Výsledky vyhledávání - "Graham, I. G."

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The radiative transport equation with heterogeneous cross-sections

Autor: Blake, J. C. H., Graham, I. G., Scheben, F., Spence, A.

We consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the integral operator in this formulation which is expl

Externí odkaz: http://arxiv.org/abs/1903.08623

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Domain Decomposition with local impedance conditions for the Helmholtz equation with absorption

Autor: Graham, I. G., Spence, E. A., Zou, J.

We consider one-level additive Schwarz preconditioners for a family of Helmholtz problems with absorption and increasing wavenumber $k$. These problems are discretized using the Galerkin method with nodal conforming finite elements of any (fixed) ord

Externí odkaz: http://arxiv.org/abs/1806.03731

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Stability and error analysis for the Helmholtz equation with variable coefficients

Autor: Graham, I. G., Sauter, S. A.

We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an existence-uniqu

Externí odkaz: http://arxiv.org/abs/1803.00966

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Recent Results on Domain Decomposition Preconditioning for the High-frequency Helmholtz Equation using Absorption

Autor: Graham, I. G., Spence, E. A., Vainikko, E.

In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with added abso

Externí odkaz: http://arxiv.org/abs/1606.07172

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Filon-Clenshaw-Curtis rules for highly-oscillatory integrals with algebraic singularities and stationary points

Autor: Dominguez, V., Graham, I. G., Kim, T.

In this paper we propose and analyse composite Filon-Clenshaw-Curtis quadrature rules for integrals of the form $I_{k}^{[a,b]}(f,g) := \int_a^b f(x) \exp(\mathrm{i}kg(x)) \rd x $, where $k \geq 0$, $f$ may have integrable singularities and $g$ may ha

Externí odkaz: http://arxiv.org/abs/1207.2283

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