Edit Profile (opens in new tab) Graham, Ivan G. Compute Distance To: Compute 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) Publications by Year all cited Publications top 5 cited Publications 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 1257.65070Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Spence, Euan A. 95 2012 A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154Chu, C.-C.; Graham, I. G.; Hou, T.-Y. 89 2010 Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. Zbl 0988.92003Chaplain, M. A. J.; Ganesh, M.; Graham, I. G. 78 2001 Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications. Zbl 1218.65009Graham, I. G.; Kuo, F. Y.; Nuyens, D.; Scheichl, R.; Sloan, I. H. 67 2011 Piecewise continuous collocation for integral equations. Zbl 0514.65094Atkinson, K.; Graham, I.; Sloan, I. 63 1983 Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Zbl 1328.65238Gander, M. J.; Graham, I. G.; Spence, E. A. 57 2015 Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H. 56 2015 A high-order algorithm for obstacle scattering in three dimensions. Zbl 1052.65108Ganesh, M.; Graham, I. G. 54 2004 Domain decomposition for multiscale PDEs. Zbl 1141.65084Graham, I. G.; Lechner, P. O.; Scheichl, R. 53 2007 Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals. Zbl 1231.65060Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P. 48 2011 A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Zbl 1169.76056Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P. 44 2007 A convergent adaptive method for elliptic eigenvalue problems. Zbl 1191.65147Giani, S.; Graham, I. G. 43 2009 Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation. Zbl 1272.76217Betcke, T.; Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Lindner, M. 38 2011 Finite elements on degenerate meshes: inverse-type inequalities and applications. Zbl 1076.65098Graham, I. G.; Hackbusch, W.; Sauter, S. A. 36 2005 Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in \(\mathbb R^3\). Zbl 1018.65139Graham, I. G.; Sloan, I. H. 35 2002 Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Zbl 1050.65110Dahmen, W.; Faermann, B.; Graham, I. G.; Hackbusch, W.; Sauter, S. A. 34 2004 Filon-Clenshaw-Curtis rules for highly oscillatory integrals with algebraic singularities and stationary points. Zbl 1345.65012Domínguez, V.; Graham, I. G.; Kim, T. 32 2013 Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. Zbl 1368.65250Graham, I. G.; Spence, E. A.; Vainikko, E. 31 2017 Condition number estimates for combined potential boundary integral operators in acoustic scattering. Zbl 1167.35030Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Lindner, Marko 29 2009 Iterated Galerkin versus iterated collocation for integral equations of the second kind. Zbl 0586.65091Graham, Ivan G.; Joe, Stephen; Sloan, Ian H. 28 1985 Galerkin methods for second kind integral equations with singularities. Zbl 0496.65068Graham, Ivan G. 28 1982 Singularity expansions for the solutions of second kind Fredholm integral equations with weakly singular convolution kernels. Zbl 0482.45003Graham, Ivan G. 27 1982 Product integration-collocation methods for noncompact integral operator equations. Zbl 0639.65074Chandler, G. A.; Graham, I. G. 26 1988 Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. Zbl 0943.65147Graham, I. G.; Hagger, M. J. 26 1999 High-order methods for linear functionals of solutions of second kind integral equations. Zbl 0661.65137Graham, I. G.; Chandler, G. A. 24 1988 An optimal order collocation method for first kind boundary integral equations on polygons. Zbl 0827.65117Elschner, J.; Graham, I. G. 21 1995 Inexact inverse iteration for symmetric matrices. Zbl 1101.65037Berns-Müller, Jörg; Graham, Ivan G.; Spence, Alastair 20 2006 A new frequency-uniform coercive boundary integral equation