Using the VBARMS method in parallel computing

TL;DR

This paper presents an enhanced parallel implementation of the VBARMS preconditioner, which automatically detects dense structures in linear systems to improve efficiency in solving large nonsymmetric problems.

Contribution

It introduces a novel graph compression algorithm for automatic dense block detection and demonstrates improved performance on large-scale Navier-Stokes simulations.

Findings

Improved reliability and throughput in parallel VBARMS

Effective detection of dense structures in linear systems

Enhanced performance on turbulent Navier-Stokes equations

Abstract

The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li,~Saad and Sosonkina [NLAA, 2003] for solving general nonsymmetric linear systems. The parallel VBARMS solver can detect automatically exact or approximate dense structures in the linear system, and exploits this information to achieve improved reliability and increased throughput during the factorization. A novel graph compression algorithm is discussed that finds these approximate dense blocks structures and requires only one simple to use parameter. A complete study of the numerical and parallel performance of parallel VBARMS is presented for the analysis of large turbulent Navier-Stokes equations on a suite of three-dimensional test cases.