How large a shift is needed in the shifted Helmholtz preconditioner for its effective inversion by multigrid?
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 …
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 …
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
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 …
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
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 …
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 …
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
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 …
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 …
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 …
truncated perfectly matched layer (PML) approximation in bounded domain of Helmholtz …
Solving Helmholtz equation at high wave numbers in exterior domains
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 …
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
Large‐scale scientific computing models are needed for the simulation of wave propagation
especially for multiple frequency and high‐frequency models in complex heterogeneous …
especially for multiple frequency and high‐frequency models in complex heterogeneous …