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Volumn 68, Issue 9, 2015, Pages 1587-1639

Coercivity of combined boundary integral equations high-frequency scattering

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EID: 84937053211     PISSN: 00103640     EISSN: 10970312     Source Type: Journal    
DOI: 10.1002/cpa.21543     Document Type: Article
Times cited : (39)

References (62)
  • 1
    • 0001254041 scopus 로고    scopus 로고
    • Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?
    • SIAM Rev. 42 (2000), no. 3, 451-484 (electronic).
    • Babuška, I. M.; Sauter, S. A. Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? Reprint of SIAM J. Numer. Anal. 34 (1997), no. 6, 2392-2423. SIAM Rev. 42 (2000), no. 3, 451-484 (electronic). doi: 10.1137/S0036142994269186
    • (1997) Reprint of SIAM J. Numer. Anal. , vol.34 , Issue.6 , pp. 2392-2423
    • Babuška, I.M.1    Sauter, S.A.2
  • 3
    • 78649846595 scopus 로고    scopus 로고
    • Condition number estimates for combined potential boundary integral operators in acoustics and their boundary element discretisation
    • Betcke, T.; Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Lindner, M. Condition number estimates for combined potential boundary integral operators in acoustics and their boundary element discretisation. Numerical Methods for Partial Differential Equations 27 (2011), no. 1, 31-69.
    • (2011) Numerical Methods for Partial Differential Equations , vol.27 , Issue.1 , pp. 31-69
    • Betcke, T.1    Chandler-Wilde, S.N.2    Graham, I.G.3    Langdon, S.4    Lindner, M.5
  • 4
    • 84898894475 scopus 로고    scopus 로고
    • Spectral decompositions and non-normality of boundary integral operators in acoustic scattering
    • Betcke, T.; Phillips, J.; Spence, E. A. Spectral decompositions and non-normality of boundary integral operators in acoustic scattering. IMA J. Numer. Anal. 34 (2014), no. 2, 700-731. doi: 10.1093/imanum/drt002
    • (2014) IMA J. Numer. Anal. , vol.34 , Issue.2 , pp. 700-731
    • Betcke, T.1    Phillips, J.2    Spence, E.A.3
  • 5
    • 80052713130 scopus 로고    scopus 로고
    • Numerical estimation of coercivity constants for boundary integral operators in acoustic scattering
    • Betcke, T.; Spence, E. A. Numerical estimation of coercivity constants for boundary integral operators in acoustic scattering. SIAM J. Numer. Anal. 49 (2011), no. 4, 1572-1601. doi: 10.1137/100788483
    • (2011) SIAM J. Numer. Anal. , vol.49 , Issue.4 , pp. 1572-1601
    • Betcke, T.1    Spence, E.A.2
  • 6
    • 84885151288 scopus 로고    scopus 로고
    • Wave-number estimates for regularized combined field boundary integral operators in acoustic scattering problems with Neumann boundary conditions
    • Boubendir, Y.; Turc, C. Wave-number estimates for regularized combined field boundary integral operators in acoustic scattering problems with Neumann boundary conditions. IMA J. Numer. Anal. 33 (2013), no. 4, 1176-1225. doi: 10.1093/imanum/drs038
    • (2013) IMA J. Numer. Anal. , vol.33 , Issue.4 , pp. 1176-1225
    • Boubendir, Y.1    Turc, C.2
  • 7
    • 84865409769 scopus 로고    scopus 로고
    • Regularized integral equations and fast high-order solvers for sound-hard acoustic scattering problems
    • Bruno, O.; Elling, T.; Turc, C. Regularized integral equations and fast high-order solvers for sound-hard acoustic scattering problems. Internat. J. Numer. Methods Engrg. 91 (2012), no. 10, 1045-1072. doi: 10.1002/nme.4302
    • (2012) Internat. J. Numer. Methods Engrg. , vol.91 , Issue.10 , pp. 1045-1072
