Efficient substructured domain-decomposition in inverse problems using Krylov subspace recycling

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 Meth-
ods (e.g. Block GMRES) and subspace recycling (e.g. GCRO-DR and its block
version) has proven to significantly reduce the iteration count[1], but with an
arithmetic overhead that mitigates these benefits for large blocks in terms of
actual compute time.
In this work, we investigate similar ideas for non-overlapping methods that
solve a substructured problem, i.e. with unknowns on the subdomain inter-
faces.
These methods have a moderately slower convergence, 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 at-
tractive when many sources are involved. We try to evaluate for both methods
the optimal block size and recycling strategy, and determine whether overlap-
ping or non-overlapping methods are the most appropriate for problems with a
massive number of sources.