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. Keywords Mesh optimization Á Mesh quality Á Target-matrix paradigm 1 Motivation A significant fraction of modeling and simulation software provides numerical solutions to partial differential equations via discretization methods. Not only do the equations themselves need to be discretized, but so does the domain on which the problem is defined. PDE software often uses mesh generation for this task. Sometimes the meshes are generated off-line before the PDE simulation and sometimes the meshes are generated dynamically or adaptively as the calculation proceeds. In either case, the quality of the mesh is an important consideration because poor quality can impact accuracy, efficiency, and in the worst case, can invalidate or prematurely terminate the calculation. There are a variety of mesh generation methods, some giving better quality than others, depending upon the circumstances. Unstructured hexahedral mesh generation is probably the least successful in terms of guaranteeing quality, but tetrahedral and structured methods can also create meshes with quality issues. As a result, a considerable number of post-processing techniques have been devised to improve the quality of an existing mesh. Some of these methods change mesh topology, some change mesh vertex positions, and some change both. Because the methods for changing mesh topology and for changing vertex positions are quite different, it is wise, in the interest of progress, to investigate the best possible technologies in each of these areas, both separately and together. In the present work, a new paradigm for changing mesh vertex coordinates via numerical optimization is described. The target-matrix paradigm has evolved gradually over the past 4 years; forerunners of the paradigm can be found in [1, 2] , and [3] . With funding provided by DOE's Office of Science, the Paradigm has in the last 4 years been formalized and has undergone rapid elaboration to ensure that it is well-formulated, complete, and powerful. Unfortunately, there is not space in this paper to describe all of the mathematical details in the Paradigm; this is done
Also, a general-purpose algorithm called the target-matrix paradigm is introduced in REF , and can be applied to a wide variety of meshes.
Introducing the target-matrix paradigm for mesh optimization via node-movement
Engineering with Computers
Engineering with Computers
Computer Science