Search

Results: 78779
A new transform method I
Euan A Spence, A S Fokas
Jan 01, 0001
A new method for solving boundary-value problems (BVPs) for linear and certain nonlinear PDEs was introduced by one of the authors in the late 1990s. For linear PDEs, this method constructs novel integral representations (IRs)...
Published by:
A new transform method II
Euan A Spence, A S Fokas
Jan 01, 0001
A new method for solving boundary-value problems (BVPs) for linear and certain nonlinear PDEs was introduced by one of the authors in the late 1990s. For linear PDEs, this method constructs novel integral representations (IRs)...
Published by:
A new transform method I
Euan A Spence, A S Fokas
Jan 01, 0001
A new method for solving boundary-value problems (BVPs) for linear and certain nonlinear PDEs was introduced by one of the authors in the late 1990s. For linear PDEs, this method constructs novel integral representations (IRs)...
Published by:
A new transform method II
Euan A Spence, A S Fokas
Jan 01, 0001
A new method for solving boundary-value problems (BVPs) for linear and certain nonlinear PDEs was introduced by one of the authors in the late 1990s. For linear PDEs, this method constructs novel integral representations (IRs)...
Published by:
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition

We prove sharp bounds on certain impedance-to-impedance maps (and their compositions) for the Helmholtz equation with large wavenumber (i.e., at high frequency) using semiclassical defect measures. Gong et al. (Numer. Math....

Published by:
Numerical estimation of coercivity constants for boundary integral operators in acoustic scattering
Timo Betcke, Euan A Spence
Jan 01, 0001
Coercivity is an important concept for proving existence and uniqueness of solutions to variational problems in Hilbert spaces. But while coercivity estimates are well known for many variational problems arising from partial...
Published by:
Numerical estimation of coercivity constants for boundary integral operators in acoustic scattering
Timo Betcke, Euan A Spence
Jan 01, 0001
Coercivity is an important concept for proving existence and uniqueness of solutions to variational problems in Hilbert spaces. But while coercivity estimates are well known for many variational problems arising from partial...
Published by:
Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption
In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations} of the Helmholtz equation $-\Delta u - (k^2+ \ri \eps)u = f$, with absorption...
Published by:
A new frequency-uniform coercive boundary integral equation for acoustic scattering
A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this...
Published by:
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification
This paper analyses the following question: let Aj, j = 1,2, be the Galerkin matrices corresponding to finite-element discretisations of the exterior Dirichlet problem for the heterogeneous Helmholtz equations ∇⋅ (Aj∇uj) +...
Published by:
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition

We prove sharp bounds on certain impedance-to-impedance maps (and their compositions) for the Helmholtz equation with large wavenumber (i.e., at high frequency) using semiclassical defect measures. Gong et al. (Numer. Math....

Published by:
Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption
In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations} of the Helmholtz equation $-\Delta u - (k^2+ \ri \eps)u = f$, with absorption...
Published by:
A new frequency-uniform coercive boundary integral equation for acoustic scattering
A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this...
Published by:
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 outgoing solutions, and the interior...
Published by:
Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems

The Restricted Additive Schwarz method with impedance transmission conditions, also known as the Optimised Restricted Additive Schwarz (ORAS) method, is a simple overlapping one-level parallel domain decomposition method...

Published by:
Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems

The Restricted Additive Schwarz method with impedance transmission conditions, also known as the Optimised Restricted Additive Schwarz (ORAS) method, is a simple overlapping one-level parallel domain decomposition method...

Published by:
Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method
Over the last ten years, results from [48], [49], [22], and [47] decomposing high-frequency Helmholtz solutions into “low”- and “high”-frequency components have had a large impact in the numerical analysis of the Helmholtz...
Published by:
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 outgoing solutions, and the interior...
Published by:

|<

<

1

2

3

4

5

>

>|