Laplace-Beltrami mesh enhancement Python3 code for unstructured meshes. The mesh is currently assumed to be quadrilaterals with node and element numbers beginning with 1 instead of 0 as in C++. The enhancement method is described in Hansen, Douglass, Zardecki, Mesh Enhancement: Selected Elliptic Methods, Foundations, and Applications, Imperial College Press, 2005 specifically in sections 9.2 and 9.3. There is also a matplotlib capability to plot initial and final unstructured meshes.

To execute the code, simply download it and type: python3 LB.py. A test problem will run (one of 2 tests in the code; remove """ - in 2 places and place them around the other test data). Execution runs through the first plot, then pauses until the plot is deleted. Execution continues in a similar vein through the plotting of the final mesh. When trhe plot is removed, execution terminates. Both plots are saved as .pdf files. There are 2 constants in the function LBsmoother which may be adjusted: epsilon and maxIter which are used to stop the solution iteration.

There are 4 variables needed to setup a new mesh problem: dofs, edofs, coords, and bdyNodes. This nomenclature is from calfem, a mesh generation code available from github.com. It is based in the solid mechanics area.

1. dofs - (degrees of freedom) contains the node numbers. Node numbering should first list all boundary nodes; then the internal nodes.
2. edof - (element degrees of freedom) contains the node numbers for each element (assuming counterclockwise listing)
3. coords - contains the x,y coordinate pairs for each node as given in dofs
4. bdyNodes - lists the boundary node numbers, the first BN nodes in dofs where BN is the number of boundary nodes.