Laplace–Beltrami enhancement for unstructured two-dimensional meshes having dendritic elements and boundary node movement

摘要

The Laplace–Beltrami mesh enhancement algorithm of Hansen et al. [1], [3], [2] has been implemented and broadened to include meshes containing dendritic elements and allowing for boundary node movement. This implementation operates on an unstructured two-dimensional mesh by forming an equivalent weak statement using finite element interpolation, assembly, and solution ideas to iteratively place those nodes allowed to move. Moving boundary nodes are constrained to follow the boundary geometry described as a Wilson–Fowler spline (e.g., [3, Section 2.1.3.1]). Implementation details concerning the element basis set modifications, the metric tensor for dendritic element treatment and boundary node movement are presented. Laplacian (e.g., [6]) enhancement is included as a special case. Results are presented which illustrate the algorithm for three test problems.