Multigrid methods for elliptical problems in unbounded domains
Journal Article
·
· SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States)
- Brookhaven National Lab., Upton, NY (United States)
The goal of this work is to study multigrid methods in connection with the numerical solution of elliptic problems in the exterior of a bounded domain. The numerical method consists of approximating the original problem by one on a truncated domain of diameter R and imposing a simple local approximate boundary condition on the outer boundary. The resulting problem is discretized using the finite element method. R must be made sufficiently large to reduce the truncation error (due to the approximate boundary condition) to the level of the discretization error. This results in a very large number of unknowns (increasing like 0(R[sup 3]) in three dimensions), when a quasi-uniform mesh is used. In previous work by the author it was shown that optimal error estimates hold with the number of unknowns independent of R using a mesh grading procedure in which the size of the elements are systematically increased as their distance from the origin increases. In the present paper it is shown that the multigrid convergence rate is independent of R using a mesh grading of this kind (with the number of unknowns increasing like log R).
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 6421153
- Journal Information:
- SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States) Vol. 30:1; ISSN 0036-1429; ISSN SJNAAM
- Country of Publication:
- United States
- Language:
- English
Similar Records
Numerical method for solving elliptic boundary value problems in unbounded domains
Multigrid methods for nonconforming finite elements
Adaptive finite element grid generation and extension for elliptic problems posed on unbounded domains
Conference
·
Tue Jul 01 00:00:00 EDT 1980
·
OSTI ID:5292562
Multigrid methods for nonconforming finite elements
Thesis/Dissertation
·
Thu Dec 31 23:00:00 EST 1987
·
OSTI ID:5903111
Adaptive finite element grid generation and extension for elliptic problems posed on unbounded domains
Technical Report
·
Tue May 01 00:00:00 EDT 1984
·
OSTI ID:6821440