There has been much recent research on preconditioning discretisations of the Helmholtz
operator Δ+ k^ 2 Δ+ k 2 (subject to suitable boundary conditions) using a discrete version of …

In this paper, we present a data-driven approach to iteratively solve the discrete
heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine …

This book describes, in a basic way, the most useful and effective iterative solvers and
appropriate preconditioning techniques for some of the most important classes of large and …

The shifted Helmholtz operator has received a lot of attention over the past decade as a
preconditioner for the iterative solution of the Helmholtz equation. The idea is that if one …

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 …

In this paper, we address the solution of three‐dimensional heterogeneous Helmholtz
problems discretized with second‐order finite difference methods with application to …

In geophysics, full waveform inversion rely on an efficient forward modeling method.
However, a direct solver is computationally expensive and requires significant in-core …

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

In this paper, we consider the numerical solution of the Helmholtz equation, arising from the
study of the wave equation in the frequency domain. The approach proposed here differs …

In finite-difference (FD) acoustic forward modelling, the parameter settings for the perfectly
matched layer (PML) are case-dependent. There is no explicit PML formula that can be …