ButterflyPACK

Abstract

ButterflyPACK is a mathematical software for rapidly solving large-scale dense linear systems that exhibit off-diagonal rank-deficiency properties. These targeted systems are either matrices arising from discretized boundary integral equations, or frontal matrices in multi-frontal solvers for differential equations. ButterflyPACK relies on low-rank and butterfly formats under Hierarchical matrix, HODLR or HSS frameworks to compress, factor/precondition and solve the linear system in quasi-linear time. ButterflyPACK is particularly useful for large-scale ill-conditioned matrices arising from high-frequency wave equations involving multiple right-hand-sides. ButterflyPACK is based on Fortran 2003, it also has interface written in C++. In addition, ButterflyPACK can be readily invoked from the software STRUMPACK. ButterflyPACK supports hybrid MPI/OpenMP programming models.