SPIKE: A parallel environment for solving banded linear systems

Abstract

The hybrid banded linear solver SPIKE is proposed as a parallel environment for solving banded systems that are either dense or sparse within the band. The SPIKE algorithm is a domain decomposition technique that allows performing independent calculations on each subdomain or partition of the original linear system. The interface problem leads to a reduced linear system of much smaller size than that of the original system. Three different members of the SPIKE family are described. Each handles the reduced system in a different way depending on the characteristics of the system and the architecture of the high-end parallel computing platform. Numerical experiments are presented that demonstrate the effectiveness of our parallel scheme. Comparison with the corresponding algorithms of ScaLAPACK are also provided for those banded systems that are dense within the band. A SPIKE scheme with multi-level parallelism is also introduced for solving large banded systems that are sparse within the band.