for acoustic scattering. Zbl 1228.35183Spence, Euan A.; Chandler-Wilde, Simon N.; Graham, Ivan G.; Smyshlyaev, Valery P. 20 2011 Analysis of circulant embedding methods for sampling stationary random fields. Zbl 1434.60114Graham, I. G.; Kuo, F. Y.; Nuyens, Dirk; Scheichl, R.; Sloan, I. H. 18 2018 Parallel computation of flow in heterogeneous media modelled by mixed finite elements. Zbl 0995.76044Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L. 18 2000 A new spectral boundary integral collocation method for three-dimensional potential problems. Zbl 0915.65115Ganesh, M.; Graham, I. G.; Sivaloganathan, J. 17 1998 Collocation methods for two dimensional weakly singular integral equations. Zbl 0469.65092Graham, Ivan G. 17 1981 The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances. Zbl 1421.35056Graham, I. G.; Pembery, O. R.; Spence, E. A. 16 2019 A pseudospectral three-dimensional boundary integral method applied to a nonlinear model problem from finite elasticity. Zbl 0815.41008Ganesh, M.; Graham, I. G.; Sivaloganathan, J. 16 1994 Robust domain decomposition algorithms for multiscale PDEs. Zbl 1141.65085Graham, I. G.; Scheichl, R. 16 2007 The convergence of Nyström methods for Wiener-Hopf equations. Zbl 0621.65138Chandler, G. A.; Graham, I. G. 15 1988 Adaptive finite element methods for computing band gaps in photonic crystals. Zbl 1241.82077Giani, S.; Graham, I. G. 15 2012 When is the error in the \(h\)-BEM for solving the Helmholtz equation bounded independently of \(k\)? Zbl 1320.65187Graham, I. G.; Löhndorf, M.; Melenk, J. M.; Spence, E. A. 14 2015 Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. Zbl 1417.65203Graham, Ivan G.; Kuo, Frances Y.; Nuyens, Dirk; Scheichl, Rob; Sloan, Ian H. 13 2018 Nyström-product integration for Wiener-Hopf equations with applications to radiative transfer. Zbl 0675.65146Graham, Ivan G.; Mendes, Wendy R. 12 1989 Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. Zbl 1224.65292Van lent, Jan; Scheichl, Robert; Graham, Ivan G. 12 2009 Anisotropic mesh refinement: The conditioning of Galerkin boundary element matrices and simple preconditioners. Zbl 1125.65111Graham, Ivan G.; McLean, William 12 2006 Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption. Zbl 1366.65113Graham, Ivan G.; Spence, Euan A.; Vainikko, Eero 12 2017 The computation of water waves modelled by Nekrasov’s equation. Zbl 0780.76059Chandler, G. A.; Graham, I. G. 11 1993 Numerical methods for integral equations of Mellin type. Zbl 0973.65129Elschner, J.; Graham, I. G. 11 2000 Mixed finite element analysis of lognormal diffusion and multilevel Monte Carlo methods. Zbl 1371.65008Graham, I. G.; Scheichl, R.; Ullmann, E. 11 2016 Stability and finite element error analysis for the Helmholtz equation with variable coefficients. Zbl 1427.35016Graham, I. G.; Sauter, S. A. 11 2020 Iterative solution of linear systems arising from the boundary integral method. Zbl 0809.65110Atkinson, Kendall E.; Graham, Ivan G. 10 1992 The computation of conical diffraction coefficients in high-frequency acoustic wave scattering. Zbl 1104.65115Bonner, B. D.; Graham, I. G.; Smyshlyaev, V. P. 10 2005 Quadrature methods for Symm’s integral equation on polygons. Zbl 0888.65123Elschner, Johannes; Graham, Ivan G. 8 1997 Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption. Zbl 1420.35398Bonazzoli, M.; Dolean, V.; Graham, I. G.; Spence, E. A.; Tournier, P.