    • Bruno, O.1    Elling, T.2    Turc, C.3
  • 8
    • 84967713031 scopus 로고
    • The free boundary for elastic-plastic torsion problems
    • Caffarelli, L. A.; Friedman, A. The free boundary for elastic-plastic torsion problems. Trans. Amer. Math. Soc. 252 (1979), 65-97. doi: 10.2307/1998078
    • (1979) Trans. Amer. Math. Soc. , vol.252 , pp. 65-97
    • Caffarelli, L.A.1    Friedman, A.2
  • 9
    • 75449087930 scopus 로고    scopus 로고
    • Condition number estimates for combined potential boundary integral operators in acoustic scattering
    • Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Lindner, M. Condition number estimates for combined potential boundary integral operators in acoustic scattering. J. Integral Equations Appl. 21 (2009), no. 2, 229-279. doi: 10.1216/JIE-2009-21-2-229
    • (2009) J. Integral Equations Appl. , vol.21 , Issue.2 , pp. 229-279
    • Chandler-Wilde, S.N.1    Graham, I.G.2    Langdon, S.3    Lindner, M.4
  • 10
    • 84861481644 scopus 로고    scopus 로고
    • Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering
    • Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Spence, E. A. Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. Acta Numer. 21 (2012), 89-305.
    • (2012) Acta Numer. , vol.21 , pp. 89-305
    • Chandler-Wilde, S.N.1    Graham, I.G.2    Langdon, S.3    Spence, E.A.4
  • 11
    • 52649128278 scopus 로고    scopus 로고
    • Wave-number-explicit bounds in time-harmonic scattering
    • Chandler-Wilde, S. N.; Monk, P. Wave-number-explicit bounds in time-harmonic scattering. SIAM J. Math. Anal. 39 (2008), no. 5, 1428-1455. doi: 10.1137/060662575
    • (2008) SIAM J. Math. Anal. , vol.39 , Issue.5 , pp. 1428-1455
    • Chandler-Wilde, S.N.1    Monk, P.2
  • 12
    • 84872081480 scopus 로고    scopus 로고
    • Coercive modifications of the double-layer potential operator on Lipschitz domains.
    • In preparation.
    • Chandler-Wilde, S. N.; Spence, E. A. Coercive modifications of the double-layer potential operator on Lipschitz domains. In preparation.
    • Chandler-Wilde, S.N.1    Spence, E.A.2
  • 13
    • 3943094700 scopus 로고    scopus 로고
    • Stability and finiteness properties of medial axis and skeleton
    • Chazal, F..; Soufflet, R. Stability and finiteness properties of medial axis and skeleton. J. Dynam. Control Systems 10 (2004), no. 2, 149-170. doi: 10.1023/B:JODS.0000024119.38784.ff
    • (2004) J. Dynam. Control Systems , vol.10 , Issue.2 , pp. 149-170
    • Chazal, F.1    Soufflet, R.2
  • 14
    • 0002754556 scopus 로고    scopus 로고
    • Mathematical theory of medial axis transform
    • Choi, H. I.; Choi, S. W.; Moon, H. P. Mathematical theory of medial axis transform. Pacific J. Math. 181 (1997), no. 1, 57-88. doi: 10.2140/pjm.1997.181.57
    • (1997) Pacific J. Math. , vol.181 , Issue.1 , pp. 57-88
    • Choi, H.I.1    Choi, S.W.2    Moon, H.P.3
  • 16
    • 0000438610 scopus 로고
    • Boundary integral operators on Lipschitz domains: elementary results
    • Costabel, M. Boundary integral operators on Lipschitz domains: elementary results. SIAM J. Math. Anal. 19 (1988), no. 3, 613-626. doi: 10.1137/0519043
    • (1988) SIAM J. Math. Anal. , vol.19 , Issue.3 , pp. 613-626
    • Costabel, M.1
  • 17
    • 34248167698 scopus 로고    scopus 로고
    • Some historical remarks on the positivity of boundary integral operators
    • Lecture Notes in Applied and Computational Mechanics, 29. Springer, Berlin
