Abstract

While it is theoretically and computationally advantageous to pose the inverse problem of subsurface recovery in the frequency domain, efficiently solving time-harmonic wave equations, the associated forward problem, in parallel, remains challenging for large 3D problems at high-frequency and in heterogeneous media. In this talk, I present an overview of our development of parallel implementations of effective solvers for this regime, built using the method of polarized traces. In particular, I will focus on the challenges of extending the already efficient 2D method to 3D while maintaining parallel scalability. I will show some recent results on applications to highly heterogeneous media in 3D. I will also introduce our variant of polarized traces, the L-sweeps method, which allows us to solve the 3D Helmholtz equation in parallel with sub-linear scaling