Graham, Ivan G.

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 Author ID: graham.ivan-g Published as: Graham, I. G.; Graham, Ivan G.; Graham, Ivan; Graham, I. Homepage: http://people.bath.ac.uk/masigg/ External Links: MGP · ORCID · ResearchGate · dblp
 Documents Indexed: 92 Publications since 1979 3 Contributions as Editor · 1 Further Contribution Co-Authors: 62 Co-Authors with 84 Joint Publications 1,577 Co-Co-Authors
all top 5

Co-Authors

 7 single-authored 16 Scheichl, Robert 13 Spence, Euan A. 10 Sloan, Ian Hugh 7 Sauter, Stefan A. 6 Chandler-Wilde, Simon N. 6 Hackbusch, Wolfgang 6 Spence, Alastair 5 Chandler, Graeme A. 5 Kuo, Frances Y. 5 Vainikko, Eero 4 Atkinson, Kendall Eugene 4 Elschner, Johannes 4 Ganesh, Mahadevan 4 Langdon, Stephen 4 Smyshlyaev, Valery P. 3 Bonazzoli, Marcella 3 Dolean, Victorita 3 Nuyens, Dirk 3 Tournier, Pierre-Henri 2 Coomer, R. K. 2 Giani, Stefano 2 Gilbert, Alexander D. 2 Hou, Thomas Yizhao 2 Lindner, Marko 2 Melenk, Jens Markus 2 Parkinson, Matthew J. 2 Pembery, O. R. 2 Scheben, Fynn 2 Sivaloganathan, Jeyabal 1 Andrews, David F. 1 Bachmayr, Markus 1 Barnett, Vic 1 Berns-Müller, Jörg 1 Betcke, Timo 1 Betteridge, Jack 1 Blake, Jack C. H. 1 Bonner, B. D. 1 Chaplain, Mark A. J. 1 Cliffe, K. Andrew 1 Dahmen, Wolfgang A. 1 Digby, P. G. N. 1 Diggle, Peter John 1 Everitt, Brian S. 1 Faermann, Birgit 1 Fienberg, Stephen Elliot 1 Gabriel, K. Ruben 1 Gander, Martin Jakob 1 Gibson, Thomas H. 1 Goldstein, Harvey 1 Gong, Shihua 1 Gower, John C. 1 Grasedyck, Lars 1 Green, Peter J. 1 Greenacre, Michael J. 1 Hagger, M. J. 1 Joe, Stephen 1 Kendall, David George 1 Lakkis, Omar 1 Langer, Ulrich 1 Lechner, P. O. 1 Lin, Qun 1 Löhndorf, Maike 1 McLean, William 1 Mendes, Wendy R. 1 Meyer, Michael M. 1 Müller, Eike Hermann 1 Nguyen, Van Kien 1 Nichols, James A. 1 Schneider, Claus B. 1 Schwab, Christoph 1 Sibson, Robin 1 Silverman, Bernard W. 1 Sini, Mourad 1 Smith, Adrian F. M. 1 Spiegelhalter, David J. 1 Stals, Linda 1 Tukey, John Wilder 1 Tukey, Paul A. 1 Ullmann, Elisabeth 1 van Lent, Jan 1 Wasserman, Stanley S. 1 Xie, Ruifeng
all top 5

Serials

 13 SIAM Journal on Numerical Analysis 12 Numerische Mathematik 10 IMA Journal of Numerical Analysis 7 Mathematics of Computation 4 Journal of Computational Physics 3 Journal of the Australian Mathematical Society, Series B 2 Numerical Methods for Partial Differential Equations 2 Journal of Integral Equations and Applications 2 SIAM Journal on Scientific Computing 1 Bulletin of the Australian Mathematical Society 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 BIT 1 Computing 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Journal of Integral Equations 1 SIAM Journal on Scientific and Statistical Computing 1 Journal of Computational Mathematics 1 Applied Numerical Mathematics 1 Linear Algebra and its Applications 1 Numerical Linear Algebra with Applications 1 Advances in Computational Mathematics 1 Concurrency and Computation: Practice & Experience 1 Acta Numerica 1 Lecture Notes in Computational Science and Engineering 1 Radon Series on Computational and Applied Mathematics 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Wiley Series in Probability and Mathematical Statistics
all top 5

Fields

 87 Numerical analysis (65-XX) 54 Partial differential equations (35-XX) 28 Integral equations (45-XX) 14 Fluid mechanics (76-XX) 9 Optics, electromagnetic theory (78-XX) 6 Probability theory and stochastic processes (60-XX) 5 Approximations and expansions (41-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 3 Potential theory (31-XX) 3 Operator theory (47-XX) 3 Mechanics of deformable solids (74-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Statistics (62-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Biology and other natural sciences (92-XX)

Citations contained in zbMATH Open

83 Publications have been cited 1,614 times in 1,129 Documents Cited by Year
Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. Zbl 1257.65070
Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Spence, Euan A.
