Lafontaine, David; Spence, Euan A. Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition. (English) Zbl 07787350 Pure Appl. Anal. 5, No. 4, 927-972 (2023). MSC: 35J05 65N55 PDFBibTeX XMLCite \textit{D. Lafontaine} and \textit{E. A. Spence}, Pure Appl. Anal. 5, No. 4, 927--972 (2023; Zbl 07787350) Full Text: DOI arXiv
Galkowski, J.; Lafontaine, D.; Spence, E. A.; Wunsch, J. Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method. (English) Zbl 1523.35135 SIAM J. Math. Anal. 55, No. 4, 3903-3958 (2023). Reviewer: Rodica Luca (Iaşi) MSC: 35J05 35J25 65N30 PDFBibTeX XMLCite \textit{J. Galkowski} et al., SIAM J. Math. Anal. 55, No. 4, 3903--3958 (2023; Zbl 1523.35135) Full Text: DOI arXiv
Galkowski, Jeffrey; Lafontaine, David; Spence, Euan Perfectly-matched-layer truncation is exponentially accurate at high frequency. (English) Zbl 1522.35164 SIAM J. Math. Anal. 55, No. 4, 3344-3394 (2023). MSC: 35J05 35P25 47A40 PDFBibTeX XMLCite \textit{J. Galkowski} et al., SIAM J. Math. Anal. 55, No. 4, 3344--3394 (2023; Zbl 1522.35164) Full Text: DOI arXiv
Galkowski, J.; Spence, E. A. Does the Helmholtz boundary element method suffer from the pollution effect? (English) Zbl 1522.65235 SIAM Rev. 65, No. 3, 806-828 (2023). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N38 65N30 65R20 35J05 33C10 78A40 78A45 78M15 35Q60 PDFBibTeX XMLCite \textit{J. Galkowski} and \textit{E. A. Spence}, SIAM Rev. 65, No. 3, 806--828 (2023; Zbl 1522.65235) Full Text: DOI arXiv
Spence, E. A.; Wunsch, J. Wavenumber-explicit parametric holomorphy of Helmholtz solutions in the context of uncertainty quantification. (English) Zbl 1519.35073 SIAM/ASA J. Uncertain. Quantif. 11, 567-590 (2023). MSC: 35J05 35R60 PDFBibTeX XMLCite \textit{E. A. Spence} and \textit{J. Wunsch}, SIAM/ASA J. Uncertain. Quantif. 11, 567--590 (2023; Zbl 1519.35073) Full Text: DOI arXiv
Chaumont-Frelet, T.; Spence, E. A. Scattering by finely layered obstacles: frequency-explicit bounds and homogenization. (English) Zbl 1514.35019 SIAM J. Math. Anal. 55, No. 2, 1319-1363 (2023). MSC: 35B27 35J05 35P25 78M40 PDFBibTeX XMLCite \textit{T. Chaumont-Frelet} and \textit{E. A. Spence}, SIAM J. Math. Anal. 55, No. 2, 1319--1363 (2023; Zbl 1514.35019) Full Text: DOI arXiv
Spence, E. A. A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation. (English) Zbl 1514.35120 Adv. Comput. Math. 49, No. 2, Paper No. 27, 25 p. (2023). MSC: 35J05 65N12 65N15 65N30 PDFBibTeX XMLCite \textit{E. A. Spence}, Adv. Comput. Math. 49, No. 2, Paper No. 27, 25 p. (2023; Zbl 1514.35120) Full Text: DOI arXiv
Gong, Shihua; Graham, Ivan G.; Spence, Euan A. Convergence of restricted additive Schwarz with impedance transmission conditions for discretised Helmholtz problems. (English) Zbl 1500.35105 Math. Comput. 92, No. 339, 175-215 (2023). MSC: 35J05 65N30 PDFBibTeX XMLCite \textit{S. Gong} et al., Math. Comput. 92, No. 339, 175--215 (2023; Zbl 1500.35105) Full Text: DOI arXiv
Galkowski, J.; Marchand, P.; Spence, E. A. High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem. (English) Zbl 1511.47095 Integral Equations Oper. Theory 94, No. 4, Paper No. 36, 68 p. (2022). MSC: 47N20 45P05 35P25 35J05 46E35 47G30 PDFBibTeX XMLCite \textit{J. Galkowski} et al., Integral Equations Oper. Theory 94, No. 4, Paper No. 36, 68 p. (2022; Zbl 1511.47095) Full Text: DOI arXiv
