49 citations · 144 across the 45 of their papers we have counts for
6 papers · 1 filter
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
David Lafontaine, Euan A. Spence
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…
Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains
Simon N. Chandler-Wilde, Euan A. Spence
We present new second-kind integral-equation formulations of the interior and exterior Dirichlet problems for Laplace's equation. The operators in these formulations are both conti…
The -FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect
Jeffrey Galkowski, David Lafontaine, Euan A. Spence +1
We consider approximation of the variable-coefficient Helmholtz equation in the exterior of a Dirichlet obstacle using perfectly-matched-layer (PML) truncation; it is well known th…
Wavenumber-explicit parametric holomorphy of Helmholtz solutions in the context of uncertainty quantification
Euan A. Spence, Jared Wunsch
A crucial role in the theory of uncertainty quantification (UQ) of PDEs is played by the regularity of the solution with respect to the stochastic parameters; indeed, a key propert…
A simple proof that the -FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation
Euan A. Spence
In dimensions, approximating an arbitrary function oscillating with frequency requires degrees of freedom. A numerical method for solving the Helmholtz…
Does the Helmholtz boundary element method suffer from the pollution effect?
Jeffrey Galkowski, Euan A. Spence
In dimensions, accurately approximating an arbitrary function oscillating with frequency requires degrees of freedom. A numerical method for solving the…