A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations

Clique

In order to implement the previously discussed techniques for scalable multifrontal factorizations and solves (via selective inversion), an open-source distributed multifrontal solver named Clique was built on top of Elemental (30), a library for distributed-memory dense linear algebra. In addition to being designed to support the techniques we discussed above: selective inversion, subtree-to-submesh mappings, and two-dimensional frontal matrix distributions, it was also written with a strong emphasis on memory scalability. This is because the sweeping preconditioner requires large numbers of factorizations of relatively small sparse matrices, and so it is crucial that the per-process memory usage for each subdomain factorization decreases inversely with the total number of processes.

We note that Clique was designed specifically to provide a memory-scalable multifrontal implementation for our parallel sweeping preconditioner, and so there is not yet support for pivoting. We plan to add a pivoted LU factorization in the near future.