The method of polarized traces for the 3D Helmholtz equation
This work addresses the computational bottleneck of solving the 3D Helmholtz equation for multiple right-hand sides, which is critical for seismic imaging applications.
The authors present a fast solver for the 3D Helmholtz equation with an empirical online runtime of O(max(1,R/n) N log N), enabling large-scale frequency-domain full waveform inversion.
We present a fast solver for the 3D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media. The solver is based on the method of polarized traces, coupled with distributed linear algebra libraries and pipelining to obtain an empirical online runtime $ \mathcal{O}(\max(1,R/n) N \log N)$ where $N = n^3$ is the total number of degrees of freedom and $R$ is the number of right-hand sides. Such a favorable scaling is a prerequisite for large-scale implementations of full waveform inversion (FWI) in frequency domain.