How large a shift is needed in the shifted Helmholtz preconditioner for its effective inversion by multigrid?

PH Cocquet, MJ Gander - SIAM Journal on Scientific Computing, 2017‏ - SIAM
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 …

FEM and CIP-FEM for Helmholtz equation with high wave number and perfectly matched layer truncation

Y Li, H Wu - SIAM Journal on Numerical Analysis, 2019‏ - SIAM
The Helmholtz scattering problem with high wave number is truncated by the perfectly
matched layer (PML) technique and then discretized by the linear continuous interior penalty …

[HTML][HTML] Scalable multi-level deflation preconditioning for highly indefinite time-harmonic waves

V Dwarka, C Vuik - Journal of Computational Physics, 2022‏ - Elsevier
Recent research efforts aimed at iteratively solving time-harmonic waves have focused on a
broad range of techniques to accelerate convergence. In particular, for the famous …

A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation

H Chen, P Lu, X Xu - Journal of Computational Physics, 2014‏ - Elsevier
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method
for the Helmholtz equation with high wave number is presented in this paper. There are two …

Is pollution effect of finite difference schemes avoidable for multi-dimensional Helmholtz equations with high wave numbers?

K Wang, YS Wong - Communications in Computational Physics, 2017‏ - cambridge.org
This paper presents an approach using the method of separation of variables applied to 2D
Helmholtz equations in the Cartesian coordinate. The solution is then computed by a series …

Stand-alone Multigrid for Helmholtz Revisited: Towards Convergence Using Standard Components

V Dwarka, C Vuik - arxiv preprint arxiv:2308.13476, 2023‏ - arxiv.org
Getting standard multigrid to work efficiently for the high-frequency Helmholtz equation has
been an open problem in applied mathematics for years. Much effort has been dedicated to …

Sixth-order finite difference scheme for the Helmholtz equation with inhomogeneous Robin boundary condition

Y Zhang, K Wang, R Guo - Advances in Difference Equations, 2019‏ - Springer
In this paper, a class of sixth-order finite difference schemes for the Helmholtz equation with
inhomogeneous Robin boundary condition is derived. This scheme is based on the sixth …

A pure source transfer domain decomposition method for Helmholtz equations in unbounded domain

Y Du, H Wu - Journal of Scientific Computing, 2020‏ - Springer
We propose a pure source transfer domain decomposition method (PSTDDM) for solving the
truncated perfectly matched layer (PML) approximation in bounded domain of Helmholtz …

Solving Helmholtz equation at high wave numbers in exterior domains

K Wang, YS Wong, J Huang - Applied Mathematics and Computation, 2017‏ - Elsevier
This paper presents effective difference schemes for solving the Helmholtz equation at high
wave numbers. Considering the problems in the polar and spherical coordinates, we show …

An efficient multigrid algorithm for heterogeneous acoustic media sign‐indefinite high‐order FEM models

M Ganesh, C Morgenstern - Numerical Linear Algebra with …, 2017‏ - Wiley Online Library
Large‐scale scientific computing models are needed for the simulation of wave propagation
especially for multiple frequency and high‐frequency models in complex heterogeneous …