Finite Element Programming for Mesh Generation

In Finite Element Analysis (FEA), mesh generation serves as a critical step that discretizes continuous physical models into finite small elements (such as triangular, quadrilateral, or hexahedral elements) for numerical computation. The quality of the mesh directly impacts the accuracy and convergence of calculation results.

Programming implementation of mesh generation typically involves the following key aspects: Geometry Model Import and Preprocessing Typically involves reading boundary information from CAD files or geometric descriptions, followed by topological verification to ensure no cracks or overlapping regions exist. In code implementation, this often utilizes geometric kernel libraries like OpenCASCADE or CGAL for robust boundary representation (B-rep) handling.

Node Generation and Element Connectivity Based on geometric shapes, nodes are distributed along boundaries and interior regions. Structured meshes (e.g., rectangular or hexahedral) are relatively straightforward to implement using coordinate mapping algorithms, while unstructured meshes (e.g., triangular or tetrahedral) often require sophisticated strategies like Delaunay triangulation (implemented using Bowyer-Watson algorithm) or Advancing Front technique with priority queue management for efficient element insertion.

Mesh Optimization Initial generated meshes may contain poorly-shaped elements (such as high aspect ratios or acute angles), requiring quality improvement through Laplacian smoothing (iterative node relocation toward centroid of connected nodes) or intelligent node repositioning algorithms that optimize quality metrics like Jacobian determinants.

Adaptive Refinement Local refinement in critical regions (e.g., stress concentration zones or boundary layers) enhances calculation accuracy while reducing overall computational burden. Implementation typically involves error estimation algorithms and quadtree/octree data structures for hierarchical mesh refinement with proper hanging node handling.

Mesh Format Export Generated mesh data is stored in formats supported by computational software (e.g., ABAQUS, ANSYS, or OpenFOAM), such as Gmsh's `.msh` format or VTK format. Programming implementation requires careful handling of node/element numbering, physical group assignments, and format-specific syntax through dedicated output modules.

Programmatic mesh generation enables flexible customization of element types and densities to adapt to complex engineering requirements. Furthermore, integration with parallel computing techniques (e.g., domain decomposition using MPI) or GPU acceleration (via CUDA/OpenCL) can significantly enhance generation efficiency for large-scale meshes.