# Items by Spence, Euan

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**18**.## Book Sections

Graham, I., Spence, E. and Vainikko, E., 2017. Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption.

*In*: Lahaye, D., Tang, J. and Vuik, K., eds.*Modern Solvers for Helmholtz Problems.*Basel, Germany: Birkhäuser Basel. (Geosystems Mathematics)Spence, E., 2015. Overview of Variational Formulations for Linear Elliptic PDEs.

*In*: Pelloni, B. and Fokas, A., eds.*Unified Transform for Boundary Value Problems: Applications and Advances.*SIAM, pp. 93-160.Spence, E., 2015. Transform Methods for Linear PDEs.

*In*: Engquist, B., ed.*Encyclopedia of Applied and Computational Mathematics.*Springer, pp. 1496-1500.## Articles

Baskin, D., Spence, E. A. and Wunsch, J., 2016. Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations.

*SIAM Journal on Mathematical Analysis (SIMA)*, 48 (1), pp. 229-267.Gander, M. J., Graham, I. G. and Spence, E. A., 2015. Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning:what is the largest shift for which wavenumber-independent convergence is guaranteed?

*Numerische Mathematik*, 131 (3), pp. 567-614.Spence, E. A., Kamotski, I. V. and Smyshlyaev, V. P., 2015. Coercivity of combined boundary integral equations in high-frequency scattering.

*Communications on Pure and Applied Mathematics*, 68 (9), pp. 1587-1639.Spence, E. A., 2015. Bounding acoustic layer potentials via oscillatory integral techniques.

*BIT Numerical Mathematics*, 55 (1), pp. 279-318.Graham, I. G., Löhndorf, M., Melenk, J. M. and Spence, E. A., 2015. When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k ?

*BIT Numerical Mathematics*, 55 (1), pp. 171-214.Betcke, T., Phillips, J. and Spence, E. A., 2014. Spectral decompositions and nonnormality of boundary integral operators in acoustic scattering.

*IMA Journal of Numerical Analysis*, 34 (2), pp. 700-731.Moiola, A. and Spence, E.A., 2014. Is the helmholtz equation really sign-indefinite?

*Siam Review*, 56 (2), pp. 274-312.Spence, E. A., 2014. Wavenumber-Explicit Bounds in Time-Harmonic Acoustic Scattering.

*SIAM Journal on Mathematical Analysis (SIMA)*, 46 (4), pp. 2987-3024.Graham, I., Spence, E., Chandler-Wilde, S. and Langdon, S., 2012. Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering.

*Acta Numerica*, 21, pp. 89-305.Fokas, A.S. and Spence, E.A., 2012. Synthesis, as Opposed to Separation, of Variables.

*Siam Review*, 54 (2), pp. 291-324.Spence, E. A., Chandler-Wilde, S. N., Graham, I. G. and Smyshlyaev, V. P., 2011. A new frequency-uniform coercive boundary integral equation for acoustic scattering.

*Communications on Pure and Applied Mathematics*, 64 (10), pp. 1384-1415.Betcke, T. and Spence, E. A., 2011. Numerical estimation of coercivity constants for boundary integral operators in acoustic scattering.

*SIAM Journal on Numerical Analysis (SINUM)*, 49 (4), pp. 1572-1601.Spence, E. A. and Fokas, A. S., 2010. A new transform method I: domain-dependent fundamental solutions and integral representations.

*Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*, 466 (2120), pp. 2259-2281.Spence, E. A. and Fokas, A. S., 2010. A new transform method II: the global relation and boundary-value problems in polar coordinates.

*Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*, 466 (2120), pp. 2283-2307.Smitheman, S. A., Spence, E. A. and Fokas, A. S., 2010. A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon.

*IMA Journal of Numerical Analysis*, 30 (4), pp. 1184-1205.