Parallel multilevel iterative methods

Parallel S.O.R. iterative methods

New explicit group S.O.R. methods suitable for use on an asynchronous MIMD computer are presented for the numerical solution of the sparse linear systems derived from the discretization of two-dimensional , second-order, elliptic boundary value problems. A comparison with existing implicit line S.O.R. schemes for the Dirichlet model problem shows the new schemes to be superior (Barlow and Evans...

Parallel Multilevel and Multigrid Methods

1. Preliminaries. Multigrid methods originated earlier this century, in the personnel computing era. Someone who needed to compute an approximation to the solution of a partial di erential equation during that era would ll a room with people. After using very simple mechanical calculators to compute parts of the approximation, these people would pass their parts to the other people in the room ...

Robust Parallel Newton{multilevel Methods

The present paper is devoted to the numerical solution of nonlinear boundary value problems arising in the magnetic eld computation and in solid mechanics. These problems are discretized by using nite elements. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely mult...

Parallel Point-oriented multilevel methods

Instead of the usual basis, we use a generating system for the discretization of PDEs that contains not only the basis functions of the nest level of discretization but additionally the basis functions of all coarser levels of discretization. The Galerkin-approach now results in a semide nite system of linear equations to be solved. Standard iterative GS-methods for this system turn out to be e...

Massively parallel Multilevel Monte Carlo methods