-H. 8 2019 Hybrid Galerkin boundary elements: Theory and implementation. Zbl 0966.65091Graham, I. G.; Hackbusch, W.; Sauter, S. A. 7 2000 Boundary integral methods in high frequency scattering. Zbl 1180.78023Chandler-Wilde, Simon N.; Graham, Ivan G. 7 2009 Piecewise-constant collocation for first-kind boundary integral equations. Zbl 0738.65097Graham, I. G.; Yan, Y. 7 1991 Iterative methods for neutron transport eigenvalue problems. Zbl 1257.82120Scheben, Fynn; Graham, Ivan G. 7 2011 Domain decomposition with local impedance conditions for the Helmholtz equation with absorption. Zbl 1465.65162Graham, Ivan G.; Spence, Euan A.; Zou, Jun 7 2020 Massively parallel methods for semiconductor device modelling. Zbl 0861.65111Coomer, R. K.; Graham, I. G. 6 1996 Two-level preconditioners for the Helmholtz equation. Zbl 1443.65416Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri 6 2018 Uniform convergence of Galerkin solutions to non-compact integral operator equations. Zbl 0628.65137Chandler, G. A.; Graham, I. G. 5 1987 Discrete boundary element methods on general meshes in 3D. Zbl 0966.65090Graham, I. G.; Hackbusch, W.; Sauter, S. A. 5 2000 Extrapolation of Nyström solutions of boundary integral equations on non-smooth domains. Zbl 0762.65062Graham, I. G.; Lin, Qun; Xie, Ruifeng 5 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 5 2012 On the compactness of certain integral operators. Zbl 0406.45021Graham, Ivan G.; Sloan, Ian H. 5 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 4 1981 On the Sloan iteration applied to integral equations of the first kind. Zbl 0781.65105Graham, Ivan G.; Atkinson, Kendall E. 4 1993 Estimates for the modulus of smoothness. Zbl 0568.41018Graham, Ivan G. 3 1985 Boundary integral methods for singularly perturbed boundary problems. Zbl 0978.65109Langdon, S.; Graham, I. G. 3 2001 Hybrid Galerkin boundary elements on degenerate meshes. Zbl 0937.65127Graham, I. G.; Hackbusch, W.; Sauter, S. A. 2 2000 Parallel iterative methods for Navier-Stokes equations and application to eigenvalue computation. Zbl 1141.76438Graham, Ivan G.; Spence, Alastair; Vainikko, Eero 2 2003 Parametrization methods for first kind integral equations on nonsmooth boundaries. Zbl 0823.65143Elschner, Johannes; Graham, Ivan G. 2 1995 Coefficient-explicit condition number bounds for overlapping additive Schwarz. Zbl 1139.65330Graham, Ivan G.; Scheichl, Rob 2 2008 Parallel iterative methods for Navier-Stokes equations and application to stability assessment. Zbl 1068.65511Graham, Ivan G.; Spence, Alastair; Vainikko, Eero 2 2002 A two-level domain-decomposition preconditioner for the time-harmonic Maxwell’s equations. Zbl 1443.65417Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri 2 2018 Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients. Zbl 1416.65018Gilbert, A. D.; Graham, I. G.; Kuo, F. Y.; Scheichl, R.; Sloan, I. H. 2 2019 Modern Monte Carlo variants for uncertainty quantification in neutron transport. Zbl 1405.65014Graham, Ivan G.; Parkinson, Matthew J.; Scheichl, Robert 1 2018 Product integration for weakly singular integral equations in \({\mathbb{R}}^ m\). Zbl 0596.65095Graham, Ivan G.; Schneider, Claus 1 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 1 2013 Adaptive numerical solution of integral equations with application to a problem with a boundary layer. Zbl 0676.65137Graham, I. G.; Shaw, R. E.; Spence, A. 1 1989 An iterative variant of the Nyström method for boundary integral equations on non smooth boundaries. Zbl 0688.65067Atkinson, Kendall E.; Graham, Ivan G. 1 1988 Domain decomposition methods for device modelling. Zbl 0817.65136Coomer, R. K.; Graham, I. G. 1 1994 Optimal panel-clustering in the presence of anisotropic mesh refinement. Zbl 1160.65062Graham, I. G.; Grasedyck, L.; Hackbusch, W.; Sauter, S. A. 1 2008 Unified analysis of periodization-based sampling methods for Matérn covariances. Zbl 1471.60047Bachmayr, Markus; Graham, Ivan G.; Nguyen, Van Kien; Scheichl, Robert 1 2020 Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients. Zbl 1452.65315Gilbert, Alexander D.; Graham, Ivan G.; Scheichl, Robert; Sloan, Ian H. 1 2020 Stability and finite element error analysis for the Helmholtz equation with variable