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Ivan G. Graham
Researcher at University of Bath
Publications - 120
Citations - 4274
Ivan G. Graham is an academic researcher from University of Bath. The author has contributed to research in topics: Domain decomposition methods & Helmholtz equation. The author has an hindex of 37, co-authored 118 publications receiving 3803 citations. Previous affiliations of Ivan G. Graham include University of Melbourne & Engineering and Physical Sciences Research Council.
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Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering ∗
TL;DR: Recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles is described.
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Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
TL;DR: A novel numerical method based on the method of lines with spherical harmonics and uses fast Fourier transforms to expedite the computation of the reaction kinetics is developed, which efficiently computes the evolution of spatial patterns and yields numerical results which coincide with those predicted by linear stability analysis when the latter is known.
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A new multiscale finite element method for high-contrast elliptic interface problems
TL;DR: A new multiscale finite element method which is able to accurately capture solutions of elliptic interface problems with high contrast coefficients by using only coarse quasiuniform meshes, and without resolving the interfaces is introduced.
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Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
TL;DR: Numerical experiments are reported, showing that the quasi-Monte Carlo method consistently outperforms the Monte Carlo method, with a smaller error and a noticeably better than O(N^-^1^/^2) convergence rate.
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Domain decomposition for multiscale PDEs
TL;DR: Estimates prove very precisely the previously made empirical observation that the use of low-energy coarse spaces can lead to robust preconditioners that are robust even for large coefficient variation inside domains when the classical method fails to be robust.