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Research Output 1994 2019

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

8 Downloads (Pure)

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 May 2019, In : Mathematics of Computation (MCOM). 88, 320, p. 2559-2604 46 p.

Research output: Contribution to journalArticle

Open Access
File
Domain Decomposition
Preconditioning
Maxwell's equations
Preconditioner
Absorption
2 Citations (Scopus)
4 Downloads (Pure)
Open Access
File
Heterogeneous Media
A Priori Bounds
Helmholtz Equation
Well-posedness
Transmission Problem
2018
5 Citations (Scopus)
16 Downloads (Pure)

Analysis of circulant embedding methods for sampling stationary random fields

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

Research output: Contribution to journalArticle

Open Access
File
Random Field
Regular hexahedron
Positive Definiteness
Circulant Matrix
Correlation Length
2 Citations (Scopus)

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

1 Citation (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
Quasi-Monte Carlo
Elliptic PDE
Monte Carlo methods
Random Field
Sampling
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

3 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

2017
10 Citations (Scopus)
22 Downloads (Pure)

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
File
Hermann Von Helmholtz
Domain Decomposition
Preconditioning
GMRES
Absorption

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

Helmholtz equation
Decomposition
Wavelength
Pollution
Experiments
2016
12 Citations (Scopus)
52 Downloads (Pure)
Open Access
File
Multilevel Methods
Mixed Finite Elements
Monte Carlo method
Finite Element Discretization
Error Bounds
2015
31 Citations (Scopus)
Helmholtz equation
GMRES
Helmholtz Equation
Preconditioning
Boundary conditions
38 Citations (Scopus)

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

Quasi-Monte Carlo Methods
Elliptic PDE
Random Coefficients
Finite Element Method
Finite element method
11 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

Helmholtz equation
Approximation Error
Helmholtz Equation
Best Approximation
Optimality
2014
93 Downloads (Pure)
File
programming
mathematics
Teaching
computer scientist
student
2013
29 Citations (Scopus)

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

Oscillatory Integrals
Stationary point
Error Estimates
Composite
Singularity
2012
17 Citations (Scopus)
86 Downloads (Pure)

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
File
Adaptive Finite Element Method
Band Gap
Photonic crystals
Photonic Crystal
Error Estimator
97 Citations (Scopus)
111 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
Boundary Integral Method
Acoustic Scattering
Acoustics
Scattering
Oscillatory Integrals
2011
27 Citations (Scopus)
87 Downloads (Pure)

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
Acoustic Scattering
Boundary integral equations
Boundary Integral Equations
Integral Operator
Stars
51 Citations (Scopus)

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

Potential Operators
Condition number
Integral Operator
Boundary Elements
Acoustics
3 Citations (Scopus)
87 Downloads (Pure)

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
File
Neutron Transport
Iterative methods
Eigenvalue Problem
Neutrons
Fluxes
72 Citations (Scopus)
87 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
pulse detonation engines
Monte Carlo method
Monte Carlo methods
coefficients
functionals
60 Citations (Scopus)

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

Oscillatory Integrals
Stability Estimates
Error Estimates
Regularity
Sharpness
2010
101 Citations (Scopus)
81 Downloads (Pure)

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
Interfaces (computer)
Boundary conditions
Finite element method
Porous materials
2009
55 Citations (Scopus)

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

Adaptive Method
Eigenvalues and eigenfunctions
Elliptic Problems
Eigenvalue Problem
Nonlinearity

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

43 Citations (Scopus)

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

Acoustic Scattering
Boundary Integral
Condition number
Integral Operator
Acoustics
26 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

Two-level Method
Schwarz Methods
Energy
Preconditioner
Overlapping

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
3 Citations (Scopus)

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

1 Citation (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

Anisotropic Mesh
Mesh Refinement
Clustering algorithms
Clustering
Mesh
19 Citations (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

2007
68 Citations (Scopus)

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

Boundary Integral Method
Acoustic Scattering
Acoustics
Infinity
Bilinear form
222 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

1 Citation (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

98 Citations (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

Coarsening
Domain Decomposition
Preconditioner
Decomposition
Porous materials
32 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

Decomposition Algorithm
Coarsening
Domain Decomposition
Decomposition
Groundwater flow
2006
14 Citations (Scopus)
Anisotropic Mesh
Ill-conditioning
Mesh Refinement
Stiffness matrix
Stiffness Matrix
34 Citations (Scopus)
55 Downloads (Pure)

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
Inverse Iteration
Iterative methods
Symmetric matrix
Linear systems
Rayleigh quotient
2005
42 Citations (Scopus)

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

Galerkin methods
Clustering algorithms
Mesh
Finite Element
Degradation
21 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

Acoustic wave scattering
Acoustic Scattering
Wave Scattering
Acoustic Waves
Diffraction
2004
80 Citations (Scopus)

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

Scattering
scattering
far fields
Acoustic waves
Helmholtz equation
4 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

Incompressible Navier-Stokes Equations
Navier Stokes equations
Elliptic PDE
Unstructured Grid
Software Design
37 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

Mortar
Mesh
Finite Element
Trace Theorem
Norm Inequality
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

4 Citations (Scopus)

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

Parallel Iterative Methods
Eigenvalue Computation
Iterative methods
Navier Stokes equations
Navier-Stokes Equations
2002
52 Citations (Scopus)

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

Boundary Integral Method
Hermann Von Helmholtz
Closed
Polynomial approximation
Helmholtz equation
2 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

Domain decomposition methods
Iterative methods
Navier Stokes equations
Decomposition
2001
5 Citations (Scopus)

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

Boundary Integral Method
Singularly Perturbed Boundary Value Problem
Boundary value problems
Infinity
Layer Potentials

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