Abstract :
[en] Full Waveform Inversion (FWI) is a technique for solving inverse scattering prob-
lems, consisting of finding an optimal model (physical parameters) to fit data by
solving wave propagation problems (the forward problem) with sequences of guess
models that are iteratively updated. An efficient implementation requires a fast res-
olution of the forward problem, as it needs to be solved for all sources of excitation,
for all models to be evaluated, and for all frequencies involved.
For large-scale time-harmonic problems, a substructured Domain Decomposition
Method can be used to solve the forward problem in parallel. In this case, a reduced
problem on the domain interfaces needs to be solved iteratively, in a matrix-free
fashion. A popular approach is to use Krylov solvers such as GMRES (Saad, Y.
and Schultz, M. (1986) ”GMRES: A Generalized Minimal Residual Algorithm for
Solving Nonsymmetric Linear Systems”. SIAM Journal on Scientific and Statistical
Computing, 7, 856-869), BiCGStab (Van der Vorst, H. A. (1992). ”Bi-CGSTAB: A
Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric
Linear Systems”. SIAM J. Sci. Stat. Comput. 13 (2): 631–644), GCRO-DR or
GCROT (Parks, M. and de Sturler, E and Mackey, G. and Johnson, D. and Maiti,
S. (2004). ”Recycling Krylov Subspaces for Sequences of Linear Systems”. SIAM
Journal on Scientific Computing. 28).
When solving for different excitations, the same linear system arises but with a
different right-hand side. On the contrary, solving with a different frequency or
model leads to a new operator. Krylov subspace recycling techniques have been
developed to reuse information from one resolution to another to accelerate the
whole sequence (e.g. Jolivet, Pierre and Tournier, Pierre-Henri. “Block Iterative
Methods and Recycling for Improved Scalability of Linear Solvers.” SC16: Inter-
national Conference for High Performance Computing, Networking, Storage and
Analysis (2016): 190-203). Some are designed for a constant operator and varying
excitation, while others can be used when both vary.
In this work, we review common recycling techniques and evaluate their efficiency
for varying sources, frequencies, and models in the context of substructured prob-
lems. For varying operators, we introduce a new preconditioner that does not re-
quire additional matrix-vector products, unlike traditional recycling methods
