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Multilevel accelerated optimization for problems in grid generation

Berndt, Markus and Mikhail Shashkov

Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.351-359, Sept. 2003

IMR
PROCEEDINGS

12th International Meshing Roundtable
September 14-17, 2003
Santa Fe, New Mexico, U.S.A.

Los Alamos National Laboratory, Los Alamos, NM, U.S.A.
berndt@lanl.gov shashkov@lanl.gov

Abstract
The qualtiy of numerical simmulations of processes that are modeled by partial differential equations strongly depends on the quality of the mesh that is used for their discretization. This quality is affected, for example, by mesh smoothness, or discretization error. To improve the mesh, a functional that is in general nonlinear must be minimized (for example, the L2 approximation error in the mesh). This minimimization is constrained by the validity of the mesh, since no mesh folding is allowed. Classical techniques such as CG, or Gauss-Seidel steepest descent, perform very poorly in this class of minimization problems. We introduce a new minimization tecnique that utilizes the underlying geometry of the problem. By coarsening the mesh successively, in a multilevel-like fashion, minimizing appropriate coarse grid quality measures, and interpolating finer meshes from coarser ones, a more rapid movement of fine mesh points results, and the overall convergence of the minimization procedure is accelerated.

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