The FEM approach to the 2D Poisson equation in 'meshes' optimized with the Metropolis algorithm

摘要

The presented article contains a 2D mesh generation routine optimized withthe Metropolis algorithm. The procedure enables to produce meshes with aprescribed size h of elements. These finite element meshes can serve asstandard discrete patterns for the Finite Element Method (FEM). Appropriatemeshes together with the FEM approach constitute an effective tool to deal withdifferential problems. Thus, having them both one can solve the 2D Poissonproblem. It can be done for different domains being either of a regular(circle, square) or of a non--regular type. The proposed routine is evencapable to deal with non--convex shapes.