2012
A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154
Chu, C.-C.; Graham, I. G.; Hou, T.-Y.
2010
Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. Zbl 0988.92003
Chaplain, M. A. J.; Ganesh, M.; Graham, I. G.
2001
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications. Zbl 1218.65009
Graham, I. G.; Kuo, F. Y.; Nuyens, D.; Scheichl, R.; Sloan, I. H.
2011
Piecewise continuous collocation for integral equations. Zbl 0514.65094
Atkinson, K.; Graham, I.; Sloan, I.
1983
Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Zbl 1328.65238
Gander, M. J.; Graham, I. G.; Spence, E. A.
2015
Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003
Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H.
2015
A high-order algorithm for obstacle scattering in three dimensions. Zbl 1052.65108
Ganesh, M.; Graham, I. G.
2004
Domain decomposition for multiscale PDEs. Zbl 1141.65084
Graham, I. G.; Lechner, P. O.; Scheichl, R.
2007
Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals. Zbl 1231.65060
Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P.
2011
A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Zbl 1169.76056
Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P.
2007
A convergent adaptive method for elliptic eigenvalue problems. Zbl 1191.65147
Giani, S.; Graham, I. G.
2009
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation. Zbl 1272.76217
Betcke, T.; Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Lindner, M.
2011
Finite elements on degenerate meshes: inverse-type inequalities and applications. Zbl 1076.65098
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2005
Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in $$\mathbb R^3$$. Zbl 1018.65139
Graham, I. G.; Sloan, I. H.
2002
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Zbl 1050.65110
Dahmen, W.; Faermann, B.; Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2004
Filon-Clenshaw-Curtis rules for highly oscillatory integrals with algebraic singularities and stationary points. Zbl 1345.65012
Domínguez, V.; Graham, I. G.; Kim, T.
2013
Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. Zbl 1368.65250
Graham, I. G.; Spence, E. A.; Vainikko, E.
2017
Condition number estimates for combined potential boundary integral operators in acoustic scattering. Zbl 1167.35030
Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Lindner, Marko
2009
Iterated Galerkin versus iterated collocation for integral equations of the second kind. Zbl 0586.65091
Graham, Ivan G.; Joe, Stephen; Sloan, Ian H.
1985
Galerkin methods for second kind integral equations with singularities. Zbl 0496.65068
Graham, Ivan G.
1982
Singularity expansions for the solutions of second kind Fredholm integral equations with weakly singular convolution kernels. Zbl 0482.45003
Graham, Ivan G.
1982
Product integration-collocation methods for noncompact integral operator equations. Zbl 0639.65074
Chandler, G. A.; Graham, I. G.
1988
Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. Zbl 0943.65147
Graham, I. G.; Hagger, M. J.
1999
High-order methods for linear functionals of solutions of second kind integral equations. Zbl 0661.65137
Graham, I. G.; Chandler, G. A.
1988
An optimal order collocation method for first kind boundary integral equations on polygons. Zbl 0827.65117
Elschner, J.; Graham, I. G.
1995
Inexact inverse iteration for symmetric matrices. Zbl 1101.65037
Berns-Müller, Jörg; Graham, Ivan G.; Spence, Alastair
2006
A new frequency-uniform coercive boundary integral equation for acoustic scattering. Zbl 1228.35183
Spence, Euan A.; Chandler-Wilde, Simon N.; Graham, Ivan G.; Smyshlyaev, Valery P.
2011
Analysis of circulant embedding methods for sampling stationary random fields. Zbl 1434.60114
Graham, I. G.; Kuo, F. Y.; Nuyens, Dirk; Scheichl, R.; Sloan, I. H.
2018
Parallel computation of flow in heterogeneous media modelled by mixed finite elements. Zbl 0995.76044
Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L.
2000
A new spectral boundary integral collocation method for three-dimensional potential problems. Zbl 0915.65115
Ganesh, M.; Graham, I. G.; Sivaloganathan, J.
1998
Collocation methods for two dimensional weakly singular integral equations. Zbl 0469.65092
Graham, Ivan G.
1981
The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances. Zbl 1421.35056
Graham, I. G.; Pembery, O. R.; Spence, E. A.
2019
A pseudospectral three-dimensional boundary integral method applied to a nonlinear model problem from finite elasticity. Zbl 0815.41008
Ganesh, M.; Graham, I. G.; Sivaloganathan, J.
