Efficient d-multigrid preconditioners for sparse-grid solution of high-dimensional partial differential equations

Authors:
H. Bin Zubair;C. C. W. Leentvaar;C. W. Oosterlee
Affiliations:
Numerical Analysis Group, Delft Institute of Applied Mathematics Delft University of Technology, The Netherlands;Numerical Analysis Group, Delft Institute of Applied Mathematics Delft University of Technology, The Netherlands;Numerical Analysis Group, Delft Institute of Applied Mathematics Delft University of Technology, The Netherlands
Venue:
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Year:
2007

Citing 7
Cited 0

BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
An Evaluation of Parallel Multigrid as a Solver and a Preconditioner for Singularly Perturbed Problems

SIAM Journal on Scientific Computing
Multigrid

Multigrid
Fourier Analysis of GMRES(m) Preconditioned by Multigrid

SIAM Journal on Scientific Computing
Sparse grid spaces for the numerical solution of the electronic Schrödinger equation

Numerische Mathematik
Algorithms for Numerical Analysis in High Dimensions

SIAM Journal on Scientific Computing
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Fast and efficient solution techniques are developed for high-dimensional parabolic partial differential equations (PDEs). In this paper we present a robust solver based on the Krylov subspace method Bi-CGSTAB combined with a powerful, and efficient, multigrid preconditioner. Instead of developing the perfect multigrid method, as a stand-alone solver for a single problem discretized on a certain grid, we aim for a method that converges well for a wide class of discrete problems arising from discretization on various anisotropic grids. This is exactly what we encounter during a sparse grid computation of a high-dimensional problem. Different multigrid components are discussed and presented with operator construction formulae. An option-pricing application is focused and presented with results computed with this method.