Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences |
| |
Authors: | Michael Griebel |
| |
Affiliation: | 1. Institut für Angewandte Mathematik, Universit?t Bonn, Wegelerstr. 6, D-53115, Bonn, Federal Republic of Germany
|
| |
Abstract: | We present a multilevel approach for the solution of partial differential equations. It is based on a multiscale basis which
is constructed from a one-dimensional multiscale basis by the tensor product approach. Together with the use of hash tables
as data structure, this allows in a simple way for adaptive refinement and is, due to the tensor product approach, well suited
for higher dimensional problems. Also, the adaptive treatment of partial differential equations, the discretization (involving
finite differences) and the solution (here by preconditioned BiCG) can be programmed easily. We describe the basic features
of the method, discuss the discretization, the solution and the refinement procedures and report on the results of different
numerical experiments. |
| |
Keywords: | 65N06 65N50 68Y99 68P05 |
本文献已被 SpringerLink 等数据库收录! |
|