A polarized-trace preconditioner for 2D Helmholtz and frequency domain full-waveform inversion
Full-waveform inversion is a method for recovering Earth's physical parameters by matching seismic observations with geophysical simulations. To avoid issues due to nonconvexity in full-waveform inversion, the problem is treated in the frequency domain. Frequency domain imaging requires scalable solvers for the Helmholtz equation to make feasible imaging in high resolution and in 3D; however, this remains an open problem. We present recent developments on a domain-decomposition preconditioner for the acoustic Helmholtz equation, based on the notion of polarization, that demonstrates substantial scalability and performance improvements over the state-of-the-art.