Task scheduling in an asynchronous distributed memory multifrontal solver

We describe the improvements to the task scheduling for MUMPS, an asynchronous distributed memory direct solver for sparse linear systems. In the new approach, we determine, during the analysis of the matrix, candidate processes for the tasks that will be dynamically scheduled during the subsequent factorization. This approach significantly improves the scalability of the solver in terms of execution time and storage. By comparison with the previous version of MUMPS, we demonstrate the efficiency and the scalability of the new algorithm on up to 512 processors. Our test cases include matrices from regular three-dimensional grids and irregular grids from real-life applications.