena characteristics, or human experience. These size constraints will serve as boundary inputs or local minimum control points in subsequent size field construction, ensuring that the mesh is sufficiently refined in key regions while avoiding over-refinement in non-key regions, achieving a balance between efficiency and accuracy.

[0060] S42: Based on local size constraints, a continuous size field covering the entire geometric domain is constructed and adaptively matched with geometric features to form a continuous function that varies with space, used to guide the size of grid cells in each region;

[0061] Specifically, the discrete size constraints are extended into a continuous size field across the entire geometric domain. A spatial function h(x,y,z) is defined, representing the target size of the mesh element at any point in space. Based on the S3 geometrically discrete background triangular mesh, control points are placed at key structural points (such as high curvature points and extremely fine areas) and assigned target sizes. Then, their influence is diffused to the surrounding area through a weighted attenuation function. Simultaneously, global minimum / maximum size constraints can be introduced to ensure the smoothness and controllability of the overall size field.

[0062] S5: Based on the discrete background triangular mesh and size field, and according to the mapping relationship, generate and merge the surface meshes of the source surface, target surface, and other surfaces; specifically, this may include the following sub-steps:

[0063] S51: Generates a line mesh for all source surfaces using the endpoints of the source boundary lines as constraints;

[0064] Specifically, a boundary line mesh controlled by a size field is generated on each source boundary line. First, the set of source boundary lines on all source surfaces is traversed, and based on their endpoint positions as anchor points, combined with the target edge length defined in the local size field, the boundary lines are segmented to generate a preliminary line mesh structure. The distribution of boundary line segmentation nodes should be as uniform as possible, conforming to the variation law of the size field, with smooth transitions to avoid excessively sharp or obtuse angles in subsequent surface meshes. The final line mesh will serve as the boundary condition for generating the source surface surface mesh and also provide support for the periodic mapping of the target surface.

[0065] S52: Based on the mapping relationship of the boundary lines, project the line mesh of the source surface onto the corresponding target boundary line;

[0066] Specifically, the source surface line mesh structure is mapped to the target surface. Based on the established geometric correspondence between the source and target boundary lines, this mapping relationship is used to sequentially project and transform the line mesh points on the source surface onto the target boundary lines on the target surface. For planar target surfaces, a direct translation transformation is used to ensure that the projected points lie on the target boundary curve. The boundary line nodes of the target surface can be accurately aligned with the source surface, achieving mesh continuity under periodic boundary conditions, improving mesh quality consistency, and avoiding common errors such as misalignment of nodes on both sides or incomplete boundary lines. Figure 10 As shown, after the source boundary line is discretized according to the size function to generate a line mesh of geometric edges, it is translated and mapped onto the target boundary line, and the two are completely consistent.

[0067] S53: Traverse the remaining boundary lines and generate the remaining boundary line mesh using the endpoints of the boundary lines as constraints;

[0068] Specifically, in addition to periodic boundary lines, the model also contains a large number of aperiodic boundary lines, which require independent line meshing, performed directly on their bodies using size-driven meshing. Based on the local target edge lengths defined in the size field, intermediate nodes are inserted between each boundary line according to the arc length, generating equidistant or gradually varying line mesh structures. Particularly, for geometrically complex regions where boundary lines exhibit abrupt curvature changes or small endpoint angles, the meshing can be appropriately refined to ensure the quality of the generated surface mesh. Simultaneously, to maintain mesh closure, it is necessary to ensure that all boundary lines ultimately form closed boundary loops.

[0069] S54: Traverse all source faces, using the boundary line mesh of each source face as a constraint, and generate the surface mesh of each source face using the leading edge propagation method;

[0070] Specifically, after obtaining a complete boundary mesh, the Advancing Front Method (AFM) is used for triangulation of all source faces. Starting with the boundary mesh as the initial front, triangular elements are gradually generated by advancing towards the interior of the region, exhibiting good adaptability and patch quality control. During algorithm execution, dense meshing is prioritized in regions with the smallest size field to ensure that structural details are fully captured. During generation, the boundaries remain unchanged, and only the internal mesh structure is optimized until the front closes and the entire region is filled. Ultimately, each source face generates a set of high-quality triangular meshes with controlled boundaries and adaptive sizes.