coefficients. Zbl 1427.35016Graham, I. G.; Sauter, S. A. 11 2020 Domain decomposition with local impedance conditions for the Helmholtz equation with absorption. Zbl 1465.65162Graham, Ivan G.; Spence, Euan A.; Zou, Jun 7 2020 Unified analysis of periodization-based sampling methods for Matérn covariances. Zbl 1471.60047Bachmayr, Markus; Graham, Ivan G.; Nguyen, Van Kien; Scheichl, Robert 1 2020 Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients. Zbl 1452.65315Gilbert, Alexander D.; Graham, Ivan G.; Scheichl, Robert; Sloan, Ian H. 1 2020 The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances. Zbl 1421.35056Graham, I. G.; Pembery, O. R.; Spence, E. A. 16 2019 Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption. Zbl 1420.35398Bonazzoli, M.; Dolean, V.; Graham, I. G.; Spence, E. A.; Tournier, P.-H. 8 2019 Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients. Zbl 1416.65018Gilbert, A. D.; Graham, I. G.; Kuo, F. Y.; Scheichl, R.; Sloan, I. H. 2 2019 Analysis of circulant embedding methods for sampling stationary random fields. Zbl 1434.60114Graham, I. G.; Kuo, F. Y.; Nuyens, Dirk; Scheichl, R.; Sloan, I. H. 18 2018 Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. Zbl 1417.65203Graham, Ivan G.; Kuo, Frances Y.; Nuyens, Dirk; Scheichl, Rob; Sloan, Ian H. 13 2018 Two-level preconditioners for the Helmholtz equation. Zbl 1443.65416Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri 6 2018 A two-level domain-decomposition preconditioner for the time-harmonic Maxwell’s equations. Zbl 1443.65417Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri 2 2018 Modern Monte Carlo variants for uncertainty quantification in neutron transport. Zbl 1405.65014Graham, Ivan G.; Parkinson, Matthew J.; Scheichl, Robert 1 2018 Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. Zbl 1368.65250Graham, I. G.; Spence, E. A.; Vainikko, E. 31 2017 Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption. Zbl 1366.65113Graham, Ivan G.; Spence, Euan A.; Vainikko, Eero 12 2017 Mixed finite element analysis of lognormal diffusion and multilevel Monte Carlo methods. Zbl 1371.65008Graham, I. G.; Scheichl, R.; Ullmann, E. 11 2016 Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Zbl 1328.65238Gander, M. J.; Graham, I. G.; Spence, E. A. 57 2015 Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H. 56 2015 When is the error in the \(h\)-BEM for solving the Helmholtz equation bounded independently of \(k\)? Zbl 1320.65187Graham, I. G.; Löhndorf, M.; Melenk, J. M.; Spence, E. A. 14 2015 Filon-Clenshaw-Curtis rules for highly oscillatory integrals with algebraic singularities and stationary points. Zbl 1345.65012Domínguez, V.; Graham, I. G.; Kim, T. 32 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 1 2013 Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. Zbl 1257.65070Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Spence, Euan A. 95 2012 Adaptive finite element methods for computing band gaps in photonic crystals. Zbl 1241.82077Giani, S.; Graham, I. G. 15 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 5 2012 Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications. Zbl 1218.65009Graham, I. G.; Kuo, F. Y.; Nuyens, D.; Scheichl, R.; Sloan, I. H. 67 2011 Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals. Zbl 1231.65060Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P. 48 2011 Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation. Zbl 1272.76217Betcke, T.; Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Lindner, M. 38 2011 A new frequency-uniform coercive boundary integral equation for acoustic scattering. Zbl 1228.35183Spence, Euan A.; Chandler-Wilde, Simon N.; Graham, Ivan G.; Smyshlyaev, Valery P. 20 2011 Iterative methods for neutron transport eigenvalue problems. Zbl 1257.82120Scheben, Fynn; Graham, Ivan G. 7 2011 A new multiscale finite element method for high-contrast elliptic interface problems. Zbl 1202.65154Chu, C.