This presentation examines the performance of selected parallel, "physics-based" preconditioning methods applied to the Laplace-Beltrami Target Metric (LBTM) mesh smoothing equations. These equations constitute a nonlinear elliptic system of partial differential equations and are primarly used for unstructured mesh generation on complex geometry. When a target metric mesh improvement method is used, the three coordinate equations are coupled through the metric. The weak form of this system is solved using a standard Jacobian-free Newton-Krylov approach, employing the NOX, EPETRA and AZTECOO packages contained in Sandia National Laboratories TRILINOS project.
Historically the use of Laplace-Beltrami mesh generation methods have been limited by the scalability and efficiency of linear solvers. This work focuses on a study of the effectiveness and parallel scalability of selected "physics-based" preconditioners applied to this problem, and presents numerical examples to support this study and to provide for comparison of the preconditioning strategies.
INL/CON-08-13810 Rev. 0 Work supported by the U.S. Department of Energy Office of Nuclear Energy, under DOE Idaho Operations Office Contract DE-AC07-05ID14517.