Unstructured surface mesh adaptation using the Laplace–Beltrami target metric approach

Abstract

This paper develops a set of adaptive surface mesh equations by using a harmonic morphism, which is a special case of a harmonic map. These equations are applicable both to structured and unstructured surface meshes, provided that the underlying surface is given in a parametric form. By representing the target metric of the mesh as a sum of a coarse-grained component and a component quadratic in surface gradients, an improved surface mesh may be obtained. The weak form of the grid equations is solved using the finite element approximation, which reduces the grid equations to a nonlinear, algebraic set. Examples of structured and unstructured meshes are used to illustrate the applicability of the proposed approach.