Gong, Shihua; Gander, Martin J.; Graham, Ivan G.; Lafontaine, David; Spence, Euan A. Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation. (English) Zbl 1497.65252 Numer. Math. 152, No. 2, 259-306 (2022). MSC: 65N55 65N22 65F08 65F10 65Y05 35J05 PDFBibTeX XMLCite \textit{S. Gong} et al., Numer. Math. 152, No. 2, 259--306 (2022; Zbl 1497.65252) Full Text: DOI arXiv
Hiptmair, Ralf; Moiola, Andrea; Spence, Euan A. Spurious quasi-resonances in boundary integral equations for the Helmholtz transmission problem. (English) Zbl 1497.35105 SIAM J. Appl. Math. 82, No. 4, 1446-1469 (2022). MSC: 35J05 35J25 45A05 78A45 PDFBibTeX XMLCite \textit{R. Hiptmair} et al., SIAM J. Appl. Math. 82, No. 4, 1446--1469 (2022; Zbl 1497.35105) Full Text: DOI arXiv
Marchand, P.; Galkowski, J.; Spence, E. A.; Spence, A. Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency? (English) Zbl 1492.65090 Adv. Comput. Math. 48, No. 4, Paper No. 37, 63 p. (2022). MSC: 65F10 65N22 35J05 65N38 PDFBibTeX XMLCite \textit{P. Marchand} et al., Adv. Comput. Math. 48, No. 4, Paper No. 37, 63 p. (2022; Zbl 1492.65090) Full Text: DOI arXiv
Lafontaine, D.; Spence, E. A.; Wunsch, J. A sharp relative-error bound for the Helmholtz \(h\)-FEM at high frequency. (English) Zbl 1481.35136 Numer. Math. 150, No. 1, 137-178 (2022). MSC: 35J05 65N15 65N30 78A45 PDFBibTeX XMLCite \textit{D. Lafontaine} et al., Numer. Math. 150, No. 1, 137--178 (2022; Zbl 1481.35136) Full Text: DOI arXiv
Gong, Shihua; Graham, Ivan G.; Spence, Euan A. Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation. (English) Zbl 1501.65151 IMA J. Numer. Anal. 41, No. 3, 2139-2185 (2021). MSC: 65N55 65N30 65F08 65F10 65N15 35J05 PDFBibTeX XMLCite \textit{S. Gong} et al., IMA J. Numer. Anal. 41, No. 3, 2139--2185 (2021; Zbl 1501.65151) Full Text: DOI arXiv
Galkowski, Jeffrey; Marchand, Pierre; Spence, Euan A. Eigenvalues of the truncated Helmholtz solution operator under strong trapping. (English) Zbl 1480.35111 SIAM J. Math. Anal. 53, No. 6, 6724-6770 (2021). MSC: 35J05 35P15 65N30 PDFBibTeX XMLCite \textit{J. Galkowski} et al., SIAM J. Math. Anal. 53, No. 6, 6724--6770 (2021; Zbl 1480.35111) Full Text: DOI arXiv
Lafontaine, David; Spence, Euan A.; Wunsch, Jared For most frequencies, strong trapping has a weak effect in frequency-domain scattering. (English) Zbl 1509.65116 Commun. Pure Appl. Math. 74, No. 10, 2025-2063 (2021). MSC: 65N30 65N38 35J05 35P25 35B05 47A40 PDFBibTeX XMLCite \textit{D. Lafontaine} et al., Commun. Pure Appl. Math. 74, No. 10, 2025--2063 (2021; Zbl 1509.65116) Full Text: DOI arXiv
Graham, I. G.; Pembery, O. R.; Spence, E. A. Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification. (English) Zbl 1473.35122 Adv. Comput. Math. 47, No. 5, Paper No. 68, 39 p. (2021). MSC: 35J05 35J25 65F08 65N22 65N30 PDFBibTeX XMLCite \textit{I. G. Graham} et al., Adv. Comput. Math. 47, No. 5, Paper No. 68, 39 p. (2021; Zbl 1473.35122) Full Text: DOI arXiv
