Optimization Strategies in Unstructured Mesh Generation

International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 39, Num 12, pp.2055 - 2071, June 1996

MESHING
RESEARCH
CORNER

E. A. Dari and G. C. Buscaglia
Instituto Balseiro, Universidad Nac. de Cuyo and Centro Atómico Bariloche, 8400 Bariloche, Comisión Nacional de Energía Atómica, Argentina

Abstract

We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.