A Parallel Version of a Multigrid Algorithm for Isotropic Transport Equations

Abstract

The focus of this paper is on a parallel algorithm for solving the transport equations in a slab geometry using multigrid. The spatial discretization scheme used is a nite element method called Modi ed Linear Discontinuous scheme (MLD). The MLD scheme represents a lumped version of the standard Linear Discontinuous scheme (LD). The parallel algorithm was implemented on the Connection Machine 2 (CM2). Convergence rates and timings for this algorithm on the CM2 and Cray-YMP are shown.

Extending the applicability of multigrid methods

“…To apply spatial multigrid to the single-group equations, a smoothing step must be identified that facilitates spatial coarsening. Early work on multigrid algorithms for this equation in slab geometry employed a block Jacobi relaxation, where the blocks correspond to two-cell pairs on the spatial grid [33]. A similar algorithm was implemented in two spatial dimensions using a block Jacobi based on 4-cell blocks [27].…”

A Parallel Davidson-Type Algorithm for Several Eigenvalues

“…In addition to the Diagonal precondioner we will present numerical results with Multigrid and ADI preconditioners. In this paper we do not intend to address parallelization issues of the multilevel or ADI preconditioners: For multigrid preconditioners several implementations are available in the literature [3,16,25]. The same is true about the parallelization of the ADI preconditioner [13,21,24].…”

Fast algorithms for transport models

“…A version of the multigrid in space algorithm was programmed on the Thinking Machines Inc. CM-200 located at Los Alamos National Laboratories [16] [17]. The two-cell/_-line relaxation is inherently parallel.…”

“…Both algorithms have been implemented on the Thinking Machines Inc. CM-200 at Los Alamos National Laboratories (LANL). The codes are highly parallel and represent the state-of-the-art for slab geometry [16] [17].…”