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Research Output

2019

Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients

Gilbert, A. D., Graham, I. G., Kuo, F. Y., Scheichl, R. & Sloan, I. H., 1 Aug 2019, In : Numerische Mathematik. 142, 4, p. 863-915 53 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

Bonazzoli, M., Dolean, V., Graham, I., Spence, E. & Tournier, P-H., 30 Nov 2019, In : Mathematics of Computation (MCOM). 88, 320, p. 2559-2604 46 p.

Research output: Contribution to journalArticle

Open Access
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1 Citation (Scopus)
17 Downloads (Pure)
Open Access
File
5 Citations (Scopus)
11 Downloads (Pure)
2018

Analysis of circulant embedding methods for sampling stationary random fields

Graham, I. G., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 31 Dec 2018, In : SIAM Journal on Numerical Analysis (SINUM). 56, 3, p. 1871-1895 25 p.

Research output: Contribution to journalArticle

Open Access
File
7 Citations (Scopus)
25 Downloads (Pure)

A two-level domain-decomposition preconditioner for the time-harmonic maxwell’s equations

Bonazzoli, M., Dolean, V., Graham, I. G., Spence, E. A. & Tournier, P. H., 1 Jan 2018, Domain Decomposition Methods in Science and Engineering XXIV. DD 2017. Bjorstad, P. (ed.). Cham, Switzerland: Springer Verlag, p. 149-157 9 p. (Lecture Notes in Computational Science and Engineering; vol. 125).

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients

Graham, I., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 1 Oct 2018, In : Numerische Mathematik. 140, 2, p. 479-511 33 p.

Research output: Contribution to journalArticle

Open Access
2 Citations (Scopus)

Modern Monte Carlo variants for uncertainty quantification in neutron transport

Graham, I. G., Parkinson, M. J. & Scheichl, R., 23 May 2018, Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing, p. 455-481 27 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Two-level preconditioners for the helmholtz equation

Bonazzoli, M., Dolean, V., Graham, I. G., Spence, E. A. & Tournier, P. H., 1 Jan 2018, Domain Decomposition Methods in Science and Engineering XXIV. DD 2017. Bjorstad, P. (ed.). Cham, Switzerland: Springer Verlag, p. 139-147 9 p. (Lecture Notes in Computational Science and Engineering; vol. 125).

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)
2017

Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption

Graham, I. G., Spence, E. A. & Vainikko, E., 2017, In : Mathematics of Computation. 86, 307, p. 2089-2127

Research output: Contribution to journalArticle

Open Access
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11 Citations (Scopus)
29 Downloads (Pure)

Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption

Graham, I., Spence, E. & Vainikko, E., 18 Feb 2017, Modern Solvers for Helmholtz Problems. Lahaye, D., Tang, J. & Vuik, K. (eds.). Basel, Germany: Birkhäuser, (Geosystems Mathematics).

Research output: Chapter in Book/Report/Conference proceedingChapter

2016
Open Access
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12 Citations (Scopus)
71 Downloads (Pure)
2015
Open Access
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32 Citations (Scopus)
7 Downloads (Pure)

Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients

Graham, I. G., Kuo, F. Y., Nichols, J. A., Scheichl, R., Schwab, C. & Sloan, I. H., Oct 2015, In : Numerische Mathematik. 131, 2, p. 329-368 40 p.

Research output: Contribution to journalArticle

40 Citations (Scopus)

When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k ?

Graham, I. G., Löhndorf, M., Melenk, J. M. & Spence, E. A., Mar 2015, In : BIT Numerical Mathematics. 55, 1, p. 171-214 44 p.

Research output: Contribution to journalArticle

11 Citations (Scopus)
2014
File
128 Downloads (Pure)
2013

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

Domínguez, V., Graham, I. G. & Kim, T., 2013, In : SIAM Journal on Numerical Analysis (SINUM). 51, 3, p. 1542-1566 25 p.

Research output: Contribution to journalArticle

30 Citations (Scopus)
2012

Adaptive finite element methods for computing band gaps in photonic crystals

Giani, S. & Graham, I. G., 2012, In : Numerische Mathematik. 121, 1, p. 31-64 34 p.

Research output: Contribution to journalArticle

Open Access
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17 Citations (Scopus)
115 Downloads (Pure)

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

Graham, I., Spence, E., Chandler-Wilde, S. & Langdon, S., May 2012, In : Acta Numerica. 21, p. 89-305 216 p.

