L. Freitag, P. Knupp, T. Munson, S. Shontz,, "A Comparison of Optimization Software for Mesh Shape-Quality Improvement Problems," Preprint ANL/MCS-P953-0502, May 2002. [pdf]
Simplicial mesh shape-quality can be improved by optimizing an objective function based on tetrahedral shape measures. If the objective function is formulated in terms of all elements in a given mesh rather than a local patch, one is confronted with a large-scale, nonlinear, constrained numerical optimization problem. We investigate the use of six general-purpose state-of-the-art solvers and two custom-developed methods to solve the resulting large-scale problem. The performance of each method is evaluated in terms of robustness, time to solution, convergence properties, and scalability on several two- and three-dimensional test cases.