A parallel hybrid banded system solver: the SPIKE algorithm

This paper describes an efficient and robust hybrid parallel solver “the SPIKE algorithm” for narrow-banded linear systems. Two versions of SPIKE with their built-in-options are described in detail: the Recursive SPIKE version for handling non-diagonally dominant systems and the Truncated SPIKE version for diagonally dominant ones. These SPIKE schemes can be used either as direct solvers, or as preconditioners for outer iterative schemes. Both versions are faster than the direct solvers in ScaLAPACK on parallel computing platforms, and quite competitive in terms of achieved accuracy for handling systems that are dense within the band.