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 Laplace equation
Papers about the Maxwell equations
Papers about the Helmholtz equation
Papers about the Helmholtz equation itself
 T. ChaumontFrelet, E.A. Spence,
Scattering by finelylayered obstacles: frequencyexplicit bounds and homogenization, SIAM J. Math. Anal., to appear
 J. Galkowski, P. Marchand, E.A. Spence, Eigenvalues of the truncated Helmholtz solution operator under strong
trapping, SIAM J. Math. Anal., Vol. 53, No. 6, pages 67246770 (2021) arxiv copy
 D. Lafontaine, E.A. Spence, J. Wunsch, For most frequencies, strong trapping has a weak effect in frequencydomain scattering, Comm. Pure Appl. Math., volume 74, issue 10, pages 20252063 (2021) arxiv copy
 J. Galkowski, E.A. Spence, J. Wunsch,
Optimal constants in nontrapping resolvent estimates and applications in numerical analysis, Pure and Applied Analysis, volume 2, number 1, pages 157202 (2020) arxiv copy
 I.G. Graham, O.R. Pembery, E.A. Spence, The Helmholtz equation in heterogeneous media: a priori bounds, wellposedness, and resonances, J. Differ. Equations, vol. 266, issue 6, 28692923 (2019), arxiv copy
 S.N. ChandlerWilde,
E.A. Spence, A. Gibbs, V. P. Smyshlyaev, Highfrequency bounds for the Helmholtz equation under parabolic trapping and applications in numerical analysis, SIAM J. Math. Anal., volume 52, issue 1, pages 845893 (2020) arxiv copy
 A. Moiola, E.A. Spence, Acoustic transmission problems: wavenumberexplicit bounds and resonancefree regions, Math. Mod. Meth. App. S., vol. 29, no. 2, 317354 (2019) arxiv copy
 D. Baskin, E.A. Spence, J. Wunsch,
Sharp highfrequency estimates for the Helmholtz equation and applications to boundary integral equations, SIAM J. Math. Anal. vol. 48, no. 1, 229267 (2016)
local official copy,
arxiv copy
 E.A. Spence, Wavenumberexplicit bounds in timeharmonic acoustic scattering, SIAM J. Math. Anal., vol. 46, no. 4, 29873024 (2014) local official copy
Papers about the accuracy of absorbing boundary conditions/PML for the Helmholtz equation
Papers about the convergence of the finite element method applied to the Helmholtz equation
 J. Galkowski, D. Lafontaine, E.A. Spence, J. Wunsch, The hpFEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect
 E.A. Spence,
A simple proof that the hpFEM does not suffer from the pollution effect for the constantcoefficient fullspace Helmholtz equation
 J. Galkowski, D. Lafontaine, E.A. Spence, J. Wunsch,
Decompositions of highfrequency Helmholtz solutions via functional calculus, and application to the finite element method
 D. Lafontaine, E.A. Spence, J. Wunsch, Wavenumberexplicit convergence of the hpFEM for the fullspace heterogeneous Helmholtz equation with smooth coefficients
, Comput. Math. Appl., vol. 113, pages 5969 (2022) arxiv copy
 D. Lafontaine, E.A. Spence, J. Wunsch,
A sharp relativeerror bound for the Helmholtz hFEM at high frequency Numer. Math., vol. 150, pages 137178 (2022) arxiv copy
Papers about uncertainty quantification for the Helmholtz equation
 E.A. Spence, J. Wunsch,
Wavenumberexplicit parametric holomorphy of Helmholtz solutions in the context of uncertainty quantification
 I.G. Graham, O.R. Pembery, E.A. Spence,
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification Adv. Comp. Math., vol. 47, article number 68 (2021) arxiv copy
 O.R. Pembery, E.A. Spence,
The Helmholtz equation in random media: wellposedness and a priori bounds, SIAM/ASA J. Uncertainty Quantification,
volume 8, number 1, pages 58–87 (2020) arxiv copy
Papers about domaindecomposition and/or preconditioning the Helmholtz equation

[New] D. Lafontaine,
E.A. Spence, Sharp bounds on Helmholtz impedancetoimpedance maps and application to overlapping domain decomposition,
 S. Gong, I.G. Graham, E.A. Spence, Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems, Math. Comp., volume 92, pages 175215 (2023)
arxiv copy
 S. Gong,
M.J. Gander,
I.G. Graham,
D. Lafontaine,
E.A. Spence, Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation, Numer. Math., volume 152, pages 259306 (2022) arxiv copy
 S. Gong, I.G. Graham, E.A. Spence,
Domain decomposition preconditioners for highorder discretisations of the heterogeneous Helmholtz equation IMA J. Num. Anal, vol. 41, no. 3, pages 21392185 (2021)
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 highfrequency Helmholtz problems with absorption, Math. Comp., vol. 86, pages 20892127 (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 wavenumberindependent convergence is guaranteed?
