Euan Spence: Complete List of Papers

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.)

Preprints:

• J. Galkowski, S. Gong, I.G. Graham, D. Lafontaine, E.A. Spence, Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems

• E.A. Spence, Y. Zou, J. Wunsch, Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed

• T. Chaumont-Frelet, E.A. Spence, The geometric error is less than the pollution error when solving the high-frequency Helmholtz equation with high-order FEM on curved domains

• M. Averseng J. Galkowski, E.A. Spence, Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies

• S. Downing, S. Gazzola, I.G. Graham, E.A. Spence, Optimisation of seismic imaging via bilevel learning

• J. Galkowski, E.A. Spence, Sharp preasymptotic error bounds for the Helmholtz h-FEM

• S.N. Chandler-Wilde, E.A. Spence, Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains

Journal Publications:

• J. Galkowski, D. Lafontaine, E.A. Spence, J. Wunsch, The hp-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect, Comm. Math. Sci., to appear

• D. Lafontaine, E.A. Spence, Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition, Pure and Applied Analysis, vol. 5, no. 4, pages 927-972, 2023, arxiv copy

• T. Chaumont-Frelet, A. Moiola, E.A. Spence, Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media. J. Math. Pure. Appl., vol. 179, pages 183-218, arxiv copy

• J. Galkowski, D. Lafontaine, E.A. Spence, Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves. IMA. J. Numer. Anal. (2023) arxiv copy

• J. Galkowski, D. Lafontaine, E.A. Spence, J. Wunsch, Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method , SIAM J. Math. Anal., vol. 55, no. 4, pages 3903-3958 (2023), arxiv copy

• E.A. Spence, A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation, Adv. Comp. Math., vol. 49, article number 27 (2023) arxiv copy

• J. Galkowski, D. Lafontaine, E.A. Spence, Perfectly-matched-layer truncation is exponentially accurate at high frequency, SIAM J. Math. Anal., vol. 55, number 4, pages 3344-3394 (2023) arxiv copy

• E.A. Spence, J. Wunsch, Wavenumber-explicit parametric holomorphy of Helmholtz solutions in the context of uncertainty quantification, SIAM/ASA J. Uncertainty Quantification, Vol. 11, number 2, pages 567-590 (2023) arxiv copy

• J. Galkowski, E.A. Spence, Does the Helmholtz boundary element method suffer from the pollution effect?, SIAM Review, vol. 65, no. 3, pages 806–828 (2023), arxiv copy

• T. Chaumont-Frelet, E.A. Spence, Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization, SIAM J. Math. Anal., Vol. 55, No. 2, pages 1319–1363 (2023) arxiv version

• 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 259-306 (2022) arxiv copy

• J. Galkowski, P. Marchand, E.A. Spence, High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem , Integr. Equat. Oper. Th., volume 94, article number 36 (2022) arxiv copy

• 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 175-215 (2023) arxiv copy

• R. Hiptmair, A. Moiola, E.A. Spence, Spurious quasi-resonances in boundary integral equations for the Helmholtz transmission problem, SIAM J. Appl. Math., vol. 82, number 4, pages 1446-1469 (2022) arxiv copy

• D. Lafontaine, E.A. Spence, J. Wunsch, Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients , Comput. Math. Appl., vol. 113, pages 59-69 (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

• S.N. Chandler-Wilde, E.A. Spence, Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains, Numer. Math., vol. 150, pages 299-371 (2022) arxiv copy, correction

• D. Lafontaine, E.A. Spence, J. Wunsch, A sharp relative-error bound for the Helmholtz h-FEM at high frequency Numer. Math., vol. 150, pages 137-178 (2022) arxiv copy

• 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 6724-6770 (2021) arxiv copy

• 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

• S. Gong, I.G. Graham, E.A. Spence, Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation IMA J. Num. Anal., vol. 41, no. 3, pages 2139-2185 (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

• D. Lafontaine, E.A. Spence, J. Wunsch, For most frequencies, strong trapping has a weak effect in frequency-domain scattering, Comm. Pure Appl. Math., volume 74, issue 10, pages 2025-2063 (2021) 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

• 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)

Chapters in Books:

• 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)

Refereed Conference Proceedings:

• 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)

Unrefereed Conference Proceedings:

• 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)

Other:

• 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)