Introduction to GMesh Mesh Options

Introduction to GMesh

2D mesh algorithm

1. MeshAdapt: ​​This is an adaptive meshing algorithm that automatically adds additional meshes when greater precision is required or a denser mesh is required in certain areas. The advantages of this algorithm include high convergence and flexibility, which allows users to add more meshes where needed, but it may also introduce more nodes and elements, thereby increasing calculation time and memory usage.
2. Automatic: This is an automatic meshing algorithm based on Delaunay triangulation, which has better mesh quality and lower memory usage. Due to its high computational efficiency, the algorithm is commonly used in large-scale calculations.
3. Initial mesh only: This algorithm only generates an initial mesh without any reshaping or refinement. It is suitable for situations where manual adjustment and optimization of the mesh is required, where users usually need to manually manipulate the mesh or use other meshing algorithms such as BAMG.
4. Delaunay: This is an algorithm based on Delaunay triangulation, which can generate high-quality meshes and has a good balance between mesh quality and computational efficiency. This algorithm is Gmsh's default algorithm because it works for the vast majority of 2D geometries.
5. Frontal-Delaunay: This is a surface meshing algorithm based on the frontal triangle algorithm, which can generate high-quality meshes when dealing with complex surfaces. This algorithm has the advantage that it can handle most surfaces, but it is computationally inefficient, especially as the complexity of the surface increases.
6. BAMG: This is a gradient-based adaptive grid algorithm that can adjust the grid density in local areas, resulting in high-quality grids. This algorithm can handle geometric shapes with variation and complexity more efficiently, but also requires more computing time and memory.
7. Frontal-Delaunay for Quads: This algorithm can generate high-quality quadrilateral meshes, especially suitable for the division of rectangular areas with different aspect ratios.
8. Packing of Parallelograms: This algorithm divides two-dimensional regions into parallelograms and generates high-quality quadrilateral meshes.
9. Quasi-structured Quad: This algorithm is a quasi-structured grid algorithm that generates high-quality quadrilateral grids. It is suitable for situations where a relatively structured grid is required.

3D mesh algorithm

1. Delaunay algorithm: It is an algorithm based on Delaunay triangulation. The algorithm treats each vertex as a Delaunay sphere, and constructs a Delaunay triangle by calculating the coplanar or cocircular relationship between adjacent spheres, and finally generates a mesh. The algorithm is generally suitable for the generation of 3D geometries of simple shapes and unstructured meshes.
2. Initial mesh only algorithm: This algorithm generates a mesh using only a hint mesh and a size function, which can be used to quickly generate meshes of simple shapes.
3. Frontal Algorithm: This algorithm uses a technique known as the Frontal method, starting with a coarser generated mesh and moving inwards until the desired accuracy is achieved. The algorithm is applicable to various types of 3D geometry.
4. MMG3D Algorithm: This algorithm uses Frontal method and post-processing technology to prune and optimize the existing mesh to generate a better mesh. The algorithm optimization effect is better, but the running speed is slower.
5. R-tree algorithm: This algorithm uses a spatial index to quickly generate a mesh, divides the three-dimensional space into a series of subregions, and then traverses these subregions to determine the mesh size and density relative to the geometry. Runs faster, but may not provide good mesh quality for irregularly shaped geometry.
6. HXT algorithm: This algorithm is an algorithm based on the Hilbert curve, which sorts the grid points according to the Hilbert curve and generates a grid, which can effectively reduce the amount of data storage and calculation.

2D recombination algorithm

These algorithms can be used to optimize and recombine existing meshes in Gmsh to improve their quality and accuracy.

1. Simple Regrouping Algorithm: This is a simple mesh regrouping algorithm that searches all mesh cells and faces in a sequential fashion and regroups them quickly. This algorithm is fast, but the resulting mesh quality is usually not very good.
2. Blossom recombination algorithm: Based on the Hungarian algorithm, it increases the weight of the grid points through multiple iterations in order to better adjust the angle, size and shape of the quadrilateral. This algorithm usually produces a mesh of higher quality than the simpler algorithm, but also takes longer to compute.
3. Simple Full Quadrilateral Recombination Algorithm: This algorithm is similar to the Simple Recombination Algorithm, but it is more efficient at recombining orthogonal quadrilaterals. This algorithm is fast, but the generated grid may not be very smooth, and post-processing is required for further optimization.
4. Blossom Full Quadrilateral Reassembly Algorithm: This is an algorithm that combines the Blossom algorithm with quadrilateral reconstruction techniques to better handle larger quadrilateral domains and produce higher quality, smoother meshes. However, due to the relatively complex algorithm, the calculation time is long.

recombine all triangular meshes

Used to recombine mesh elements based on existing triangular meshes to generate higher quality, more regular quadrilateral meshes. Using this command can effectively improve the mesh quality, reduce noise and deformation, and have faster calculation speed. Specifically, the command will recombine all existing triangular mesh elements and select the optimal mesh element from a combination of various types such as quadrilaterals, hexagons, octagons, etc. It should be noted that using this command may change the existing grid structure and topology, so it is recommended to back up the original grid file for emergency when optimizing the grid.

smoothing steps

Smoothing Steps refers to the number of iterations to execute the smoothing algorithm (Laplace or Jacobi algorithm) during mesh generation or mesh optimization. A smoothing operation is an algorithm that makes a mesh mesh more uniform and smooth by iterating through the mesh's vertex coordinates. In order to control the operation of the algorithm and avoid infinite iterations, Gmsh provides smoothing step parameters that can be set.

With a low number of smoothing steps, the mesh may not be fully smoothed, resulting in irregularly shaped elements or sharp corners, but faster mesh generation or optimization times may be obtained. Conversely, more smoothing steps effectively smooth the mesh and reduce element sharp corners and distortion, but take longer to generate or optimize the mesh. Therefore, this parameter needs to consider the mesh quality and optimization speed comprehensively, and make the most appropriate choice.

In short, given an appropriate smoothing number, the generated mesh can be made more stable and the element shape more regular, so as to better support the operation of subsequent physical simulations or simulations.

Use Incomplete Elements

Can be used to set whether to use incomplete elements when generating polygon/polyhedral meshes. Incomplete elements are finite elements that do not match between regions and boundaries. In this case, the finite elements are drawn from the top cell of the input file down to the lower side, using incomplete elements.

This option is used to handle the following situations:

1. The boundary of the region does not correspond exactly to the interface of the region given in the input file, for example, cell walls such as walls do not exactly correspond to the boundary.
2. Polygonal regions or polyhedral volumes have regions with different topological characteristics using different regions, for example, a circular hole in the center of the square, or a hollow in a polyhedron.

Using incomplete elements generally degrades the quality of the finite element mesh, but for some specific problems it can improve computational speed and efficiency. Therefore, whether to use or not to use incomplete elements needs to be selected according to the actual situation.