Triangular and quadrilateral surface mesh quality optimization using local parametrization

• Published in: Computer methods in applied mechanics and engineering Vol. 193; no. 9; pp. 913 - 928
• Main Authors: Garimella, Rao V., Shashkov, Mikhail J., Knupp, Patrick M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 05-03-2004
• Subjects: Element quality; Jacobian condition number; Numerical optimization; Quadrilaterals; Reference Jacobian matrices; Triangles; Unstructured surface mesh; Element quality; 48; Numerical optimization; Jacobian condition number; 28; Triangles; Quadrilaterals; 61; Reference Jacobian matrices; Unstructured surface mesh
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2003.08.004

A procedure is presented to improve the quality of surface meshes while maintaining the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices in a series of element-based local parametric spaces such that the vertices remain on the original discrete surface. The movement of the mesh vertices is driven by a non-linear numerical optimization process. Two optimization approaches are described, one which improves the quality of elements as much as possible and the other which improves element quality but also keeps the new mesh as close as possible to the original mesh.