A Comparison Of Optimization Software For Mesh Shape-Quality Improvement Problems

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.

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