MueLu

MueLu is a distributed memory parallel direct linear solver for systems of equations. Developed by Eric Chow and others at the Lawrence Berkeley National Laboratory, MueLu addresses some of the same issues as other packages like PETSc and MUMPS. However, MueLu is a standalone package not part of the larger PETSc package.

MueLu offers scalability and flexibility. It is designed to interact with other libraries and can be integrated into a wide range of applications. This is due in part to MueLu's use of a two-level overlapping Schwarz (2L.OS) domain decomposition method, which is a parallel direct solver.

The solution process involves three main stages: first, it establishes the solver data structures; second, it sets up the level-decomposition; and finally, it performs Gaussian elimination. MueLu is built with the use of shared memory and task parallelism, allowing it to effectively utilize multi-core processors. This potential for multi-core utilization, combined with its 2L.OS domain decomposition method, positions MueLu as a potentially high-performance tool for various systems of equations.

MueLu supports direct solvers for small and medium-sized systems and is capable of solving systems on several shared memory processors and hundreds of GPUs. The software can also be compiled with or without GPU support.