Linear Sources for Mesh Generation

Abstract

Sources offer a convenient way to prescribe a size distribution in space. For each newly created mesh point, the mesh generator queries the local size distribution, either to create a new point or element, depending on the underlying mesh generation method, to smooth the mesh, or to get a local relevant length scale. Sources may have different shapes such as points, edges, triangles, or boxes. They provide the size distribution given some user defined parameters and the distance of a point location to the source. Traditionally, the source strength is considered as constant. In this work, extensions to linear sources in space are proposed. It is shown that in the case of curvature refined mesh generation, substantial savings may occur due to the much better approximation of the curvature variation for a simple modification of traditional sources. Even though curvature refinement is the main application of this work, improvements through linear sources are relevant to other contexts such as user defined sources. The technique is very general as it deals with a fundamental aspect of mesh generation and can be easily incorporated into an existing mesh generator with traditional sources. Thorough details of source approximations and source filtering are provided. Relations with lower envelopes are highlighted. Practical examples illustrate the accuracy and efficiency of the method.