Galkowski, Jeffrey; Lafontaine, David; Spence, Euan A. Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves. arXiv:2101.02154 Preprint, arXiv:2101.02154 [math.NA] (2021). MSC: 35J05 65N99 BibTeX Cite \textit{J. Galkowski} et al., ``Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves'', Preprint, arXiv:2101.02154 [math.NA] (2021) Full Text: arXiv OA License
Graham, Ivan G.; Spence, Euan A.; Zou, Jun Domain decomposition with local impedance conditions for the Helmholtz equation with absorption. (English) Zbl 1465.65162 SIAM J. Numer. Anal. 58, No. 5, 2515-2543 (2020). MSC: 65N55 65N30 65N22 65F08 65F10 35J05 PDFBibTeX XMLCite \textit{I. G. Graham} et al., SIAM J. Numer. Anal. 58, No. 5, 2515--2543 (2020; Zbl 1465.65162) Full Text: DOI arXiv
Pembery, O. R.; Spence, E. A. The Helmholtz equation in random media: well-posedness and a priori bounds. (English) Zbl 1436.35085 SIAM/ASA J. Uncertain. Quantif. 8, 58-87 (2020). MSC: 35J05 35R60 60H15 PDFBibTeX XMLCite \textit{O. R. Pembery} and \textit{E. A. Spence}, SIAM/ASA J. Uncertain. Quantif. 8, 58--87 (2020; Zbl 1436.35085) Full Text: DOI arXiv
Chandler-Wilde, S. N.; Spence, E. A.; Gibbs, A.; Smyshlyaev, V. P. High-frequency bounds for the Helmholtz equation under parabolic trapping and applications in numerical analysis. (English) Zbl 1431.35020 SIAM J. Math. Anal. 52, No. 1, 845-893 (2020). MSC: 35J05 35J25 35P25 65N30 65N38 78A45 PDFBibTeX XMLCite \textit{S. N. Chandler-Wilde} et al., SIAM J. Math. Anal. 52, No. 1, 845--893 (2020; Zbl 1431.35020) Full Text: DOI arXiv
Galkowski, Jeffrey; Spence, Euan A.; Wunsch, Jared Optimal constants in nontrapping resolvent estimates and applications in numerical analysis. (English) Zbl 1439.35142 Pure Appl. Anal. 2, No. 1, 157-202 (2020). MSC: 35J05 47A10 65N30 PDFBibTeX XMLCite \textit{J. Galkowski} et al., Pure Appl. Anal. 2, No. 1, 157--202 (2020; Zbl 1439.35142) Full Text: DOI arXiv
Galkowski, Jeffrey; Spence, Euan A. Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators. (English) Zbl 1417.31008 Integral Equations Oper. Theory 91, No. 1, Paper No. 6, 35 p. (2019). MSC: 31B10 31B25 35J05 35J25 PDFBibTeX XMLCite \textit{J. Galkowski} and \textit{E. A. Spence}, Integral Equations Oper. Theory 91, No. 1, Paper No. 6, 35 p. (2019; Zbl 1417.31008) Full Text: DOI arXiv
Galkowski, Jeffrey; Müller, Eike H.; Spence, Euan A. Wavenumber-explicit analysis for the Helmholtz \(h\)-BEM: error estimates and iteration counts for the Dirichlet problem. (English) Zbl 1414.35054 Numer. Math. 142, No. 2, 329-357 (2019). MSC: 35J05 35J25 65N22 65N38 65R20 PDFBibTeX XMLCite \textit{J. Galkowski} et al., Numer. Math. 142, No. 2, 329--357 (2019; Zbl 1414.35054) Full Text: DOI arXiv
Moiola, Andrea; Spence, Euan A. Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions. (English) Zbl 1414.35057 Math. Models Methods Appl. Sci. 29, No. 2, 317-354 (2019). MSC: 35J05 PDFBibTeX XMLCite \textit{A. Moiola} and \textit{E. A. Spence}, Math. Models Methods Appl. Sci. 29, No. 2, 317--354 (2019; Zbl 1414.35057) Full Text: DOI arXiv
Diwan, Ganesh C.; Moiola, Andrea; Spence, Euan A. Can coercive formulations lead to fast and accurate solution of the Helmholtz equation? (English) Zbl 1410.65445 J. Comput. Appl. Math. 352, 110-131 (2019). MSC: 65N30 35J05 65F10 PDFBibTeX XMLCite \textit{G. C. Diwan} et al., J. Comput. Appl. Math. 352, 110--131 (2019; Zbl 1410.65445) Full Text: DOI arXiv