Research output: Contribution to journalArticle

Open Access
File
101 Citations (Scopus)
139 Downloads (Pure)
2011

A new frequency-uniform coercive boundary integral equation for acoustic scattering

Spence, E. A., Chandler-Wilde, S. N., Graham, I. G. & Smyshlyaev, V. P., Oct 2011, In : Communications on Pure and Applied Mathematics. 64, 10, p. 1384-1415 32 p.

Research output: Contribution to journalArticle

File
27 Citations (Scopus)
114 Downloads (Pure)

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

Betcke, T., Chandler-Wilde, S. N., Graham, I. G., Langdon, S. & Lindner, M., Jan 2011, In : Numerical Methods for Partial Differential Equations. 27, 1, p. 31-69 39 p.

Research output: Contribution to journalArticle

53 Citations (Scopus)

Iterative methods for neutron transport eigenvalue problems

Scheben, F. & Graham, I. G., 2011, In : SIAM Journal on Scientific Computing. 33, 5, p. 2785-2804 20 p.

Research output: Contribution to journalArticle

Open Access
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4 Citations (Scopus)
117 Downloads (Pure)

Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications

Graham, I. G., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 10 May 2011, In : Journal of Computational Physics. 230, 10, p. 3668-3694 27 p.

Research output: Contribution to journalArticle

Open Access
File
78 Citations (Scopus)
118 Downloads (Pure)

Stability and error estimates for Filon-Clenshaw-Curtis rules for highly-oscillatory integrals

Dominguez, V., Graham, I. & Smyshlyaev, V., 2011, In : IMA Journal of Numerical Analysis. 31, 4, p. 1253-1280 28 p.

Research output: Contribution to journalArticle

62 Citations (Scopus)
2010

A new multiscale finite element method for high-contrast elliptic interface problems

Chu, C. C., Graham, I. G. & Hou, T. Y., Oct 2010, In : Mathematics of Computation (MCOM). 79, 272, p. 1915-1955 41 p.

Research output: Contribution to journalArticle

File
106 Citations (Scopus)
110 Downloads (Pure)
2009

A convergent adaptive method for elliptic eigenvalue problems

Giani, S. & Graham, I. G., 2009, In : SIAM Journal on Numerical Analysis (SINUM). 47, 2, p. 1067-1091 25 p.

Research output: Contribution to journalArticle

55 Citations (Scopus)

Boundary integral methods in high frequency scattering

Chandler-Wilde, S. N. & Graham, I. G., Jul 2009, Highly Oscillatory Problems. Engquist, B., Fokas, A., Hairer, E. & Iserles, A. (eds.). 366 ed. Cambridge University Press, p. 154-193 40 p. (London Mathematical Society Lecture Note Series).

Research output: Chapter in Book/Report/Conference proceedingChapter

Condition number estimates for combined potential boundary integral operators in acoustic scattering

Chandler-Wilde, S. N., Graham, I. G., Langdon, S. & Lindner, M., Jul 2009, In : Journal of Integral Equations and Applications. 21, 2, p. 229-279 51 p.

Research output: Contribution to journalArticle

43 Citations (Scopus)

Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs

Van Lent, J., Scheichl, R. & Graham, I. G., Oct 2009, In : Numerical Linear Algebra with Applications. 16, 10, p. 775-799 25 p.

Research output: Contribution to journalArticle

26 Citations (Scopus)

JIEA: A special issue for the UKBIM6 meeting

Graham, I. G., Trevelyan, B. & Chandler-Wilde, S. N., 2009, In : Journal of Integral Equations and Applications. 21, 3, p. 329-330 2 p.

Research output: Contribution to journalEditorial

2008

Coefficient-explicit condition number bounds for overlapping additive Schwarz

Graham, I. G. & Scheichl, R., Jan 2008, Domain Decomposition Methods in Science and Engineering XVII. Langer, U., Discacciati, M., Keyes, D. E., Widlund, O. B. & Zulehner, W. (eds.). Berlin, Germany: Springer, p. 365-372 8 p. (Lecture Notes in Computational Science and Engineering; vol. 60).

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Optimal panel-clustering in the presence of anisotropic mesh refinement

Graham, I. G., Grasedyck, L., Hackbusch, W. & Sauter, S. A., 2008, In : SIAM Journal on Numerical Analysis (SINUM). 46, 1, p. 517-543 27 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Towards a rigorously justified algebraic preconditioner for high-contrast diffusion problems

Aksoylu, B., Graham, I. G., Klie, H. & Scheichl, R., Sep 2008, In : Computing and Visualization in Science. 11, 4-6, p. 319-331 13 p.

Research output: Contribution to journalArticle

20 Citations (Scopus)
2007

A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering

Dominguez, V., Graham, I. G. & Smyshlyaev, V. P., 2007, In : Numerische Mathematik. 106, 3, p. 471-510 40 p.

