Below is a list of the majority of my papers and preprints organised by subject area. A complete list of my papers can be found here.
Papers about the Maxwell equations
Papers about the Helmholtz equation
Papers about the Helmholtz equation itself
- O.R. Pembery, E.A. Spence,
The Helmholtz equation in random media: well-posedness and a priori bounds
- I.G. Graham, O.R. Pembery, E.A. Spence, The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances, J. Differ. Equations, arxiv copy
- S.N. Chandler-Wilde,
E.A. Spence, A. Gibbs, V. P. Smyshlyaev, High-frequency bounds for the Helmholtz equation under parabolic trapping and applications in numerical analysis
- A. Moiola,
E.A. Spence, Acoustic
transmission problems: wavenumber-explicit bounds and resonance-free
regions
- D. Baskin, E.A. Spence, J. Wunsch,
Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations SIAM J. Math. Anal. vol. 48, no. 1, 229-267 (2016)
local official copy,
arxiv copy
- E.A. Spence, Wavenumber-explicit bounds in time-harmonic acoustic scattering SIAM J. Math. Anal., vol. 46, no. 4, 2987-3024 (2014) local official copy
Papers about preconditioning the Helmholtz equation
- I.G. Graham, E.A. Spence, J. Zou,
Domain Decomposition with local impedance condition for the Helmholtz equation
- I.G. Graham, E.A. Spence, E. Vainikko,
Domain Decomposition preconditioning for high-frequency Helmholtz problems using absorption, Math. Comp., vol. 86, pages 2089-2127 (2017) arxiv copy
- 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., vol. 131, issue 3, page 567-614(2015) local unofficial copy
(Note that this is a revision of the
preprint titled How should one choose the shift for the shifted Laplacian to be a good preconditioner for the Helmholtz equation?)
Papers about coercive formulations of the Helmholtz equation
Papers about boundary integral equations for the Helmholtz equation
- J. Galkowski, E.A. Spence, Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators
- J. Galkowski, E.H. Müller, E.A. Spence, Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem
- E.A. Spence, I.V. Kamotski, V.P. Smyshlyaev, Coercivity of combined boundary integral equations in high-frequency scattering, Comm. Pure Appl. Math., vol. 68, issue 9, pages 1587-1639 (2015), local unofficial copy
- I.G. Graham, M. Löhndorf, J.M. Melenk, 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), local unofficial copy
- E.A. Spence, Bounding acoustic layer potentials via oscillatory integral techniques BIT Num. Math., vol. 55, no. 1., 279-318 (2015) local unoffical copy
- T. Betcke, J. Phillips, E.A. Spence, Spectral decompositions and nonnormality of boundary integral operators in acoustic scattering, IMA J. Num. Anal., vol. 34, no. 2, 700-731 (2014)
- 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
- T. Betcke, E.A. Spence, Numerical estimation of coercivity constants for boundary integral operators in acoustic scattering, SIAM J. Num. Anal. vol. 49, issue 4, 1572-1601 (2011) local official copy
- E.A. Spence, S.N. Chandler-Wilde, I.G. Graham, V. P. Smyshlyaev A new frequency-uniform coercive boundary integral equation for acoustic scattering, Comm. Pure Appl. Math. vol. 64, issue 10, 1384-1415, (2011) unofficial copy
Review articles
- I.G. Graham, E.A. Spence, E. Vainikko, Recent Results on Domain Decomposition Preconditioning for the High-frequency Helmholtz equation using absorption in "Modern Solvers for Helmholtz Problems", D. Lahaye, J. Tang, C. Vuik eds., Springer (2017)
- E.A. Spence, "When all else fails, integrate by parts" - an overview of new and old variational formulations for linear elliptic PDEs in "Unified Transform Method for Boundary Value Problems: Applications and Advances", A.S. Fokas and B. Pelloni eds., SIAM (2015)
Papers about asymptotics of integrals
Papers about transform methods for linear PDEs
- E.A. Spence, The Watson transformation revisited, (2014)
- E.A. Spence, Transform methods for linear PDEs, in
Encyclopedia of Applied and Computational Mathematics, Springer (2015)
- A.S. Fokas, E.A. Spence Synthesis, as opposed to separation, of variables, SIAM Review, vol. 54, no. 2, 291-324 (2012) local official copy
- E.A. Spence, A.S. Fokas,
A New Transform Method I: Domain Dependent Fundamental
Solutions and Integral Representations. Proc. Roy. Soc. A. vol.
466, 2259-2281 (2010)
- E.A. Spence, A.S. Fokas,
A New Transform Method II: the Global Relation, and Boundary Value Problems in Polar Co-ordinates. Proc. Roy. Soc. A. vol 466, 2283-2307 (2010) Corrections
- S.A. Smitheman, E.A. Spence, A.S. Fokas, A spectral collocation
method for the Laplace and modified Helmholtz equations in a convex
polygon IMA J. Num. Anal. 30(4): 1184-1205 (2010)
- A.S. Fokas, N. Flyer, S.A. Smitheman, E.A. Spence,
A semi-analytical numerical method for solving evolution and elliptic partial differential equations,
J. Comp. Appl. Math. Volume 227, Issue 1, 59-74 (2009) (Invited Paper)
- E.A. Spence, Boundary Value Problems for Linear Elliptic PDEs, PhD thesis, Cambridge, submitted 23/03/2009, viva 05/02/2010