Mathematical Modeling and Analysis An Efficient, Numerically Stable, and Scalable Parallel Tridiagonal Solver

Abstract

We describe a stable, efficient, parallel algorithm for the solution of diagonally dominant tridiagonal linear systems that scales well on distributed memory parallel computers. This algorithm is in the class of partitioning algorithms. Its multi-level recursive design makes it well suited for distributed memory parallel computers with very large numbers of processors. The need to solve large tridiagonal systems arises in many numerical analysis applications. In our work, they arise in line relaxations needed by robust multigrid methods, such as the parallel BoxMG code [1], for structured grid problems. The following figure illustrates the importance of having efficient line relaxation methods as the majority of time in a multigrid solve is spent performing these relaxation steps.

Cite this paper

@inproceedings{Ketelsen2006MathematicalMA, title={Mathematical Modeling and Analysis An Efficient, Numerically Stable, and Scalable Parallel Tridiagonal Solver}, author={Christian Ketelsen}, year={2006} }