[0071] S55: Based on the mapping relationship of the boundary surfaces, project the surface mesh of the source surface onto the corresponding target surface;

[0072] Specifically, after the source mesh is generated, it can be directly copied to the target surface, achieving automatic construction of periodic surface meshes. Based on the mapping relationship of the previous boundary surfaces, the coordinates of all vertices in the source mesh are transformed to the geometry of the target surface through translation transformation, forming a corresponding surface mesh set. During the copying process, the vertex connectivity and local geometric topology are kept consistent, ensuring that the mesh nodes between the two surfaces are completely aligned. The one-to-one mapping operation significantly reduces the amount of computation and maximizes the consistency of the splicing boundary and the accuracy of periodic copying. Figure 11 As shown, after the source surface discretizes the geometric surface mesh according to the size function, it is translated and mapped onto the target surface, and the two are completely identical.

[0073] S56: Traverse the remaining boundary surfaces, using the boundary line mesh of each surface as a constraint, and generate the surface mesh of each surface using the leading edge propagation method;

[0074] Specifically, for all boundary surfaces that do not participate in periodic mapping, triangulation is performed independently based on their boundary line mesh, using the same method as S54. Size field control is further applied during this process to achieve adaptive mesh refinement of the in-surface structural details. All periodic and non-periodic surface meshes within the entire geometric domain are completed, forming a set of high-quality discrete surface meshes that balance size adaptability and topological consistency. For example... Figure 12 As shown, a mesh with varying density is generated based on a global size function, with a denser mesh at the interlayer and a sparser mesh further away from the interlayer. For example... Figure 13 As shown, the fine circular pattern on the interlayer surface is well preserved, and its dimensions are reasonably set. Figure 14 As shown, the source and target surface meshes are compared, and both remain symmetrical and consistent.

[0075] S57: Remove duplicates from the generated surface mesh, merge duplicate points, and generate a complete surface mesh.

[0076] Specifically, a large number of duplicate vertices may exist among the triangular meshes generated from the source surface, target surface, and other surfaces, especially at the splicing boundaries. Different facets may independently store nodes in the same spatial location, resulting in redundant points within the accuracy error range in the overall mesh. To improve mesh consistency and subsequent simulation efficiency, the vertices of all triangular meshes are uniformly numbered and their positions are normalized. The system determines vertices within a set tolerance range as the same point, merges them into a common node, and synchronously updates the vertex indices of all associated triangular facets. This effectively reduces data redundancy, improves the clarity of the facet topology, ensures node continuity and seamless facet connection at splicing boundaries, and provides a high-quality discrete foundation for subsequent simulations.

[0077] S6: Based on the surface mesh, and according to the replication direction and number, batch replicate and merge the surface mesh to generate a large-scale electromagnetic surface mesh with periodic fine features across scales; specifically, this may include the following sub-steps:

[0078] S61: Based on the boundary mapping relationship between the source surface and the target surface and the number and direction of the copies, separate the source surface, the target surface, and the remaining surfaces that need to be copied;

[0079] Specifically, based on the specified copying direction (x, y, or z axis) in geometric space, triangles located at the source and target faces are selected, and the identified triangles are classified according to the set copying direction parameters. First, the set coordinate axis direction is determined, which may be the x-axis, y-axis, or z-axis; all triangle faces in the mesh are traversed, and their recorded regions attributes are compared with the periodic boundary conditions set in S2 to determine whether they are located on the source face, target face, or other faces. For example... Figure 15 As shown, the triangular mesh located on the source and target faces is separated without needing to be copied. Figure 16 As shown, the remaining triangular mesh faces that need to be copied in batches are separated out.

[0080] S62: Based on the number and direction of the copies, fix the source surface, move the target surface, and batch copy the remaining surfaces except for the source surface and the target surface;

[0081] Specifically, by performing several translation and copy operations along a specified copy coordinate axis on the boundary triangle to be copied, multiple topologically consistent and geometrically continuous triangular facets are constructed, achieving face stretching or structural extension along a specific direction. The copy direction and number of operations are set according to S1. and the geometric offset between each layer The distance between the source and target surfaces determines the number of copies and the geometric distance after copying. The offset vector for each copy is defined as follows:

[0082]

[0083] Where n represents the nth copy, with values ​​ranging from 1 to numLayers, and e represents the unit vector (1,0,0), (0,1,0), or (0,0,1), corresponding to the x, y, or z axis directions. To avoid topological repetition and maintain geometric continuity, the vertices of the boundary triangle are copied sequentially. For example... Figure 17 As shown, the target surface is moved along the periodic replication direction. Distance. For example... Figure 18 As shown, batch copy the remaining faces. Second-rate.

[0084] S63: Merge the source surface, the moved target surface, and the remaining copied surfaces to generate a large-scale electromagnetic surface mesh with periodic fine features across scales.