Research output: Contribution to journalArticle

69 Citations (Scopus)

Coefficient-explicit Condition Number Bounds for Overlapping Additive Schwarz

Graham, I. G. & Scheichl, R., Jun 2007, p. 1-8. 8 p.

Research output: Contribution to conferencePaper

241 Citations (Scopus)

Domain decomposition for heterogeneous media

Graham, I. G. & Lechner, P. O., 2007, Domain decomposition methods in science and engineering XVI. Widlund, O. B. & Keyes, D. E. (eds.). Berlin: Springer, Vol. 55. p. 573-578 6 p. (Lecture Notes in Computational Science and Engineering).

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Domain decomposition for multiscale PDEs

Graham, I. G., Lechner, P. O. & Scheichl, R., Jun 2007, In : Numerische Mathematik. 106, 4, p. 589-626 38 p.

Research output: Contribution to journalArticle

99 Citations (Scopus)

Robust domain decomposition algorithms for multiscale PDEs

Graham, I. G. & Scheichl, R., 2007, In : Numerical Methods for Partial Differential Equations. 23, 4, p. 859-878 20 p.

Research output: Contribution to journalArticle

32 Citations (Scopus)
2006
14 Citations (Scopus)

Inexact inverse iteration for symmetric matrices

Berns-Müller, J., Graham, I. G. & Spence, A., 15 Jul 2006, In : Linear Algebra and its Applications. 416, 2-3, p. 389-413 25 p.

Research output: Contribution to journalArticle

File
36 Citations (Scopus)
76 Downloads (Pure)
2005

Finite elements on degenerate meshes: inverse-type inequalities and applications

Graham, I. G., Hackbusch, W. & Sauter, S. A., 2005, In : IMA Journal of Numerical Analysis. 25, 2, p. 379-407 29 p.

Research output: Contribution to journalArticle

45 Citations (Scopus)

The computation of conical diffraction coefficients in high-frequency acoustic wave scattering

Bonner, B. D., Graham, I. G. & Smyshlyaev, V. P., 2005, In : SIAM Journal on Numerical Analysis (SINUM). 43, 3, p. 1202-1230 29 p.

Research output: Contribution to journalArticle

21 Citations (Scopus)
2004

A high-order algorithm for obstacle scattering in three dimensions

Ganesh, M. & Graham, I. G., 2004, In : Journal of Computational Physics. 198, 1, p. 211-242 32 p.

Research output: Contribution to journalArticle

81 Citations (Scopus)

A parallel solver for PDE systems and application to the incompressible Navier-Stokes equations

Vainikko, E. & Graham, I. G., 2004, In : Applied Numerical Mathematics. 49, 1, p. 97-116 20 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method

Dahmen, W., Faermann, B., Graham, I. G., Hackbusch, W. & Sauter, S. A., 2004, In : Mathematics of Computation (MCOM). 73, 247, p. 1107-1138 32 p.

Research output: Contribution to journalArticle

37 Citations (Scopus)
2003

Mathematical Modelling of Solid Tumour Growth: Applications and pre-pattern formation

Chaplain, M. J., Ganesh, M. & Graham, I. G., 2003, Morphogenesis and Pattern Formation in Biological Systems. Sekimura, T., Noji, S., Ueno, N. & Maini, P. K. (eds.). Springer, p. 10 1 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Parallel iterative methods for Navier-Stokes equations and application to eigenvalue computation

Graham, I. G., Spence, A. & Vainikko, E., Sep 2003, In : Concurrency and Computation-Practice & Experience. 15, 11-12, p. 1151-1168 18 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)
2002

Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in R-3

Graham, I. G. & Sloan, I. H., 2002, In : Numerische Mathematik. 92, 2, p. 289-323 35 p.

Research output: Contribution to journalArticle

53 Citations (Scopus)

Parallel iterative methods for Navier-Stokes equations and application to stability assessment

Graham, I. G., Spence, A. & Vainikko, E., 2002, Euro-Par 2002 Parallel Processing, Proceedings. Vol. 2400. p. 705-714 10 p. (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)
2001

Boundary integral methods for singularly perturbed boundary value problems

Langdon, S. & Graham, I. G., 2001, In : IMA Journal of Numerical Analysis. 21, 1, p. 217-237 21 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)

Numerical aspects of conical diffraction coefficient calculations

Bonner, B. D., Graham, I. G. & Harris, P. J. (ed.), 2001, p. 57--67. 11 p.

Research output: Contribution to conferencePaper