Abstract :
[en] Full Waveform Inversion in the frequency domain requires the resolution of sequences of Helmholtz-like problems, each one of them with many right-hand sides (i.e. many different excitations). For large-scale 3D problems, Domain Decomposition Methods are a popular choice, but usual Krylov methods do not handle multiple right-hand sides efficiently.
Coupling Optimized Restrictive Additive Schwarz with Block Krylov Methods (e.g. Block GMRES) has proven to significantly reduce the iteration count [1], but with an overhead that mitigates these benefits for large blocks. In this work, we investigate similar ideas for non-overlapping methods that solve a substructured problem, i.e. with unknowns on the subdomain interfaces. We show that this approach has comparable convergence properties, but can handle larger blocks due to the reduced size of the vectors managed by the Krylov method. This property makes substructured non-overlapping methods particularly attractive when a large number of sources is involved.
[1] P. Jolivet and P.-H. Tournier, "Block Iterative Methods and Recycling for Improved Scalability of Linear Solvers," SC '16: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Salt Lake City, UT, USA, 2016, pp. 190-203.
