On the Design of Initial Mesh and Mesh Quality Measures

AMD-Vol. 220 Trends in Unstructured Mesh Generation, ASME, pp.97-108, July 1997

MESHING
RESEARCH
CORNER

Wa Kwok: Development Engineer, Ansys, Inc., Southpointe, 275 technology Drive Canonsburg, PA 15317, (412) 514-2899, (412) 514-1900 (fax)
email: wa.kwok@ansys.com
Kamyar Haghighi:Professor, Agricultural & Biological Engineering, Purdue University -1 146 ABE, West Lafayeffe, IN 47907-1146, (765) 494-1182, (765) 496-1115 (fax)
email: haghighi@ecn.purdue.edu

presented at
The 1997 Joint ASME/ASCE/SES Summer Meeting
June 29-July 2, 1997
Northwestern University
Evanston Illinois

Abstract
A fuzzy logic knowledge-based mesh generator for adaptive finite element analysis is developed and used to study initial mesh design issues and to develop and evaluate some mesh quality measures. In this approach, the fuzzy knowledge-based system (FUZZYMESH) makes expert decisions about the initial mesh design by considering the geometric information, as well as the boundary and loading conditions. The decision process includes determination of criticality of hot points/regions with large gradients in the problem domain and the prediction of mesh sizes for them. The mesh size information is then used to construct a high quality initial mesh with an automatic mesh generator, that is based on a more efficient and enhanced version of the advancing front mesh generation technique. In this mesh generation scheme, each critical point/region is assigned a mesh size function to allow users to create a desired graded initial mesh in less time and with minimum amount of effort. A mesh size function can be linear, quadratic or exponential, depending on the expected gradient of an initial mesh. This provides a more flexible and powerful tool for the construction of an initial mesh that is as close to an optimal mesh as possible.

In addition, a new criterion, Mesh Index of Quality (Mesh IQ), as well as mesh performance measures are proposed to examine the quality of a finite element mesh and in turn determine the accuracy of the associated solution. This criterion is based on the global as well as local errors and their distribution in the problem domain. In addition, suitability of strongly graded meshes versus moderately graded meshes for problems with strong singularity was investigated. Several examples were used to evaluate the performance of the proposed techniques. The results confirm the validity and superiority of the proposed methods for the examples studied.