Ivan Graham -- Publications

Here is a list of papers which are available in electronic form

J. Galkowski, S. Gong, I.G. Graham, D. Lafontaine, E.A. Spence, Schwarz methods with PMLs for Helmholtz problems: fast convergence at high frequency, 29th August 2024 preprint
J. Galkowski, S. Gong, I.G. Graham, D. Lafontaine, E.A. Spence, Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems, 2 April 2024, preprint
S. Downing, S. Gazzola, I.G. Graham and E.A. Spence, Optimisation of seismic imaging via bilevel learning, Inverse Problems, to appear preprint
Z. Wu, I. G. Graham, D. Ma, Z. Zhang A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation, Math. Comput. published electronically, August 15 2024 Published paper Final preprint longer version of the paper
N. Bootland, V. Dolean, I. G. Graham, C. Ma and R. Scheichl, Overlapping Schwarz methods with GenEO coarse spaces for indefinite and non-self-adjoint problems, IMA J.Numer. Anal. 43, 1899–1936 (2023). final preprint
S. Gong, I. G. Graham and E.A. Spence, Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems, Math. Comput. 92, 175–215 (2023). final preprint
S. Gong, M.J. Gander, I.G. Graham, D. Lafontaine and E.A. Spence, Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation, Numer. Math. 152, 259–306 (2022). Published paper Final Preprint.
N. Bootland, V. Dolean, I. G. Graham, C. Ma, R. Scheichl, GenEO coarse spaces for heterogeneous indefinite elliptic problems, Domain Decomposition Methods in Science and Engineering XXVI, 117--125, Springer 2023. preprint
S. Gong, M.J. Gander, I.G. Graham and E.A. Spence, A variational interpretation of Restricted Additive Schwarz with impedance transmission condition for the Helmholtz problem, Domain Decomposition Methods in Science and Engineering XXVI, 291--298, Springer 2023. preprint
I.G. Graham, O.R. Pembery, E.A. Spence, Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification, Advances in Computational Mathematics 47 (2021) p68 (39pp) final preprint published article
J.D. Betteridge, T.H. Gibson, I.G. Graham, E.H. Mueller, Multigrid preconditioners for the hybridized Discontinuous Galerkin discretisation of the shallow water equations, submitted 20th April 2020, Journal of Computational Physics, 426, 109948 (2021) preprint
S. Gong, I.G. Graham and E.A. Spence, Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation, IMA J. Numer. Anal. 41, 2139–2185 (2021). final preprint Final published version
I.G. Graham, E.A. Spence and J. Zou, Domain Decomposition with local impedance conditions for the Helmholtz equation with absorption, SIAM J. Numer. Anal. 58(5), pp 2515–2543 (2020) final preprint Final published version
M. Bachmayr, I.G. Graham, V. K. Nguyen and R. Scheichl, Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances, SIAM J. Numer. Anal. 58(5), 2953–2980 (2020) final preprint final published version
I.G. Graham, M.J. Parkinson, R. Scheichl, Error Analysis and Uncertainty Quantification for the Heterogeneous Transport Equation in Slab Geometry, IMA J. Numer. Anal. 41, 2331–2361 (2021). final preprint Final published version
I.G. Graham and S.A. Sauter, Stability and error analysis for the Helmholtz equation with variable coefficients. Math. Comp. 89 (2020), 105-138 Final preprint Final published version
J.C.H. Blake, I.G. Graham, F. Scheben and A. Spence, The radiative transport equation with heterogeneous cross-sections, In: On the Frontiers of High Dimensional Computation, F. Kuo (Guest Editor) 2018 MATRIX Annals, D.R. Wood, J. de Gier, C.E. Praeger, T. Tao, (Eds.), Springer Verlag 2020. link to published version preprint
A.D. Gilbert, I. G. Graham, F. Y. Kuo, R. Scheichl, and I. H. Sloan, Bounding the spectral gap for random elliptic eigenvalue problems, In: On the Frontiers of High Dimensional Computation, F. Kuo (Guest Editor) 2018 MATRIX Annals, D.R. Wood, J. de Gier, C.E. Praeger, T. Tao, (Eds.), Springer Verlag 2020. link to published version preprint
A.D. Gilbert, I. G. Graham, F. Y. Kuo, R. Scheichl, and I. H. Sloan, Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients, Numer. Math. 142, 863–915 (2019). final preprint Final published version
I.G. Graham, O.R. Pembery and E.A. Spence The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances, Journal of Differential Equations 266 (2019) 2869-2923. Final preprint Final published version
M. Bonazzoli, V. Dolean, I.G. Graham, E. A. Spence, P.-H. Tournier, Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption, Math. Comp. 88 (2019), 2559-2604 Final preprint Final published version
I. G. Graham, F. Y. Kuo, D. Nuyens, R. Scheichl, and I. H. Sloan, Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients, Numer. Math. 140, 479–511 (2018). Final preprint Final published version
I. G. Graham, F. Y. Kuo, D. Nuyens, R. Scheichl, and I. H. Sloan, Analysis of circulant embedding methods for sampling stationary random fields, SIAM J. Numer. Anal. 56(3), 1871–1895 (2018). Final preprint Final published version
M. Bonazzoli, V. Dolean, I.G. Graham, E. A. Spence, P.-H. Tournier, A two-level domain-decomposition preconditioner for the time-harmonic Maxwell's equations, in P.E. Bjorstad, et. al. EDS, Domain Decomposition Methods 24, Springer LNCSE 125, 2018 Final preprint
M. Bonazzoli, V. Dolean, I.G. Graham, E. A. Spence, P.-H. Tournier, Two-level preconditioners for the Helmholtz equation in P.E. Bjorstad, et. al. EDS, Domain Decomposition Methods 24, Springer LNCSE 125, 2018. Final preprint
I.G. Graham, M.J. Parkinson and R. Scheichl, Modern Monte Carlo Variants for Uncertainty Quantification in Neutron Transport, in "Contemporary Computational Mathematics-A Celebration of the 80th Birthday of Ian Sloan", J. Dick, F.Y. Kuo, and H. Wozniakowski Eds., Springer-Verlag, 455-481 (2018). Final preprint
I.G. Graham, E.A. Spence and E. Vainikko, Recent Results on Domain Decomposition Preconditioning for the High-frequency Helmholtz Equation using Absorption, In: Modern Solvers for Helmholtz problems, edited by D. Lahaye, J. Tang and C. Vuik, Springer Geosystems Mathematics series, 2017. Final preprint
I.G. Graham, E.A. Spence and E. Vainikko, Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. Math. Comp. 86 (2017), 2089-2127 Final preprint Final published version
M.J. Gander, I.G. Graham, E.A. Spence, Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? Numer. Math. 131, 567–614 (2015). Final preprint Final published version