Graham, I. G.; Pembery, O. R.; Spence, E. A. The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances. (English) Zbl 1421.35056 J. Differ. Equations 266, No. 6, 2869-2923 (2019). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35J05 35J25 PDFBibTeX XMLCite \textit{I. G. Graham} et al., J. Differ. Equations 266, No. 6, 2869--2923 (2019; Zbl 1421.35056) Full Text: DOI arXiv
Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri A two-level domain-decomposition preconditioner for the time-harmonic Maxwell’s equations. (English) Zbl 1443.65417 Bjørstad, Petter E. (ed.) et al., Domain decomposition methods in science and engineering XXIV. Proceedings of the 24th international conference, Svalbard, Norway, February 6–10, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 125, 149-157 (2018). MSC: 65N55 65N30 65F08 65F10 78A25 35J05 35Q61 PDFBibTeX XMLCite \textit{M. Bonazzoli} et al., Lect. Notes Comput. Sci. Eng. 125, 149--157 (2018; Zbl 1443.65417) Full Text: DOI arXiv
Bonazzoli, Marcella; Dolean, Victorita; Graham, Ivan G.; Spence, Euan A.; Tournier, Pierre-Henri Two-level preconditioners for the Helmholtz equation. (English) Zbl 1443.65416 Bjørstad, Petter E. (ed.) et al., Domain decomposition methods in science and engineering XXIV. Proceedings of the 24th international conference, Svalbard, Norway, February 6–10, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 125, 139-147 (2018). MSC: 65N55 65N30 65F08 65F10 65F15 65Y05 35J05 PDFBibTeX XMLCite \textit{M. Bonazzoli} et al., Lect. Notes Comput. Sci. Eng. 125, 139--147 (2018; Zbl 1443.65416) Full Text: DOI arXiv
Graham, Ivan G.; Spence, Euan A.; Vainikko, Eero Recent results on domain decomposition preconditioning for the high-frequency Helmholtz equation using absorption. (English) Zbl 1366.65113 Lahaye, Domenico (ed.) et al., Modern solvers for Helmholtz problems. Basel: Birkhäuser/Springer (ISBN 978-3-319-28831-4/hbk; 978-3-319-28832-1/ebook). Geosystems Mathematics, 3-26 (2017). MSC: 65N55 35J05 65F08 65N30 PDFBibTeX XMLCite \textit{I. G. Graham} et al., in: Modern solvers for Helmholtz problems. Basel: Birkhäuser/Springer. 3--26 (2017; Zbl 1366.65113) Full Text: DOI arXiv
Graham, I. G.; Spence, E. A.; Vainikko, E. Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption. (English) Zbl 1368.65250 Math. Comput. 86, No. 307, 2089-2127 (2017). Reviewer: Marius Ghergu (Dublin) MSC: 65N55 65F08 35J05 65F10 65N30 PDFBibTeX XMLCite \textit{I. G. Graham} et al., Math. Comput. 86, No. 307, 2089--2127 (2017; Zbl 1368.65250) Full Text: DOI arXiv
Baskin, Dean; Spence, Euan A.; Wunsch, Jared Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations. (English) Zbl 1341.35013 SIAM J. Math. Anal. 48, No. 1, 229-267 (2016). Reviewer: Vladimir Mityushev (Kraków) MSC: 35J05 35J25 65N38 78A45 PDFBibTeX XMLCite \textit{D. Baskin} et al., SIAM J. Math. Anal. 48, No. 1, 229--267 (2016; Zbl 1341.35013) Full Text: DOI arXiv
