Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: what is the largest shift for which wavenumber-independent convergence is …
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 …
operator Δ+ k^ 2 Δ+ k 2 (subject to suitable boundary conditions) using a discrete version of …
The Burton and Miller method: Unlocking another mystery of its coupling parameter
S Marburg - Journal of Computational Acoustics, 2016 - World Scientific
The phenomenon of irregular frequencies or spurious modes when solving the Kirchhoff–
Helmholtz integral equation has been extensively studied over the last six or seven …
Helmholtz integral equation has been extensively studied over the last six or seven …
[HTML][HTML] The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, ie the
equation∇⋅(A∇ u)+ k 2 nu=− f where both A and n are functions of position. We prove new …
equation∇⋅(A∇ u)+ k 2 nu=− f where both A and n are functions of position. We prove new …
Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions
We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz
obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds …
obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds …
Is the Helmholtz equation really sign-indefinite?
The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in
the sense that the bilinear forms cannot be bounded below by a positive multiple of the …
the sense that the bilinear forms cannot be bounded below by a positive multiple of the …
Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations
We consider three problems for the Helmholtz equation in interior and exterior domains in
R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for …
R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for …
Chapter 6: Overview of Variational Formulations for Linear Elliptic PDEs
EA Spence - Unified Transform for Boundary Value Problems …, 2014 - SIAM
6.1▪“When All Else Fails, Integrate by Parts”: New and Old Variational Formulations for
Linear Elliptic PDEs 6.1. 1▪ Introduction Although the motto “when all else fails, integrate by …
Linear Elliptic PDEs 6.1. 1▪ Introduction Although the motto “when all else fails, integrate by …
Wavenumber-explicit bounds in time-harmonic acoustic scattering
EA Spence - SIAM Journal on Mathematical Analysis, 2014 - SIAM
We prove wavenumber-explicit bounds on the Dirichlet-to-Neumann map for the Helmholtz
equation in the exterior of a bounded obstacle when one of the following three conditions …
equation in the exterior of a bounded obstacle when one of the following three conditions …
High-frequency bounds for the Helmholtz equation under parabolic trapping and applications in numerical analysis
This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation
posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the …
posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the …
Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem
We consider solving the exterior Dirichlet problem for the Helmholtz equation with the h-
version of the boundary element method (BEM) using the standard second-kind combined …
version of the boundary element method (BEM) using the standard second-kind combined …