1994
Robust domain decomposition algorithms for multiscale PDEs. Zbl 1141.65085
Graham, I. G.; Scheichl, R.
2007
The convergence of Nyström methods for Wiener-Hopf equations. Zbl 0621.65138
Chandler, G. A.; Graham, I. G.
1988
Adaptive finite element methods for computing band gaps in photonic crystals. Zbl 1241.82077
Giani, S.; Graham, I. G.
2012
When is the error in the $$h$$-BEM for solving the Helmholtz equation bounded independently of $$k$$? Zbl 1320.65187
Graham, I. G.; Löhndorf, M.; Melenk, J. M.; Spence, E. A.
2015
Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. Zbl 1417.65203
Graham, Ivan G.; Kuo, Frances Y.; Nuyens, Dirk; Scheichl, Rob; Sloan, Ian H.
2018
Nyström-product integration for Wiener-Hopf equations with applications to radiative transfer. Zbl 0675.65146
Graham, Ivan G.; Mendes, Wendy R.
1989
Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. Zbl 1224.65292
Van lent, Jan; Scheichl, Robert; Graham, Ivan G.
2009
Anisotropic mesh refinement: The conditioning of Galerkin boundary element matrices and simple preconditioners. Zbl 1125.65111
Graham, Ivan G.; McLean, William
2006
Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption. Zbl 1366.65113
Graham, Ivan G.; Spence, Euan A.; Vainikko, Eero
2017
The computation of water waves modelled by Nekrasov’s equation. Zbl 0780.76059
Chandler, G. A.; Graham, I. G.
1993
Numerical methods for integral equations of Mellin type. Zbl 0973.65129
Elschner, J.; Graham, I. G.
2000
Mixed finite element analysis of lognormal diffusion and multilevel Monte Carlo methods. Zbl 1371.65008
Graham, I. G.; Scheichl, R.; Ullmann, E.
2016
Stability and finite element error analysis for the Helmholtz equation with variable coefficients. Zbl 1427.35016
Graham, I. G.; Sauter, S. A.
2020
Iterative solution of linear systems arising from the boundary integral method. Zbl 0809.65110
Atkinson, Kendall E.; Graham, Ivan G.
1992
The computation of conical diffraction coefficients in high-frequency acoustic wave scattering. Zbl 1104.65115
Bonner, B. D.; Graham, I. G.; Smyshlyaev, V. P.
2005
Quadrature methods for Symm’s integral equation on polygons. Zbl 0888.65123
Elschner, Johannes; Graham, Ivan G.
1997
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption. Zbl 1420.35398
Bonazzoli, M.; Dolean, V.; Graham, I. G.; Spence, E. A.; Tournier, P.-H.
2019
Hybrid Galerkin boundary elements: Theory and implementation. Zbl 0966.65091
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2000
Boundary integral methods in high frequency scattering. Zbl 1180.78023
Chandler-Wilde, Simon N.; Graham, Ivan G.
2009
Piecewise-constant collocation for first-kind boundary integral equations. Zbl 0738.65097
Graham, I. G.; Yan, Y.
1991
Iterative methods for neutron transport eigenvalue problems. Zbl 1257.82120
Scheben, Fynn; Graham, Ivan G.
2011
Domain decomposition with local impedance conditions for the Helmholtz equation with absorption. Zbl 1465.65162
Graham, Ivan G.; Spence, Euan A.; Zou, Jun
2020
Massively parallel methods for semiconductor device modelling. Zbl 0861.65111
Coomer, R. K.; Graham, I. G.
1996
Two-level preconditioners for the Helmholtz equation. Zbl 1443.65416
Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri
2018
Uniform convergence of Galerkin solutions to non-compact integral operator equations. Zbl 0628.65137
Chandler, G. A.; Graham, I. G.
1987
Discrete boundary element methods on general meshes in 3D. Zbl 0966.65090
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2000
Extrapolation of Nyström solutions of boundary integral equations on non-smooth domains. Zbl 0762.65062
Graham, I. G.; Lin, Qun; Xie, Ruifeng
1992
Numerical analysis of multiscale problems. Selected papers based on the presentations at the 91st London Mathematical Society symposium, Durham, UK, July 5–15, 2010. Zbl 1234.65007
2012
On the compactness of certain integral operators. Zbl 0406.45021
Graham, Ivan G.; Sloan, Ian H.
1979
Interpreting multivariate data. Proceedings of the Conference on Looking at Multivariate Data held in the University of Sheffield, Sheffield, March 24-27, 1980. Zbl 0597.62002
1981
On the Sloan iteration applied to integral equations of the first kind. Zbl 0781.65105
Graham, Ivan G.; Atkinson, Kendall E.