-C.; Graham, I. G.; Hou, T.-Y. 89 2010 A convergent adaptive method for elliptic eigenvalue problems. Zbl 1191.65147Giani, S.; Graham, I. G. 43 2009 Condition number estimates for combined potential boundary integral operators in acoustic scattering. Zbl 1167.35030Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Lindner, Marko 29 2009 Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. Zbl 1224.65292Van lent, Jan; Scheichl, Robert; Graham, Ivan G. 12 2009 Boundary integral methods in high frequency scattering. Zbl 1180.78023Chandler-Wilde, Simon N.; Graham, Ivan G. 7 2009 Coefficient-explicit condition number bounds for overlapping additive Schwarz. Zbl 1139.65330Graham, Ivan G.; Scheichl, Rob 2 2008 Optimal panel-clustering in the presence of anisotropic mesh refinement. Zbl 1160.65062Graham, I. G.; Grasedyck, L.; Hackbusch, W.; Sauter, S. A. 1 2008 Domain decomposition for multiscale PDEs. Zbl 1141.65084Graham, I. G.; Lechner, P. O.; Scheichl, R. 53 2007 A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Zbl 1169.76056Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P. 44 2007 Robust domain decomposition algorithms for multiscale PDEs. Zbl 1141.65085Graham, I. G.; Scheichl, R. 16 2007 Inexact inverse iteration for symmetric matrices. Zbl 1101.65037Berns-Müller, Jörg; Graham, Ivan G.; Spence, Alastair 20 2006 Anisotropic mesh refinement: The conditioning of Galerkin boundary element matrices and simple preconditioners. Zbl 1125.65111Graham, Ivan G.; McLean, William 12 2006 Finite elements on degenerate meshes: inverse-type inequalities and applications. Zbl 1076.65098Graham, I. G.; Hackbusch, W.; Sauter, S. A. 36 2005 The computation of conical diffraction coefficients in high-frequency acoustic wave scattering. Zbl 1104.65115Bonner, B. D.; Graham, I. G.; Smyshlyaev, V. P. 10 2005 A high-order algorithm for obstacle scattering in three dimensions. Zbl 1052.65108Ganesh, M.; Graham, I. G. 54 2004 Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method. Zbl 1050.65110Dahmen, W.; Faermann, B.; Graham, I. G.; Hackbusch, W.; Sauter, S. A. 34 2004 Parallel iterative methods for Navier-Stokes equations and application to eigenvalue computation. Zbl 1141.76438Graham, Ivan G.; Spence, Alastair; Vainikko, Eero 2 2003 Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in \(\mathbb R^3\). Zbl 1018.65139Graham, I. G.; Sloan, I. H. 35 2002 Parallel iterative methods for Navier-Stokes equations and application to stability assessment. Zbl 1068.65511Graham, Ivan G.; Spence, Alastair; Vainikko, Eero 2 2002 Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. Zbl 0988.92003Chaplain, M. A. J.; Ganesh, M.; Graham, I. G. 78 2001 Boundary integral methods for singularly perturbed boundary problems. Zbl 0978.65109Langdon, S.; Graham, I. G. 3 2001 Parallel computation of flow in heterogeneous media modelled by mixed finite elements. Zbl 0995.76044Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L. 18 2000 Numerical methods for integral equations of Mellin type. Zbl 0973.65129Elschner, J.; Graham, I. G. 11 2000 Hybrid Galerkin boundary elements: Theory and implementation. Zbl 0966.65091Graham, I. G.; Hackbusch, W.; Sauter, S. A. 7 2000 Discrete boundary element methods on general meshes in 3D. Zbl 0966.65090Graham, I. G.; Hackbusch, W.; Sauter, S. A. 5 2000 Hybrid Galerkin boundary elements on degenerate meshes. Zbl 0937.65127Graham, I. G.; Hackbusch, W.; Sauter, S. A. 2 2000 Unstructured additive Schwarz-conjugate gradient method for elliptic problems with highly discontinuous coefficients. Zbl 0943.65147Graham, I. G.; Hagger, M. J. 26 1999 A new spectral boundary integral collocation method for three-dimensional potential problems. Zbl 