Spence, E. A. Overview of variational formulations for linear elliptic PDEs. (English) Zbl 1346.65060 Fokas, Athanassios S. (ed.) et al., Unified transform for boundary value problems. Applications and advances. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-381-5/pbk; 978-1-61197-382-2/ebook). Other Titles in Applied Mathematics 141, 93-159 (2015). MSC: 65N30 35J25 PDFBibTeX XMLCite \textit{E. A. Spence}, Other Titles Appl. Math. 141, 93--159 (2015; Zbl 1346.65060)
Spence, Euan A.; Kamotski, Ilia V.; Smyshlyaev, Valery P. Coercivity of combined boundary integral equations in high-frequency scattering. (English) Zbl 1342.35202 Commun. Pure Appl. Math. 68, No. 9, 1587-1639 (2015). Reviewer: Hideo Nakazawa (Tokyo) MSC: 35P25 65N38 35J05 PDFBibTeX XMLCite \textit{E. A. Spence} et al., Commun. Pure Appl. Math. 68, No. 9, 1587--1639 (2015; Zbl 1342.35202) Full Text: DOI
Gander, M. J.; Graham, I. G.; Spence, E. A. Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: What is the largest shift for which wavenumber-independent convergence is guaranteed? (English) Zbl 1328.65238 Numer. Math. 131, No. 3, 567-614 (2015). Reviewer: Adhemar Bultheel (Leuven) MSC: 65N30 65F08 65F10 78A45 35J05 65N12 PDFBibTeX XMLCite \textit{M. J. Gander} et al., Numer. Math. 131, No. 3, 567--614 (2015; Zbl 1328.65238) Full Text: DOI
Spence, E. A. Bounding acoustic layer potentials via oscillatory integral techniques. (English) Zbl 1316.35099 BIT 55, No. 1, 279-318 (2015). Reviewer: Vladimir Mityushev (Kraków) MSC: 35J05 45M05 31B10 65N38 PDFBibTeX XMLCite \textit{E. A. Spence}, BIT 55, No. 1, 279--318 (2015; Zbl 1316.35099) Full Text: DOI Link
Graham, I. G.; Löhndorf, M.; Melenk, J. M.; Spence, E. A. When is the error in the \(h\)-BEM for solving the Helmholtz equation bounded independently of \(k\)? (English) Zbl 1320.65187 BIT 55, No. 1, 171-214 (2015). Reviewer: Jan Lovíšek (Bratislava) MSC: 65N38 35J05 PDFBibTeX XMLCite \textit{I. G. Graham} et al., BIT 55, No. 1, 171--214 (2015; Zbl 1320.65187) Full Text: DOI
Spence, E. A. Wavenumber-explicit bounds in time-harmonic acoustic scattering. (English) Zbl 1302.35139 SIAM J. Math. Anal. 46, No. 4, 2987-3024 (2014). MSC: 35J05 35J25 65N30 65N38 78A45 PDFBibTeX XMLCite \textit{E. A. Spence}, SIAM J. Math. Anal. 46, No. 4, 2987--3024 (2014; Zbl 1302.35139) Full Text: DOI Link
Moiola, Andrea; Spence, Euan A. Is the Helmholtz equation really sign-indefinite? (English) Zbl 1305.35021 SIAM Rev. 56, No. 2, 274-312 (2014). MSC: 35J05 35J20 65N30 PDFBibTeX XMLCite \textit{A. Moiola} and \textit{E. A. Spence}, SIAM Rev. 56, No. 2, 274--312 (2014; Zbl 1305.35021) Full Text: DOI Link
Betcke, T.; Phillips, J.; Spence, E. A. Spectral decompositions and nonnormality of boundary integral operators in acoustic scattering. (English) Zbl 1296.65173 IMA J. Numer. Anal. 34, No. 2, 700-731 (2014). Reviewer: Gunther Schmidt (Berlin) MSC: 65N38 45P05 47G10 35J05 76Q05 76M15 PDFBibTeX XMLCite \textit{T. Betcke} et al., IMA J. Numer. Anal. 34, No. 2, 700--731 (2014; Zbl 1296.65173) Full Text: DOI Link
Chandler-Wilde, Simon N.; Graham, Ivan G.; Langdon, Stephen; Spence, Euan A. Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. (English) Zbl 1257.65070 Acta Numerica 21, 89-305 (2012). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N38 35J05 65N12 PDFBibTeX XMLCite \textit{S. N. Chandler-Wilde} et al., Acta Numerica 21, 89--305 (2012; Zbl 1257.65070) Full Text: DOI