1993
Estimates for the modulus of smoothness. Zbl 0568.41018
Graham, Ivan G.
1985
Boundary integral methods for singularly perturbed boundary problems. Zbl 0978.65109
Langdon, S.; Graham, I. G.
2001
Hybrid Galerkin boundary elements on degenerate meshes. Zbl 0937.65127
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2000
Parallel iterative methods for Navier-Stokes equations and application to eigenvalue computation. Zbl 1141.76438
Graham, Ivan G.; Spence, Alastair; Vainikko, Eero
2003
Parametrization methods for first kind integral equations on nonsmooth boundaries. Zbl 0823.65143
Elschner, Johannes; Graham, Ivan G.
1995
Coefficient-explicit condition number bounds for overlapping additive Schwarz. Zbl 1139.65330
Graham, Ivan G.; Scheichl, Rob
2008
Parallel iterative methods for Navier-Stokes equations and application to stability assessment. Zbl 1068.65511
Graham, Ivan G.; Spence, Alastair; Vainikko, Eero
2002
A two-level domain-decomposition preconditioner for the time-harmonic Maxwell’s equations. Zbl 1443.65417
Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri
2018
Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients. Zbl 1416.65018
Gilbert, A. D.; Graham, I. G.; Kuo, F. Y.; Scheichl, R.; Sloan, I. H.
2019
Modern Monte Carlo variants for uncertainty quantification in neutron transport. Zbl 1405.65014
Graham, Ivan G.; Parkinson, Matthew J.; Scheichl, Robert
2018
Product integration for weakly singular integral equations in $${\mathbb{R}}^ m$$. Zbl 0596.65095
Graham, Ivan G.; Schneider, Claus
1985
Direct and inverse problems in wave propagation and applications. Selected papers of the workshop on wave propagation and scattering, inverse problems and applications in energy and the environment, Linz, Austria, November 21–25, 2011. Zbl 1272.78001
2013
Adaptive numerical solution of integral equations with application to a problem with a boundary layer. Zbl 0676.65137
Graham, I. G.; Shaw, R. E.; Spence, A.
1989
An iterative variant of the Nyström method for boundary integral equations on non smooth boundaries. Zbl 0688.65067
Atkinson, Kendall E.; Graham, Ivan G.
1988
Domain decomposition methods for device modelling. Zbl 0817.65136
Coomer, R. K.; Graham, I. G.
1994
Optimal panel-clustering in the presence of anisotropic mesh refinement. Zbl 1160.65062
Graham, I. G.; Grasedyck, L.; Hackbusch, W.; Sauter, S. A.
2008
Unified analysis of periodization-based sampling methods for Matérn covariances. Zbl 1471.60047
Bachmayr, Markus; Graham, Ivan G.; Nguyen, Van Kien; Scheichl, Robert
2020
Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients. Zbl 1452.65315
Gilbert, Alexander D.; Graham, Ivan G.; Scheichl, Robert; Sloan, Ian H.
2020
Stability and finite element error analysis for the Helmholtz equation with variable coefficients. Zbl 1427.35016
Graham, I. G.; Sauter, S. A.
2020
Domain decomposition with local impedance conditions for the Helmholtz equation with absorption. Zbl 1465.65162
Graham, Ivan G.; Spence, Euan A.; Zou, Jun
2020
Unified analysis of periodization-based sampling methods for Matérn covariances. Zbl 1471.60047
Bachmayr, Markus; Graham, Ivan G.; Nguyen, Van Kien; Scheichl, Robert
2020
Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients. Zbl 1452.65315
Gilbert, Alexander D.; Graham, Ivan G.; Scheichl, Robert; Sloan, Ian H.
2020
The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances. Zbl 1421.35056
Graham, I. G.; Pembery, O. R.; Spence, E. A.
2019
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption. Zbl 1420.35398
Bonazzoli, M.; Dolean, V.; Graham, I. G.; Spence, E. A.; Tournier, P.-H.
2019
Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients. Zbl 1416.65018
Gilbert, A. D.; Graham, I. G.; Kuo, F. Y.; Scheichl, R.; Sloan, I. H.
2019
Analysis of circulant embedding methods for sampling stationary random fields. Zbl 1434.60114
Graham, I. G.; Kuo, F. Y.; Nuyens, Dirk; Scheichl, R.; Sloan, I. H.
2018
Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. Zbl 1417.65203
Graham, Ivan G.; Kuo, Frances Y.; Nuyens, Dirk; Scheichl, Rob; Sloan, Ian H.
