Speaker
Description
We discuss the adaptive coarse-space basis functions for the multi-level overlapping additive Schwarz preconditioners implemented in FROSch. The basis functions are formed based on the discrete Harmonic extensions of the local subdomain interface functions. The basis functions for the interface are composed of the eigenvectors corresponding to the small eigenvalues of the generalized eigenvalue problems formed by the local Schur complements on the interface. This leads to a provably-robust multi-level preconditioner for solving heterogeneous elliptic problems. We present numerical results to demonstrate that the iterations count stays relatively constant even with the increasing number of subdomains for solving problems with large coefficients jumps. Our performance results on NERSC Perlmutter supercomputer will then demonstrate the scalability of the method for solving large-scale problems.