Numer. Math., vol. 131, issue 3, pages 567614(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 boundary integral equations for the Helmholtz equation
 J. Galkowski, E.A. Spence,
Does the Helmholtz boundary element method suffer from the pollution effect?, SIAM Review, to appear
 R. Hiptmair, A. Moiola, E.A. Spence, Spurious quasiresonances in boundary integral equations for the Helmholtz transmission problem, SIAM J. Appl. Math.,
vol. 82, number 4, pages 14461469 (2022) arxiv copy
 J. Galkowski, P. Marchand, E.A. Spence,
Highfrequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem
, Integr. Equat. Oper. Th., volume 94, article number 36 (2022)
arxiv copy
 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? Adv. Comp. Math., vol. 48, article number 37 (2022) arxiv copy
 J. Galkowski, E.A. Spence, Wavenumberexplicit regularity estimates on the acoustic single and doublelayer operators Integr. Equat. Oper. Th., vol. 91, issue 1, article 6 (2019), arxiv copy
 J. Galkowski, E.H. Müller, E.A. Spence, Wavenumberexplicit analysis for the Helmholtz hBEM: error estimates and iteration counts for the Dirichlet problem Numer. Math., vol. 142, issue 2, pages 329357 (2019) arxiv copy
 E.A. Spence, I.V. Kamotski, V.P. Smyshlyaev, Coercivity of combined boundary integral equations in highfrequency scattering Comm. Pure Appl. Math., vol. 68, issue 9, pages 15871639 (2015), local unofficial copy
 I.G. Graham, M. Löhndorf, J.M. Melenk, E.A. Spence, When is the error in the hBEM for solving the Helmholtz equation bounded independently of k? BIT Num. Math., vol. 55, no. 1, 171214 (2015), local unofficial copy
 E.A. Spence, Bounding acoustic layer potentials via oscillatory integral techniques BIT Num. Math., vol. 55, no. 1., 279318 (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, 700731 (2014)
 S.N. ChandlerWilde, I.G. Graham, S. Langdon, E.A. Spence, Numericalasymptotic boundary integral methods in highfrequency acoustic scattering, Acta Numerica, vol. 21, 89305 (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, 15721601 (2011) local official copy
 E.A. Spence, S.N. ChandlerWilde, I.G. Graham, V. P. Smyshlyaev A new frequencyuniform coercive boundary integral equation for acoustic scattering, Comm. Pure Appl. Math. vol. 64, issue 10, 13841415, (2011) unofficial copy
Papers about coercive formulations of the Helmholtz equation
Review articles
 I.G. Graham, E.A. Spence, E. Vainikko, Recent Results on Domain Decomposition Preconditioning for the Highfrequency 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, 291324 (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, 22592281 (2010)
 E.A. Spence, A.S. Fokas,
A New Transform Method II: the Global Relation, and Boundary Value Problems in Polar Coordinates. Proc. Roy. Soc. A. vol 466, 22832307 (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): 11841205 (2010)
 A.S. Fokas, N. Flyer, S.A. Smitheman, E.A. Spence,
A semianalytical numerical method for solving evolution and elliptic partial differential equations,
J. Comp. Appl. Math. Volume 227, Issue 1, 5974 (2009) (Invited Paper)
 E.A. Spence, Boundary Value Problems for Linear Elliptic PDEs, PhD thesis, Cambridge, submitted 23/03/2009, viva 05/02/2010