    • Costabel, M. Some historical remarks on the positivity of boundary integral operators. Boundary element analysis, 1-27. Lecture Notes in Applied and Computational Mechanics, 29. Springer, Berlin, 2007. doi: 10.1007/978-3-540-47533-0_1
    • (2007) Boundary element analysis , pp. 1-27
    • Costabel, M.1
  • 18
    • 32644451827 scopus 로고    scopus 로고
    • Sharp regularity coefficient estimates for complex-valued acoustic and elastic Helmholtz equations
    • Cummings, P.; Feng, X. Sharp regularity coefficient estimates for complex-valued acoustic and elastic Helmholtz equations. Math. Models Methods Appl. Sci. 16 (2006), no. 1, 139-160. doi: 10.1142/S021820250600108X
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.1 , pp. 139-160
    • Cummings, P.1    Feng, X.2
  • 19
    • 34248169761 scopus 로고    scopus 로고
    • A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering
    • Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P. A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Numer. Math. 106 (2007), no. 3, 471-510. doi: 10.1007/s00211-007-0071-4
    • (2007) Numer. Math. , vol.106 , Issue.3 , pp. 471-510
    • Domínguez, V.1    Graham, I.G.2    Smyshlyaev, V.P.3
  • 20
    • 0000011239 scopus 로고
    • Variational iterative methods for nonsymmetric systems of linear equations
    • Eisenstat, S. C.; Elman, H. C.; Schultz, M. H. Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20 (1983), no. 2, 345-357. doi: 10.1137/0720023
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.2 , pp. 345-357
    • Eisenstat, S.C.1    Elman, H.C.2    Schultz, M.H.3
  • 22
    • 84975041576 scopus 로고    scopus 로고
    • On stability of discretizations of the Helmholtz equation
    • Lecture Notes in Computational Science and Engineering, 83. Springer, Heidelberg
    • Esterhazy, S.; Melenk, J. M. On stability of discretizations of the Helmholtz equation. Numerical analysis of multiscale problems, 285-324. Lecture Notes in Computational Science and Engineering, 83. Springer, Heidelberg, 2012. doi: 10.1007/978-3-642-22061-6_9
    • (2012) Numerical analysis of multiscale problems , pp. 285-324
    • Esterhazy, S.1    Melenk, J.M.2
  • 23
    • 0003228130 scopus 로고    scopus 로고
    • Partial differential equations
    • American Mathematical Society, Providence, R.I.
    • Evans, L. C. Partial differential equations. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, R.I., 1998.
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 24
    • 84959822569 scopus 로고
    • Sobolev embeddings for generalized ridged domains
    • Evans, W. D.; Harris, D. J. Sobolev embeddings for generalized ridged domains. Proc. London Math. Soc. (3) 54 (1987), no. 1, 141-175. doi: 10.1112/plms/s3-54.1.141
    • (1987) Proc. London Math. Soc. (3) , vol.54 , Issue.1 , pp. 141-175
    • Evans, W.D.1    Harris, D.J.2
  • 25
    • 84968513647 scopus 로고
    • Regularity of the distance function
    • Foote, R. L. Regularity of the distance function. Proc. Amer. Math. Soc. 92 (1984), no. 1, 153-155. doi: 10.2307/2045171
    • (1984) Proc. Amer. Math. Soc. , vol.92 , Issue.1 , pp. 153-155
    • Foote, R.L.1
  • 26
    • 77958474587 scopus 로고    scopus 로고
    • A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions
    • Ganesh, M.; Hawkins, S. C. A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions. J. Comput. Phys. 230 (2011), no. 1, 104-125. doi: 10.1016/j.jcp.2010.09.014
    • (2011) J. Comput. Phys. , vol.230 , Issue.1 , pp. 104-125
    • Ganesh, M.1    Hawkins, S.C.2
  • 28
    • 84937047934 scopus 로고    scopus 로고
    • When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k?
