# A parallel block cyclic reduction algorithm for the fast solution of elliptic equations

Session 6B: Parallel Numeric Methods

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## Abstract

This paper presents an adaptation of the Block Cyclic Reduction (BCR) algorithm for a multi-vector processor. The main bottleneck of BCR lies in the solution of linear systems whose coefficient matrix is the product of tridiagonal matrices. This bottleneck is handled by expressing the rational function corresponding to the inverse of this product as a sum of elementary fractions. As a result the solution of this system leads to parallel solutions of tridiagonal systems. Numerical experiments performed on an Alliant FX/8 are reported.

## Keywords

Fast Fourier Transform Outer Loop Matrix Polynomial Vector Length Elliptic Partial Differential Equation
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© Springer-Verlag Berlin Heidelberg 1988