0915.65115Ganesh, M.; Graham, I. G.; Sivaloganathan, J. 17 1998 Quadrature methods for Symm’s integral equation on polygons. Zbl 0888.65123Elschner, Johannes; Graham, Ivan G. 8 1997 Massively parallel methods for semiconductor device modelling. Zbl 0861.65111Coomer, R. K.; Graham, I. G. 6 1996 An optimal order collocation method for first kind boundary integral equations on polygons. Zbl 0827.65117Elschner, J.; Graham, I. G. 21 1995 Parametrization methods for first kind integral equations on nonsmooth boundaries. Zbl 0823.65143Elschner, Johannes; Graham, Ivan G. 2 1995 A pseudospectral three-dimensional boundary integral method applied to a nonlinear model problem from finite elasticity. Zbl 0815.41008Ganesh, M.; Graham, I. G.; Sivaloganathan, J. 16 1994 Domain decomposition methods for device modelling. Zbl 0817.65136Coomer, R. K.; Graham, I. G. 1 1994 The computation of water waves modelled by Nekrasov’s equation. Zbl 0780.76059Chandler, G. A.; Graham, I. G. 11 1993 On the Sloan iteration applied to integral equations of the first kind. Zbl 0781.65105Graham, Ivan G.; Atkinson, Kendall E. 4 1993 Iterative solution of linear systems arising from the boundary integral method. Zbl 0809.65110Atkinson, Kendall E.; Graham, Ivan G. 10 1992 Extrapolation of Nyström solutions of boundary integral equations on non-smooth domains. Zbl 0762.65062Graham, I. G.; Lin, Qun; Xie, Ruifeng 5 1992 Piecewise-constant collocation for first-kind boundary integral equations. Zbl 0738.65097Graham, I. G.; Yan, Y. 7 1991 Nyström-product integration for Wiener-Hopf equations with applications to radiative transfer. Zbl 0675.65146Graham, Ivan G.; Mendes, Wendy R. 12 1989 Adaptive numerical solution of integral equations with application to a problem with a boundary layer. Zbl 0676.65137Graham, I. G.; Shaw, R. E.; Spence, A. 1 1989 Product integration-collocation methods for noncompact integral operator equations. Zbl 0639.65074Chandler, G. A.; Graham, I. G. 26 1988 High-order methods for linear functionals of solutions of second kind integral equations. Zbl 0661.65137Graham, I. G.; Chandler, G. A. 24 1988 The convergence of Nyström methods for Wiener-Hopf equations. Zbl 0621.65138Chandler, G. A.; Graham, I. G. 15 1988 An iterative variant of the Nyström method for boundary integral equations on non smooth boundaries. Zbl 0688.65067Atkinson, Kendall E.; Graham, Ivan G. 1 1988 Uniform convergence of Galerkin solutions to non-compact integral operator equations. Zbl 0628.65137Chandler, G. A.; Graham, I. G. 5 1987 Iterated Galerkin versus iterated collocation for integral equations of the second kind. Zbl 0586.65091Graham, Ivan G.; Joe, Stephen; Sloan, Ian H. 28 1985 Estimates for the modulus of smoothness. Zbl 0568.41018Graham, Ivan G. 3 1985 Product integration for weakly singular integral equations in \({\mathbb{R}}^ m\). Zbl 0596.65095Graham, Ivan G.; Schneider, Claus 1 1985 Piecewise continuous collocation for integral equations. Zbl 0514.65094Atkinson, K.; Graham, I.; Sloan, I. 63 1983 Galerkin methods for second kind integral equations with singularities. Zbl 0496.65068Graham, Ivan G. 28 1982 Singularity expansions for the solutions of second kind Fredholm integral equations with weakly singular convolution kernels. Zbl 0482.45003Graham, Ivan G. 27 1982 Collocation methods for two dimensional weakly singular integral equations. Zbl 0469.65092Graham, Ivan G. 17 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 4 1981 On the compactness of certain integral operators. Zbl 0406.45021Graham, Ivan G.; Sloan, Ian H. 5 1979 all cited Publications top 5 cited Publications all top 5 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 all top 5 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 all top 5 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) Citations by Year