I.G. Graham, R. Scheichl and E. Ullmann, Mixed Finite Element Analysis of Lognormal Diffusion and Multilevel Monte Carlo Methods, Stochastic Partial Differential Equations, Analysis and Computation, 4, 41–75 (2016) Final preprint Final published version

I.G. Graham, M. Loehndorf, J.M. Melenk and E.A. Spence, When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k? BIT Num. Math., vol. 55, no. 1, 171-214 (2015), Final preprint

I.G. Graham, F.Y. Kuo, J.A. Nicholls, R. Scheichl, Ch. Schwab and I.H. Sloan, Quasi-Monte Carlo Finite Element Methods for Elliptic PDEs with Log-normal Random Coefficients, Numer. Math. 131 (2), 329-368 (2015). Final preprint Final published version

I.G. Graham, U. Langer, J.M. Melenk, and M. Sini (Editors) Direct and Inverse Problems in Wave Propagation and Applications , Radon Series on Computational and Applied Mathematics 14, de Gruyter, September 2013. ISBN:978-3-11-028228-3

V. Dominguez, I. G. Graham and T. Kim, Filon-Clenshaw-Curtis rules for highly-oscillatory integrals with algebraic singularities and stationary points. Preprint: http://arxiv.org/abs/1207.2283 SIAM J. Numerical Analysis 51(3): 1542-1566 (2013)

S.N. Chandler-Wilde, I.G. Graham, S. Langdon, E.A. Spence, Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering, Acta Numerica, vol. 21, 89--305 (2012) local (official) copy
I.G. Graham, T.Y. Hou, O. Lakkis and R. Scheichl (Editors) Numerical Analysis of Multiscale Problems , Springer Lecture Notes in Computational Science and Engineering 83, 2011.

E.A. Spence, S. N. Chandler-Wilde, I. G. Graham, V. P. Smyshlyaev, A new frequency-uniform coercive boundary integral equation for acoustic scattering, Communications on Pure and Applied Mathematics 64(10) (2011) 1384-1415. preprint
T. Betcke, S.N. Chandler-Wilde, I.G. Graham, S. Langdon, M. Lindner, Condition number estimates for combined potential operators in acoustics and their boundary element discretisation. Numerical Methods for PDEs 27 (2011), 31-69 preprint

F. Scheben and I. G. Graham, Iterative methods for neutron transport eigenvalue problems, SIAM Journal on Scientific Computing, 33 (2011), 2785-2804. Preprint, February 18th 2011

S. Giani and I. G. Graham, Adaptive finite element methods for computing band gaps in photonic crystals. Numerische Mathematik 121(1), 31-64, 2012. Revised version, dated 21st January 2011.

