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.

- M. Bonazzoli, V. Dolean, I.G. Graham, E.A. Spence, P.-H. Tournier,
*Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell's equations with absorption.*Math. Comp. (2019) arxiv copy

**[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

**[New]**J. Galkowski, D. Lafontaine, E.A. Spence,*Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves*

**[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*

- I.G. Graham, O.R. Pembery, E.A. Spence,
*Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification* - O.R. Pembery, E.A. Spence,
*The Helmholtz equation in random media: well-posedness and a priori bounds*, SIAM/ASA J. Uncertainty Quantification, volume 8, number 1, pages 58–87 (2020) arxiv copy

- 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?*)

- G. Diwan, A. Moiola, E.A. Spence,
*Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?*J. Comp. Appl. Math. vol. 352, 110-131 (2019) arxiv copy - A.
Moiola, E.A. Spence,
*Is the Helmholtz equation really sign-indefinite?*SIAM Review, vol. 56, no. 2, 274-312 (2014) local official copy

**[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

- 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)

- A. Fernandez, E.A. Spence, A.S. Fokas,
*Uniform asymptotics as a stationary point approaches an endpoint*, IMA J. Appl. Math. vol. 83, issue 1, 202-242 (2018) arxiv copy

- 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