2018
Two-level preconditioners for the Helmholtz equation. Zbl 1443.65416
Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri
2018
A two-level domain-decomposition preconditioner for the time-harmonic Maxwell’s equations. Zbl 1443.65417
Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri
2018
Modern Monte Carlo variants for uncertainty quantification in neutron transport. Zbl 1405.65014
Graham, Ivan G.; Parkinson, Matthew J.; Scheichl, Robert
2018
Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. Zbl 1368.65250
Graham, I. G.; Spence, E. A.; Vainikko, E.
2017
Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption. Zbl 1366.65113
Graham, Ivan G.; Spence, Euan A.; Vainikko, Eero
2017
Mixed finite element analysis of lognormal diffusion and multilevel Monte Carlo methods. Zbl 1371.65008
Graham, I. G.; Scheichl, R.; Ullmann, E.
2016
Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Zbl 1328.65238
Gander, M. J.; Graham, I. G.; Spence, E. A.
2015
Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003
Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H.
2015
When is the error in the $$h$$-BEM for solving the Helmholtz equation bounded independently of $$k$$? Zbl 1320.65187
Graham, I. G.; Löhndorf, M.; Melenk, J. M.; Spence, E. A.
2015
Filon-Clenshaw-Curtis rules for highly oscillatory integrals with algebraic singularities and stationary points. Zbl 1345.65012
Domínguez, V.; Graham, I. G.; Kim, T.
2013
Direct and inverse problems in wave propagation and applications. Selected papers of the workshop on wave propagation and scattering, inverse problems and applications in energy and the environment, Linz, Austria, November 21–25, 2011. Zbl 1272.78001
2013
Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. Zbl 1257.65070
Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Spence, Euan A.
2012
Adaptive finite element methods for computing band gaps in photonic crystals. Zbl 1241.82077
Giani, S.; Graham, I. G.
2012
Numerical analysis of multiscale problems. Selected papers based on the presentations at the 91st London Mathematical Society symposium, Durham, UK, July 5–15, 2010. Zbl 1234.65007
2012
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications. Zbl 1218.65009
Graham, I. G.; Kuo, F. Y.; Nuyens, D.; Scheichl, R.; Sloan, I. H.
2011
Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals. Zbl 1231.65060
Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P.
2011
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation. Zbl 1272.76217
Betcke, T.; Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Lindner, M.
2011
A new frequency-uniform coercive boundary integral equation for acoustic scattering. Zbl 1228.35183
Spence, Euan A.; Chandler-Wilde, Simon N.; Graham, Ivan G.; Smyshlyaev, Valery P.
2011
Iterative methods for neutron transport eigenvalue problems. Zbl 1257.82120
Scheben, Fynn; Graham, Ivan G.
2011
A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154
Chu, C.-C.; Graham, I. G.; Hou, T.-Y.
2010
A convergent adaptive method for elliptic eigenvalue problems. Zbl 1191.65147
Giani, S.; Graham, I. G.
2009
Condition number estimates for combined potential boundary integral operators in acoustic scattering. Zbl 1167.35030
Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Lindner, Marko
2009
Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. Zbl 1224.65292
Van lent, Jan; Scheichl, Robert; Graham, Ivan G.
2009
Boundary integral methods in high frequency scattering. Zbl 1180.78023
Chandler-Wilde, Simon N.; Graham, Ivan G.
2009
Coefficient-explicit condition number bounds for overlapping additive Schwarz. Zbl 1139.65330
Graham, Ivan G.; Scheichl, Rob
2008
Optimal panel-clustering in the presence of anisotropic mesh refinement. Zbl 1160.65062
Graham, I. G.; Grasedyck, L.; Hackbusch, W.; Sauter, S. A.
2008
Domain decomposition for multiscale PDEs. Zbl 1141.65084
Graham, I. G.; Lechner, P. O.; Scheichl, R.
2007
A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Zbl 1169.76056
Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P.
2007
Robust domain decomposition algorithms for multiscale PDEs. Zbl 1141.65085
Graham, I. G.; Scheichl, R.
2007
Inexact inverse iteration for symmetric matrices. Zbl 1101.65037
Berns-Müller, Jörg; Graham, Ivan G.; Spence, Alastair
2006
Anisotropic mesh refinement: The conditioning of Galerkin boundary element matrices and simple preconditioners. Zbl 1125.65111
Graham, Ivan G.; McLean, William
2006
Finite elements on degenerate meshes: inverse-type inequalities and applications. Zbl 1076.65098
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2005
The computation of conical diffraction coefficients in high-frequency acoustic wave scattering. Zbl 1104.65115
Bonner, B. D.; Graham, I. G.; Smyshlyaev, V. P.
2005
A high-order algorithm for obstacle scattering in three dimensions. Zbl 1052.65108
Ganesh, M.; Graham, I. G.
