Performance characterization of nonlinear optimization methods for mesh quality improvement

摘要

We characterize the performance of gradient-and Hessian-based optimization methods for mesh quality improvement. In particular, we consider the steepest descent and Polack-Ribiere conjugate gradient methods which are gradient based. In the Hessian-based category, we consider the quasi-Newton, trust region, and feasible Newton methods. These techniques are used to improve the quality of a mesh by repositioning the vertices, where the overall mesh quality is measured by the sum of the squares of individual elements according to the aspect ratio metric. The effects of the desired degree of accuracy in the improved mesh, problem size, initial mesh configuration, and heterogeneity in element volume on the performance of the optimization solvers are characterized on a series of tetrahedral meshes.