I. G. Graham, F. Y. Kuo, D. Nuyens, R. Scheichl, and I. H. Sloan, Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications, J. Comp. Phys. 230 (10), 3668-3694 (2011) Final preprint
Final published version

V. Dominguez, I.G. Graham and V.P. Smyshlyaev, Stability and error estimates for Filon-Clenshaw-Curtis rules for highly-oscillatory integrals, IMA J. Numer. Anal. 31, 1253–1280 (2011). Final pdf

C.-C. Chu, I.G.Graham and T.-Y. Hou, A new multiscale finite element method for high-contrast elliptic interface problems, Math. Comp. 79 (2010) 1915-1955. Preprint Final Published Paper

J. Van lent, R. Scheichl and I.G. Graham, Energy Minimizing Coarse Spaces for Two-level Schwarz Methods for Multiscale PDEs, Numer. Linear Algebra Appl. 16, 775–799 (2009). preprint

S.N. Chandler-Wilde and I.G. Graham, Boundary integral methods in high-frequency scattering, in ``Highly Oscillatory Problems'', B. Engquist, T. Fokas, E. Hairer, A. Iserles, editors, LMS Lecture Note Series 366, Cambridge University Press, 2009. Details

Burak Aksoylu, Ivan G. Graham, Hector Klie, and Robert Scheichl Towards A Rigorously Justified Algebraic Preconditioner For High-Contrast Diffusion Problems Computing and Visualization in Science 11 (2008), 319-331. Details

Simon N. Chandler-Wilde, Ivan G. Graham, Stephen Langdon, and Marko Lindner, Condition Number Estimates for Combined Potential Boundary Integral Operators in Acoustic Scattering, Journal of Integral Equations and Applications 21 (2009), 229 - 279. Details

S. Giani and I.G. Graham, A convergent adaptive method for elliptic eigenvalue problems SIAM J Numer Anal, 47 (2009), 1067-1091. DOI: 10.1137/070697264 Details

L. Grasedyck, I.G. Graham, W. Hackbusch and S.A. Sauter, Optimal Panel-Clustering in the Presence of Anisotropic Mesh Refinement. Bath Institute for Complex Systems Preprint number 16/06, University of Bath (2006), SIAM J. Numer. Anal., 46 (2008), 517-543. Details

I.G. Graham and R. Scheichl, Coefficient-explicit Condition Number Bounds for Overlapping Additive Schwarz, in Domain Decomposition methods in Science and Engineering XVII, Lecture Notes in Computational Science and Engineering Vol 60, U. Langer, M. Discacciati, D. Keyes, O. Widlund and W. Zulehner (Eds) (2008). ISBN: 978-3-540-75198-4 . Details

I.G. Graham and R. Scheichl, Robust Domain Decomposition Algorithms for Multiscale PDEs Bath Institute for Complex Systems Preprint number 14/06, University of Bath (2006), Numerical Methods for Partial Differential Equations published online 26th April 2007 Details

I.G. Graham. P.O. Lechner and R. Scheichl, Domain Decomposition for Multiscale PDEs, Bath Institute for Complex Systems Preprint number 11/06, University of Bath (2006), Numerische Mathematik 106 (2007), 589-626 . Details

V. Dominguez, I.G. Graham and V.P. Smyshlyaev, A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering, Bath Institute for Complex Systems Preprint number 1/06, University of Bath (2006), Numerische Mathematik 106 (2007), 471-510. Details

B.D. Bonner. I.G.Graham and V.P.Smyshlyaev, The computation of conical diffraction coefficients in high-frequency acoustic wave scattering, SIAM J. Numer. Anal., 43 (2005), 1202-1230. Details

J. Berns-Mueller, I.G. Graham and A. Spence, Inexact inverse iteration for symmetric matrices, has appeared in Linear Algebra and its Applications 416 (2006), 389-413 . Details

I.G. Graham, W. Hackbusch and S.A. Sauter, Finite elements on degenerate meshes: inverse-type inequalities and applications, IMA J. Numer. Anal., 25 (2005), 379-407. doi:10.1093/imanum/drh017 Details

I.G.Graham and W.McLean, Anisotropic Mesh Refinement,the Conditioning of Galerkin boundary element matrices and simple preconditioners, SIAM J. Numer. Anal. 44 (2006), 1487-1513 Details

[Ivan Graham ] [ Department of Mathematical Sciences ] [University of Bath ]