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
- [New] J. Galkowski, P. Marchand, E.A. Spence,
Eigenvalues of the truncated Helmholtz solution operator under strong
trapping
- D. Lafontaine, E.A. Spence, J. Wunsch, For most frequencies, strong trapping has a weak effect in frequency-domain scattering, Comm. Pure Appl. Math. (2020) arxiv copy
- J. Galkowski, E.A. Spence, J. Wunsch,
Optimal constants in non-trapping resolvent estimates and applications in numerical analysis, Pure and Applied Analysis, volume 2, number 1, pages 157-202 (2020) arxiv copy
- 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, vol. 266, issue 6, 2869-2923 (2019), 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, SIAM J. Math. Anal., volume 52, issue 1, pages 845-893 (2020) arxiv copy
- A. Moiola, E.A. Spence, Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions, Math. Mod. Meth. App. S., vol. 29, no. 2, 317-354 (2019) arxiv copy
- 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 the accuracy of absorbing boundary conditions for the Helmholtz equation
Papers about the convergence of the finite element method applied to the Helmholtz equation
- [New] D. Lafontaine, E.A. Spence, J. Wunsch,
Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method
- D. Lafontaine, E.A. Spence, J. Wunsch,
Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients
- D. Lafontaine, E.A. Spence, J. Wunsch,
A sharp relative-error bound for the Helmholtz h-FEM at high frequency
Papers about uncertainty quantification for the Helmholtz equation
Papers about preconditioning the Helmholtz equation
- S. Gong, I.G. Graham, E.A. Spence,
Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation IMA J. Num. Anal, to appear,
arxiv copy
- I.G. Graham, E.A. Spence, J. Zou,
Domain Decomposition with local impedance condition for the Helmholtz equation with absorption, SIAM J. Num. Anal.,
vol. 58, number 5, pages 2515–2543 (2020)
arxiv copy
- I.G. Graham, E.A. Spence, E. Vainikko,
Domain Decomposition preconditioning for high-frequency Helmholtz problems with 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
- [New] P. Marchand, J. Galkowski, A. Spence, E.A. Spence,
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?
- J. Galkowski, E.A. Spence, Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators Integr. Equat. Oper. Th., vol. 91, issue 1, article 6 (2019), arxiv copy
- 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 Numer. Math., vol. 142, issue 2, pages 329-357 (2019) arxiv copy
- 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