When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

The eikonal equation is instrumental in many applications in several fields ranging from
computer vision to geoscience. This equation can be efficiently solved using the iterative …

We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous
acoustic media, with online parallel complexity that scales optimally as O (NL), where N is …

Deflating the shifted Laplacian with geometric multigrid vectors yields speedup. To verify this
claim, we investigate a simplified variant of Erlangga and Nabben presented in [Erlangga …

We study the convergence of multigrid schemes for the Helmholtz equation, focusing in
particular on the choice of the coarse scale operators. Let G_\rmc denote the number of …

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in
highly heterogeneous media usually require finely discretized mesh to represent the …

In this paper, we solve the Helmholtz equation with multigrid preconditioned Krylov
subspace methods. The class of shifted Laplacian preconditioners is known to significantly …

We present a deep learning-based iterative approach to solve the discrete heterogeneous
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …

Seismic waveform inversion aims at obtaining detailed estimates of subsurface medium
parameters, such as the spatial distribution of soundspeed, from multiexperiment seismic …

Full waveform inversion (FWI) is a process in which seismic numerical simulations are fit to
observed data by changing the wave velocity model of the medium under investigation. The …