Ivan Graham -- Preprints

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

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, to appear in Numerical Methods for PDEs. preprint , Numerical Methods for PDEs.

F. Scheben and I. G. Graham, Iterative methods for neutron transport eigenvalue problems
Preprint 08/10, Bath Institute for Complex Systems, 2010.
Revised version, February 18th 2011 Accepted for SIAM J. Scientific Computing, 22nd February 2011.

S. Giani and I. G. Graham, Adaptive finite element methods for computing band gaps in photonic crystals, submitted April 2010. Accepted for Numerische Mathematik (Sept 2011). 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 Original Preprint 04/10, Bath Institute for Complex Systems, 2010.
Revised version (with a change of title), December 2010.
Appeared online Journal of Computational Physics, April 4th 2011. DOI: 10.1016/j.jcp.2011.01.023

V. Dominguez, I.G. Graham and V.P. Smyshlyaev, Stability and error estimates for Filon-Clenshaw-Curtis rules for highly-oscillatory integrals, Preprint 02/10, Bath Institute for Complex Systems, 2010. Revised version
Abstract of final version, appeared in IMA J. Numer. Anal. 2011
Pdf of final version, appeared in IMA J. Numer. Anal. 2011

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, Numerical Linear Algebra with Applications doi 10.1002/nla.641, published online, 12th March 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