1. Three lectures on high frequency Helmholtz problems - January 2016
brief outline
Lecture 1
Lecture 2
Lecture 3
2. One lecture on PDEs with random data - April 2016:
Slides
Here are some papers which are available electronically:
High frequency problems
-
I.G. Graham, E.A. Spence and E. Vainikko,
Domain decomposition preconditioning for high-frequency Helmholtz
problems using absorption.
preprint submitted 7th July 2015
-
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? Numerische
Mathematik, 2015. DoI: 10.1007/s00211-015-0700-2
Final preprint
-
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
-
V. Dominguez, I. G. Graham and T. Kim,
Filon-Clenshaw-Curtis rules for highly-oscillatory integrals with
algebraic singularities and stationary points, submitted 10th July
2012. 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. Published online 25th October 2010.
DOI: 10.1002/num.20643.
Numerical Methods for PDEs
27 (2011), 31-69
preprint
-
V. Dominguez, I.G. Graham and V.P. Smyshlyaev,
Stability and error estimates for Filon-Clenshaw-Curtis rules for
highly-oscillatory integrals,
Pdf of final version, appeared in IMA J. Numer. Anal. 2011
-
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
- 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
-
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
Further reading on Hybrid Numerical Asymptotic Methods:
-
S N Chandler-Wilde & P Monk,
Existence, uniqueness and variational methods for scattering by unbounded rough surfaces.
SIAM Journal on Mathematical Analysis 37, 598-618, 2005. Link
-
D. P. Hewett, S. Langdon, J. M. Melenk, A high frequency hp boundary element method for
scattering by convex polygons, SIAM J. Num. Anal., 51(1), 2013
-
S. N. Chandler-Wilde, D. P. Hewett, S. Langdon, A. Twigger, A high frequency boundary
element method for scattering by a class of nonconvex obstacles, Numer. Math., 129(4), 2015
-
S. P. Groth, D. P. Hewett, S. Langdon, Hybrid numerical-asymptotic approximation for high
frequency scattering by penetrable convex polygons, IMA J. Appl. Math., 80(2), 2015
-
D. P. Hewett, S. Langdon, S. N. Chandler-Wilde, A frequency-independent boundary element
method for scattering by two-dimensional screens and apertures, IMA J. Numer. Anal., 35(4),
2015
-
D. P. Hewett, Shadow boundary effects in hybrid numerical-asymptotic methods for high
frequency scattering, Euro. J. Appl. Math., 26(5), 2015
PDEs with random data
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, June 2015. DoI:
10.1007/s40072-015-0051-0
preprint arxiv 1312.6047
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, Numerische Mathematik
December 2014. DoI: 10.1007/s00211-014-0689-y.
SAM Report 2013-14, Seminar for Applied Mathematics, ETH Zurich.
preprint
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.
[Ivan Graham ] [ Department of Mathematical
Sciences ] [University of Bath
]