2004
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Zbl 1050.65110
Dahmen, W.; Faermann, B.; Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2004
Parallel iterative methods for Navier-Stokes equations and application to eigenvalue computation. Zbl 1141.76438
Graham, Ivan G.; Spence, Alastair; Vainikko, Eero
2003
Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in $$\mathbb R^3$$. Zbl 1018.65139
Graham, I. G.; Sloan, I. H.
2002
Parallel iterative methods for Navier-Stokes equations and application to stability assessment. Zbl 1068.65511
Graham, Ivan G.; Spence, Alastair; Vainikko, Eero
2002
Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. Zbl 0988.92003
Chaplain, M. A. J.; Ganesh, M.; Graham, I. G.
2001
Boundary integral methods for singularly perturbed boundary problems. Zbl 0978.65109
Langdon, S.; Graham, I. G.
2001
Parallel computation of flow in heterogeneous media modelled by mixed finite elements. Zbl 0995.76044
Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L.
2000
Numerical methods for integral equations of Mellin type. Zbl 0973.65129
Elschner, J.; Graham, I. G.
2000
Hybrid Galerkin boundary elements: Theory and implementation. Zbl 0966.65091
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2000
Discrete boundary element methods on general meshes in 3D. Zbl 0966.65090
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2000
Hybrid Galerkin boundary elements on degenerate meshes. Zbl 0937.65127
Graham, I. G.; Hackbusch, W.; Sauter, S. A.
2000
Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. Zbl 0943.65147
Graham, I. G.; Hagger, M. J.
1999
A new spectral boundary integral collocation method for three-dimensional potential problems. Zbl 0915.65115
Ganesh, M.; Graham, I. G.; Sivaloganathan, J.
1998
Quadrature methods for Symm’s integral equation on polygons. Zbl 0888.65123
Elschner, Johannes; Graham, Ivan G.
1997
Massively parallel methods for semiconductor device modelling. Zbl 0861.65111
Coomer, R. K.; Graham, I. G.
1996
An optimal order collocation method for first kind boundary integral equations on polygons. Zbl 0827.65117
Elschner, J.; Graham, I. G.
1995
Parametrization methods for first kind integral equations on nonsmooth boundaries. Zbl 0823.65143
Elschner, Johannes; Graham, Ivan G.
1995
A pseudospectral three-dimensional boundary integral method applied to a nonlinear model problem from finite elasticity. Zbl 0815.41008
Ganesh, M.; Graham, I. G.; Sivaloganathan, J.
1994
Domain decomposition methods for device modelling. Zbl 0817.65136
Coomer, R. K.; Graham, I. G.
1994
The computation of water waves modelled by Nekrasov’s equation. Zbl 0780.76059
Chandler, G. A.; Graham, I. G.
1993
On the Sloan iteration applied to integral equations of the first kind. Zbl 0781.65105
Graham, Ivan G.; Atkinson, Kendall E.
1993
Iterative solution of linear systems arising from the boundary integral method. Zbl 0809.65110
Atkinson, Kendall E.; Graham, Ivan G.
1992
Extrapolation of Nyström solutions of boundary integral equations on non-smooth domains. Zbl 0762.65062
Graham, I. G.; Lin, Qun; Xie, Ruifeng
1992
Piecewise-constant collocation for first-kind boundary integral equations. Zbl 0738.65097
Graham, I. G.; Yan, Y.
1991
Nyström-product integration for Wiener-Hopf equations with applications to radiative transfer. Zbl 0675.65146
Graham, Ivan G.; Mendes, Wendy R.
1989
Adaptive numerical solution of integral equations with application to a problem with a boundary layer. Zbl 0676.65137
Graham, I. G.; Shaw, R. E.; Spence, A.
1989
Product integration-collocation methods for noncompact integral operator equations. Zbl 0639.65074
Chandler, G. A.; Graham, I. G.
1988
High-order methods for linear functionals of solutions of second kind integral equations. Zbl 0661.65137
Graham, I. G.; Chandler, G. A.
1988
The convergence of Nyström methods for Wiener-Hopf equations. Zbl 0621.65138
Chandler, G. A.; Graham, I. G.
1988
An iterative variant of the Nyström method for boundary integral equations on non smooth boundaries. Zbl 0688.65067
Atkinson, Kendall E.; Graham, Ivan G.
1988
Uniform convergence of Galerkin solutions to non-compact integral operator equations. Zbl 0628.65137
Chandler, G. A.; Graham, I. G.
1987
Iterated Galerkin versus iterated collocation for integral equations of the second kind. Zbl 0586.65091
Graham, Ivan G.; Joe, Stephen; Sloan, Ian H.
1985
Estimates for the modulus of smoothness. Zbl 0568.41018
Graham, Ivan G.
