Efficient Handling of Multiple Sources and Operators in Domain Decomposition Methods for Full Waveform Inversion

Abstract. 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 sources). 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 [P. Jolivet and P.-H. Tournier, "Block Iterative Methods and Recycling for Improved Scalability of Linear Solvers", 2016], 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 many sources are involved.

We also explore the problem of subspace recycling for a changing operator (i.e. different iterations in the inversion process): Once the problem has been solved for a given model, can we efficiently reuse information to accelerate the solution of the next one, again for all sources ? We compare three approaches involving deflation and preconditionners for the new problem.