[0085] First, vertex information from each input mesh is extracted and stored uniformly for subsequent construction of the global vertex set. Second, vertex index offset processing is performed on the triangle faces in each input mesh to adapt them to the unified vertex numbering system after merging, and the attribute identifiers (such as region IDs) corresponding to the faces are recorded during this process. A tolerance-based point duplication detection algorithm is used to deduplicate the global vertex set and establish a mapping relationship between the original vertices and the deduplicated vertices. Subsequently, the indices of all faces are reconstructed based on this mapping relationship, achieving accurate reconstruction of face data in the merged topology. Finally, the attribute information of the original faces is appended to the output mesh in face order to ensure that the semantic information of the merged mesh is not lost. Figure 19 As shown, the source surface, the moved target surface, and the remaining replicated surfaces are merged to obtain a complete large-scale electromagnetic surface mesh with periodic fine features across scales.

[0086] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0087] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for generating a cross-scale large-scale electromagnetic surface mesh with periodic fine features, characterized in that, The application relates to a method for generating a large-scale electromagnetic surface grid with periodic fine features and cross-scale features. The method comprises the following steps: reading a cross-scale electromagnetic geometry model with periodic fine features, setting a replication direction and number; setting a periodic boundary condition of the electromagnetic geometry model, determining a source surface and a target surface in the replication direction, extracting a boundary line, and establishing a mapping relationship between the source surface and the target surface and the boundary line; discretizing the electromagnetic geometry model to generate a discrete background triangular grid; generating a size field of the whole geometry according to the periodic fine features and the cross-scale features of the electromagnetic geometry model; generating and merging surface grids of the source surface, the target surface and the remaining surfaces according to the mapping relationship, the discrete background triangular grid and the size field; batch replicating and merging the surface grids according to the replication direction and number to generate a large-scale electromagnetic surface grid with periodic fine features and cross-scale features; wherein the step of setting the periodic boundary condition of the electromagnetic geometry model, determining the source surface and the target surface in the replication direction, extracting the boundary line, and establishing the mapping relationship between the source surface and the target surface and the boundary line comprises the following steps: marking a periodic boundary condition on a boundary surface of the electromagnetic geometry model, including the source surface, the target surface and the remaining surfaces in the replication direction; finding a source boundary line on the source surface and a target boundary line on the target surface according to the source surface and the target surface boundary conditions of the electromagnetic geometry model, and establishing a mapping relationship between the source surface and the source boundary line and a mapping relationship between the target surface and the target boundary line; 2. The method of claim 1, wherein, finding a boundary line with an equal distance between end points of the source boundary line and the target boundary line and a geometric surface distance of the source surface and the target surface, and establishing a mapping relationship between the source boundary line and the target boundary line. The method comprises the following steps: reading a cross-scale electromagnetic geometry model with periodic fine features; 3. The method of claim 1, wherein, setting a replication direction and number according to a distribution of the periodic fine features and a size of a target grid. The method comprises the following steps: parameterizing and mapping a continuous curved surface to generate a finite number of local triangular units, and then splicing the triangular units into an overall closed discrete background triangular grid; 4. The method of claim 1, wherein, merging and repeating points of the generated discrete background triangular grid to generate an overall discrete background triangular grid. The method comprises the following steps: setting a local size limit condition for a region with a large scale span and a fine feature region according to overall structural features of the electromagnetic geometry model; 5. The method of claim 1, wherein, constructing a continuous size field covering the entire electromagnetic geometry model according to the local size limit condition, and forming a continuous function varying with space to guide sizes of grid units in different regions. The method comprises the following steps: generating line grids of all the source surfaces with end points of the source boundary line as constraints; projecting the line grids of the source surfaces to corresponding target boundary lines according to the mapping relationship of the boundary lines; Traverse the rest of the boundary lines to generate the rest of the boundary line grids with the end points of the boundary lines as constraints; Traverse all the source surfaces to generate the surface grid of each source surface with the boundary line grid of each source surface as constraints by using the front propagation method; Project the surface grid of the source surface to the corresponding target surface according to the mapping relationship of the boundary surfaces; Traverse the rest of the boundary surfaces to generate the surface grid of each surface with the boundary line grid of each surface as constraints by using the front propagation method; Merge the generated surface grids to generate the overall surface grid.

6. The method of claim 1, wherein, According to the surface grid, batch copy and merge the surface grid according to the replication direction and number to generate a cross-scale large-scale electromagnetic surface grid with periodic small features, comprising: According to the mapping relationship of the source surface and the target surface boundary, the number and direction of replication, separate the source surface, the target surface and the rest of the surfaces that need to be replicated; According to the number and direction of replication, fix the source surface, move the target surface, and batch copy the rest of the surfaces except the source surface and the target surface; Merge the source surface, the moved target surface and the replicated rest of the surfaces to generate a cross-scale large-scale electromagnetic surface grid with periodic small features.

Images