1985
Product integration for weakly singular integral equations in $${\mathbb{R}}^ m$$. Zbl 0596.65095
Graham, Ivan G.; Schneider, Claus
1985
Piecewise continuous collocation for integral equations. Zbl 0514.65094
Atkinson, K.; Graham, I.; Sloan, I.
1983
Galerkin methods for second kind integral equations with singularities. Zbl 0496.65068
Graham, Ivan G.
1982
Singularity expansions for the solutions of second kind Fredholm integral equations with weakly singular convolution kernels. Zbl 0482.45003
Graham, Ivan G.
1982
Collocation methods for two dimensional weakly singular integral equations. Zbl 0469.65092
Graham, Ivan G.
1981
Interpreting multivariate data. Proceedings of the Conference on Looking at Multivariate Data held in the University of Sheffield, Sheffield, March 24-27, 1980. Zbl 0597.62002
1981
On the compactness of certain integral operators. Zbl 0406.45021
Graham, Ivan G.; Sloan, Ian H.
1979
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Cited by 1,465 Authors

 39 Graham, Ivan G. 31 Scheichl, Robert 25 Ganesh, Mahadevan 24 Sloan, Ian Hugh 24 Spence, Euan A. 22 Praetorius, Dirk 20 Chung, Tsz Shun Eric 17 Efendiev, Yalchin R. 17 Kuo, Frances Y. 17 Nelakanti, Gnaneshwar 17 Schwab, Christoph 16 Xiang, Shuhuang 15 Chandler-Wilde, Simon N. 15 Xu, Yuesheng 13 Melenk, Jens Markus 11 Allouch, Chafik 11 Feischl, Michael 11 Kulkarni, Rekha P. 11 Nuyens, Dirk 11 Sauter, Stefan A. 11 Sbibih, Driss 10 Galvis, Juan 10 Gander, Martin Jakob 10 Giani, Stefano 10 Hawkins, Stuart Collin 10 Le Louër, Frédérique 10 Madzvamuse, Anotida 10 Peterseim, Daniel 10 Vainikko, Gennadi 9 Chapko, Roman 9 Führer, Thomas 9 Karkulik, Michael 9 Laurita, Concetta 9 Leung, Wingtat 9 Sayas, Francisco-Javier 9 Tahrichi, Mohamed 8 Chen, Zhongying 8 Huybrechs, Daan 8 Kress, Rainer 8 Long, Guangqing 8 Vuik, Cornelis 7 Dolean, Victorita 7 Ecevit, Fatih 7 Hewett, David P. 7 Huang, Jin 7 Langdon, Stephen 7 Ullmann, Elisabeth 6 Boubendir, Yassine 6 Carstensen, Carsten 6 Dehghan Takht Fooladi, Mehdi 6 Domínguez, Víctor 6 Elschner, Johannes 6 Herrmann, Lukas 6 Kaneko, Hideaki 6 Kang, Hongchao 6 Li, Guanglian 6 Moiola, Andrea 6 Pedas, Arvet 6 Rapún, María-Luisa 6 Sarkis, Marcus V. 6 Tournier, Pierre-Henri 6 Wu, Qinghua 5 Assari, Pouria 5 Aurada, Markus 5 Betcke, Timo 5 Bonazzoli, Marcella 5 Chaillat, Stéphanie 5 Chen, Yanping 5 Ferraz-Leite, Samuel 5 Galkowski, Jeffrey 5 Gil’, Michael Iosif 5 Guo, Ruchi 5 Harbrecht, Helmut 5 He, Guo 5 Hiptmair, Ralf 5 Hou, Thomas Yizhao 5 Ivanyshyn, Olha 5 Johansson, B. Tomas 5 Lazarov, Raytcho D. 5 Lin, Tao 5 Ma, Junjie 5 Majidian, Hassan 5 Monegato, Giovanni 5 Nabben, Reinhard 5 Nobile, Fabio 5 Pechstein, Clemens 5 Rahimian, Abtin 5 Stephan, Ernst Peter 5 Teckentrup, Aretha L. 5 Vainikko, Eero 5 Vassilevski, Panayot Spirov 5 Zhang, Zhiwen 5 Zorin, Denis N. 4 Anand, Akash 4 Antoine, Xavier 4 Atkinson, Kendall Eugene 4 Bruno, Oscar P. 4 Calo, Victor Manuel 4 Chandler, Graeme A. 4 Cocquet, Pierre-Henri ...and 1,365 more Authors
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Cited in 185 Serials

 85 Journal of Computational and Applied Mathematics 77 Numerische Mathematik 76 Journal of Computational Physics 47 Mathematics of Computation 47 Journal of Integral Equations and Applications 40 SIAM Journal on Scientific Computing 38 Computers & Mathematics with Applications 37 Applied Numerical Mathematics 37 Journal of Scientific Computing 35 Computer Methods in Applied Mechanics and Engineering 28 Applied Mathematics and Computation 27 SIAM Journal on Numerical Analysis 22 SIAM/ASA Journal on Uncertainty Quantification 21 Advances in Computational Mathematics 19 Numerical Algorithms 17 BIT 16 Multiscale Modeling & Simulation 15 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 14 International Journal of Computer Mathematics 12 Engineering Analysis with Boundary Elements 12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 11 Wave Motion 10 Numerical Functional Analysis and Optimization 9 Computational and Applied Mathematics 8 Calcolo 8 Numerical Methods for Partial Differential Equations 8 Numerical Linear Algebra with Applications 7 Journal of Mathematical