Spence, Euan A.; Chandler-Wilde, Simon N.; Graham, Ivan G.; Smyshlyaev, Valery P. A new frequency-uniform coercive boundary integral equation for acoustic scattering. (English) Zbl 1228.35183 Commun. Pure Appl. Math. 64, No. 10, 1384-1415 (2011). MSC: 35Q35 76Q05 35J05 65N30 45N05 PDFBibTeX XMLCite \textit{E. A. Spence} et al., Commun. Pure Appl. Math. 64, No. 10, 1384--1415 (2011; Zbl 1228.35183) Full Text: DOI
Smitheman, S. A.; Spence, E. A.; Fokas, A. S. A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon. (English) Zbl 1202.65161 IMA J. Numer. Anal. 30, No. 4, 1184-1205 (2010). MSC: 65N35 PDFBibTeX XMLCite \textit{S. A. Smitheman} et al., IMA J. Numer. Anal. 30, No. 4, 1184--1205 (2010; Zbl 1202.65161) Full Text: DOI
Spence, E. A.; Fokas, A. S. A new transform method. II: The global relation and boundary-value problems in polar coordinates. (English) Zbl 1200.35072 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 466, No. 2120, 2283-2307 (2010). Reviewer: Yakov Yakubov (Tel-Aviv) MSC: 35J15 35J05 35A08 35C15 30E25 PDFBibTeX XMLCite \textit{E. A. Spence} and \textit{A. S. Fokas}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 466, No. 2120, 2283--2307 (2010; Zbl 1200.35072) Full Text: DOI Link
Spence, E. A.; Fokas, A. S. A new transform method. I: Domain-dependent fundamental solutions and integral representations. (English) Zbl 1200.35071 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 466, No. 2120, 2259-2281 (2010). Reviewer: Yakov Yakubov (Tel-Aviv) MSC: 35J15 35J05 35J08 30E25 PDFBibTeX XMLCite \textit{E. A. Spence} and \textit{A. S. Fokas}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 466, No. 2120, 2259--2281 (2010; Zbl 1200.35071) Full Text: DOI Link
Fokas, Athanasios S.; Spence, Euan A. Novel analytical and numerical methods for elliptic boundary value problems. (English) Zbl 1180.37104 Engquist, Bjorn (ed.) et al., Highly oscillatory problems. Cambridge: Cambridge University Press (ISBN 978-0-521-13443-9/pbk). London Mathematical Society Lecture Note Series 366, 194-239 (2009). MSC: 37K15 35J05 35Q53 35A22 PDFBibTeX XMLCite \textit{A. S. Fokas} and \textit{E. A. Spence}, Lond. Math. Soc. Lect. Note Ser. 366, 194--239 (2009; Zbl 1180.37104)
Spence, Euan A. A new method for boundary value problems and its numerical implementation. (English) Zbl 1179.65153 Charalambopoulos, A. (ed.) et al., Advanced topics in scattering and biomedical engineering. Proceedings of the 8th international workshop on mathematical methods in scattering theory and biomedical engineering, Lefkada, Greece, September 27–29, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-281-484-5/hbk). 188-196 (2008). MSC: 65N38 35A22 35J05 65R20 PDFBibTeX XMLCite \textit{E. A. Spence}, in: Advanced topics in scattering and biomedical engineering. Proceedings of the 8th international workshop on mathematical methods in scattering theory and biomedical engineering, Lefkada, Greece, September 27--29, 2007. Hackensack, NJ: World Scientific. 188--196 (2008; Zbl 1179.65153)