The copyright of each article is owned by the respective journal. When an official or unofficial copy is posted, this is in line with that journal's copyright policy.

(List of papers by subject area here.)

- S. Gong, I.G. Graham, E.A. Spence,
*Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation* - D. Lafontaine, E.A. Spence, J. Wunsch,
*A sharp relative-error bound for the Helmholtz h-FEM at high frequency*

- I.G. Graham, E.A. Spence, J. Zou,
*Domain Decomposition with local impedance condition for the Helmholtz equation*, SIAM J. Num. Anal., to appear - D. Lafontaine, E.A. Spence, J. Wunsch,
*For most frequencies, strong trapping has a weak effect in frequency-domain scattering*, Comm. Pure Appl. Math., to appear - 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 - 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 - 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 - 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 - 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 - 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 - 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,
*Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions.*Math. Mod. Meth. App. S., vol. 29, no. 2, 317-354 (2019), 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 - 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 - 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 - 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 - 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?*) - 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 - 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 - A.
Moiola, E.A. Spence,
*Is the Helmholtz equation really sign-indefinite?*SIAM Review, vol. 56, no. 2, 274-312 (2014) local official 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 - 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 - 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 - 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)

- 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) - E.A. Spence,
*Transform methods for linear PDEs*, in Encyclopedia of Applied and Computational Mathematics, Springer (2016) - A.S. Fokas, E.A. Spence,
*Novel analytical and numerical methods for elliptic boundary value problems*, in Highly Oscillatory Problems, London Mathematical Society Lecture Note Series (No. 366), CUP (2009)

- M. Bonazzoli, V. Dolean, I.G. Graham, E.A. Spence, P.-H. Tournier,
*A two-level domain-decomposition preconditioner for the time-harmonic Maxwell's equations*, Proceedings of the 24th International Conference on Domain Decomposition Methods (DD24) - M. Bonazzoli, V. Dolean, I.G. Graham, E.A. Spence, P.-H. Tournier,
*Two-level preconditioners for the Helmholtz equation*, Proceedings of the 24th International Conference on Domain Decomposition Methods (DD24) - M. Bonazzoli, V. Dolean, I.G. Graham, E.A. Spence, P.-H. Tournier,
E. Vainikko,
*Domain-decomposition preconditioning for high-frequency Helmholtz and Maxwell problems with absorption*, Proceedings of the 13th International Conference on Mathematical and Numerical Aspects of Waves (2017), - D. Baskin, E.A. Spence, J. Wunsch,
*Sharp high-frequency estimates for the Helmholtz equation*Proceedings of the 12th International Conference on Mathematical and Numerical Aspects of Waves (2015), - A.
Moiola, E.A. Spence,
*Is the Helmholtz equation really sign-indefinite?*, Proceedings of the 11th International Conference on Mathematical and Numerical Aspects of Waves (2013), - V.P. Smyshlyaev,
E.A. Spence,
*Coercivity of boundary integral equations in high-frequency scattering*, Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves (2011)

- E.A. Spence,
*Is the Helmholtz equation really sign-indefinite?*, in Mathematisches Forschungsinstitut Oberwolfach Report No. 55/2012, (2012), doi:10.4171/owr/2012/15 - E.A. Spence,
*Coercivity of boundary integral equations in high frequency scattering*, in Mathematisches Forschungsinstitut Oberwolfach Report No. 10/2010, (2010), doi:10.4171/owr/2010/10 - E.A. Spence,
*A new method for boundary value problems and its numerical implementation*, Proceedings of the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, World Scientific (2007)

- E.A. Spence,
*Boundary Value Problems for Linear Elliptic PDEs*, PhD thesis, Cambridge, submitted 23/03/2009, viva 05/02/2010 - E.A. Spence,
*The Watson transformation revisited*, unpublished report, (2014)