𝙼𝚄𝙼𝙿𝚂: MUltifrontal Massively Parallel Solver for the direct solution of sparse linear equations

Abstract

The scientific library 𝙼𝚄𝙼𝙿𝚂 (MUltifrontal Massively Parallel Solver) solves large systems of sparse linear equations using a direct method. It is an open-source software library distributed under the CeCILL-C license which can be downloaded from the 𝙼𝚄𝙼𝙿𝚂 solver website.

Direct methods are widely appreciated for their numerical robustness, reliability, and ease of use. They are commonly used either to compute the solution or as a preconditioner within iterative methods. However, they are also known for their high computational complexity.

In this communication, we briefly describe the main features of the 𝙼𝚄𝙼𝙿𝚂 solver. We then explain how data sparsity with block low-rank (BLR) approximations and mixed precision can be used to reduce the complexity of direct methods. We conclude by showing results on large real-world applications (matrices of order several hundred million) and describing ongoing research work.