HR: 0830h
AN: NG11A-0172    [PDF]
TI: Adaptive Multilevel Second-Generation Wavelet Collocation Elliptic Solver: A Cure for High Viscosity Contrasts
AU: Kevlahan, N N
AF: McMaster University, Department of Mathematics & Statistics, Hamilton, ON L8S 4K1 Canada
AU: * Vasilyev, O V
EM: Oleg.Vasilyev@Colorado.EDU
AF: University of Colorado, Department of Mechanical Engineering, Boulder, CO 80309 United States
AU: Yuen, D A
AF: Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55415 United States
AU: Yuen, D A
AF: University of Minnesota, Department of Geology and Geophysics, Minneapolis, MN 55415 United States
AB: An adaptive multilevel wavelet collocation method for solving multi-dimensional elliptic problems with localized structures is developed. The method is based on the general class of multi-dimensional second generation wavelets and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems. Wavelet decomposition is used for grid adaptation and interpolation, while O(N) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid. In order to accelerate the convergence of the iterative solver, an iterative procedure analogous to the multigrid algorithm is developed. For the problems with slowly varying viscosity simple diagonal preconditioning works. For problems with large laterally varying viscosity contrasts either direct solver on shared-memory machines or multilevel iterative solver with incomplete LU preconditioner may be used. The method is demonstrated for the solution of a number of two-dimensional elliptic test problems with both constant and spatially varying viscosity with multiscale character.
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3230 Numerical solutions
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting