Introducing the target-matrix paradigm for mesh optimization via node-movement.

Abstract

A general-purpose algorithm for mesh optimization via node movement, known as the Target-Matrix Paradigm, is introduced. The algorithm is general purpose in that it can be applied to a wide variety of mesh and element types, and to various commonly recurring mesh optimization problems such as shape improvement, and to more unusual problems like boundary-layer preservation with sliver removal, high-order mesh improvement, and edge-length equalization. The algorithm can be considered to be a direct optimization method in which weights are automatically constructed to enable definitions of application-specific mesh quality. The high-level concepts of the paradigm have been implemented in the Mesquite mesh-improvement library, along with a number of concrete algorithms that address mesh quality issues such as those shown in the examples of the present paper.