FEM Triangular Mesh Generator - MATLAB-based Automatic Generation Tool for Finite Element Triangular Mesh
The finite element method is widely used in numerical calculations, and the first step in the finite element solution is to generate discrete triangular (or quadrilateral, hexagonal) meshes. For complex geometric shapes, manually generating triangular meshes is very tedious, so a fast and efficient automatic generation tool is needed, and the FEM triangular mesh generator is born for this purpose.
This article will introduce a MATLAB-based automatic generation tool for finite element triangular meshes, and provide the corresponding source code.
First, we need to prepare the geometric information of the area to be solved. Here, a two-dimensional hollow circle is taken as an example for illustration. Assuming that the coordinates of the center of the circle are (0,0), the outer radius is 1, and the inner radius is 0.3, then we can use the following code to generate the discrete data of the circle:
theta=linspace(0,2*pi,100)';
outer_radius=ones(size(theta));
inner_radius=0.3*ones(size(theta));
x=[outer_radius.*cos(theta);inner_radius.*cos(flipud(theta))];
y=[outer_radius.*sin(theta);inner_radius.*sin(flipud(theta))];
xy=[x,y];
Next, we can use the Delaunay triangulation algorithm to transform the above discrete data into a triangular mesh. MATLAB comes with the Delaunay function, so we only need to extract the triangle nodes and elements. code show as below:
DT=delaunayTriangulation(xy);
tri=DT.ConnectivityList;
node=DT.Points;
Of course, the above algorithm is only the most basic method of generating triangular meshes