A Parallel Fast Direct Solver for the Discrete Solution of Separable Elliptic Equations.
Tuomo Rossi, Jari Toivanen · 1997
A parallel fast direct solver based on the Divide & Conquer method is considered for linear systems with separable block tridiagonal matrices. Such systems are obtained, for example, by discretizing the two--dimensional Poisson equation posed on rectangular domains with the continuous piecewise linear finite elements on nonuniform triangulated rectangular meshes. The Divide & Conquer method has the arithmetical complexity O(N log N ), and it is closely related to the cyclic reduction, but instead of using the matrix polynomial factorization, the so--called partial solution technique is employed. The parallel implementation using the MPI standard is described and a good parallel scalability of the proposed method is demonstrated on an IBM SP2 parallel computer. Also, the sequential performance is compared with the well--known BLKTRI--implementation of the generalized cyclic reduction method using a single processor of IBM SP2. 1 Introduction The fast direct solution of linear elliptic ...