Analysis and Applications 7 Applied Mathematical Modelling 7 SIAM Journal on Mathematical Analysis 7 Computational Methods in Applied Mathematics 6 Computing 6 Integral Equations and Operator Theory 6 Computational Geosciences 6 Communications in Computational Physics 6 Science China. Mathematics 5 Journal of Mathematical Biology 5 Bulletin of Mathematical Biology 5 SIAM Journal on Matrix Analysis and Applications 5 ETNA. Electronic Transactions on Numerical Analysis 5 Computing and Visualization in Science 5 International Journal of Numerical Analysis and Modeling 5 Advances in Applied Mathematics and Mechanics 4 Inverse Problems 4 International Journal for Numerical Methods in Engineering 4 Journal of Complexity 4 Computational Mechanics 4 Foundations of Computational Mathematics 4 SIAM Journal on Applied Dynamical Systems 4 Journal of Theoretical Biology 4 Stochastic and Partial Differential Equations. Analysis and Computations 3 Mathematics and Computers in Simulation 3 Acta Mathematicae Applicatae Sinica. English Series 3 Applied Mathematics Letters 3 Mathematical and Computer Modelling 3 Linear Algebra and its Applications 3 Mathematical Problems in Engineering 3 Abstract and Applied Analysis 3 The ANZIAM Journal 3 Mathematical Modelling and Analysis 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Applied Mathematics and Computing 3 Advances in Difference Equations 3 East Asian Journal on Applied Mathematics 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 SN Partial Differential Equations and Applications 2 Applicable Analysis 2 Communications on Pure and Applied Mathematics 2 Journal of Engineering Mathematics 2 Journal of Fluid Mechanics 2 Journal of Approximation Theory 2 Mathematische Nachrichten 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Quarterly of Applied Mathematics 2 Acta Applicandae Mathematicae 2 Physica D 2 European Journal of Applied Mathematics 2 SIAM Journal on Applied Mathematics 2 SIAM Review 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 The Journal of Analysis 2 Applied and Computational Harmonic Analysis 2 Turkish Journal of Mathematics 2 Discrete and Continuous Dynamical Systems 2 The Journal of Fourier Analysis and Applications 2 Archives of Computational Methods in Engineering 2 Journal of the Australian Mathematical Society 2 Journal of Computational Acoustics 2 Inverse Problems in Science and Engineering 2 Inverse Problems and Imaging 2 SIAM Journal on Imaging Sciences 2 Afrika Matematika 2 Mathematical Sciences 2 Research in the Mathematical Sciences 2 Communications on Applied Mathematics and Computation 1 Advances in Applied Probability 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society 1 Computer Physics Communications 1 International Journal for Numerical Methods in Fluids ...and 85 more Serials
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Cited in 41 Fields

 971 Numerical analysis (65-XX) 498 Partial differential equations (35-XX) 241 Integral equations (45-XX) 137 Fluid mechanics (76-XX) 84 Optics, electromagnetic theory (78-XX) 72 Probability theory and stochastic processes (60-XX) 55 Approximations and expansions (41-XX) 53 Mechanics of deformable solids (74-XX) 42 Biology and other natural sciences (92-XX) 35 Operator theory (47-XX) 21 Statistical mechanics, structure of matter (82-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 19 Statistics (62-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 16 Ordinary differential equations (34-XX) 15 Potential theory (31-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 12 Computer science (68-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 Special functions (33-XX) 8 Geophysics (86-XX) 7 Real functions (26-XX) 7 Integral transforms, operational calculus (44-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Functional analysis (46-XX) 5 Functions of a complex variable (30-XX) 5 Quantum theory (81-XX) 4 Differential geometry (53-XX) 4 Operations research, mathematical programming (90-XX) 4 Systems theory; control (93-XX) 4 Information and communication theory, circuits (94-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX)