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

Proceedings, 11th International Meshing Roundtable, Sandia National Laboratories, pp.29-40, September 15-18 2002

MESHING
RESEARCH
CORNER

11th International Meshing Roundtable
Ithaca, New York, USA
September 15-18, 2002

Lori Freitag, Todd Munson
Mathematics and Computer Science Division
Argonne National Laboratory, Argonne, IL 60439
freitag,tmunson@mcs.anl.gov

Patrick Knupp
Parallel Computing Sciences Department
Sandia National Laboratories, Albuquerque, NM 87185
pknupp@sandia.gov

Suzanne Shontz
Center for Applied Mathematics
Cornell University, Ithaca, NY 14853
shontz@cam.cornell.edu

Abstract
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 onseveral two- and three-dimensional test cases.

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