    • to appear.
    • 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? BIT. Numerical Mathematics, to appear.
    • BIT. Numerical Mathematics
    • Graham, I.G.1    Löhndorf, M.2    Melenk, J.M.3    Spence, E.A.4
  • 29
    • 35349016240 scopus 로고    scopus 로고
    • Stability estimates for a class of Helmholtz problems
    • Hetmaniuk, U. Stability estimates for a class of Helmholtz problems. Commun. Math. Sci. 5 (2007), no. 3, 665-678.
    • (2007) Commun. Math. Sci. , vol.5 , Issue.3 , pp. 665-678
    • Hetmaniuk, U.1
  • 30
    • 82155186224 scopus 로고    scopus 로고
    • Stability results for the time-harmonic Maxwell equations with impedance boundary conditions
    • Hiptmair, R.; Moiola, A.; Perugia, I. Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Math. Models Methods Appl. Sci. 21 (2011), no. 11, 2263-2287. doi: 10.1142/S021820251100574X
    • (2011) Math. Models Methods Appl. Sci. , vol.21 , Issue.11 , pp. 2263-2287
    • Hiptmair, R.1    Moiola, A.2    Perugia, I.3
  • 31
    • 33747535085 scopus 로고
    • A finite element method for some integral equations of the first kind
    • Hsiao, G. C.; Wendland, W. L. A finite element method for some integral equations of the first kind. J. Math. Anal. Appl. 58 (1977), no. 3, 449-481. doi: 10.1016/0022-247X(77)90186-X
    • (1977) J. Math. Anal. Appl. , vol.58 , Issue.3 , pp. 449-481
    • Hsiao, G.C.1    Wendland, W.L.2
  • 34
    • 0000537762 scopus 로고
    • Équations intégrales pour le probléme du potentiel électrique dans le plan
    • Le Roux, M. N. Équations intégrales pour le probléme du potentiel électrique dans le plan. C. R. Acad. Sci. Paris Sér. A 278 (1974), 541-544.
    • (1974) C. R. Acad. Sci. Paris Sér. A , vol.278 , pp. 541-544
    • Le Roux, M.N.1
  • 35
    • 10244245453 scopus 로고    scopus 로고
    • The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations
    • Li, Y. Y.; Nirenberg, L. The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations. Comm. Pure Appl. Math. 58 (2005), no. 1, 85-146. doi: 10.1002/cpa.20051
    • (2005) Comm. Pure Appl. Math. , vol.58 , Issue.1 , pp. 85-146
    • Li, Y.Y.1    Nirenberg, L.2
  • 36
    • 2942755983 scopus 로고    scopus 로고
    • n has the same homotopy type as its medial axis
    • n has the same homotopy type as its medial axis. Computer-Aided Design 36 (2004), no. 11, 1029-1046. doi: 10.1016/j.cad.2004.01.011
    • (2004) Computer-Aided Design , vol.36 , Issue.11 , pp. 1029-1046
    • Lieutier, A.1
  • 37
    • 0348134603 scopus 로고    scopus 로고
    • Hamilton-Jacobi equations and distance functions on Riemannian manifolds
    • Mantegazza, C.; Mennucci, A. C. Hamilton-Jacobi equations and distance functions on Riemannian manifolds. Appl. Math. Optim. 47 (2003), no. 1, 1-25. doi: 10.1007/s00245-002-0736-4
    • (2003) Appl. Math. Optim. , vol.47 , Issue.1 , pp. 1-25
    • Mantegazza, C.1    Mennucci, A.C.2
  • 38
    • 0036000820 scopus 로고    scopus 로고
    • Six boundary elements per wavelength: is that enough?
    • Marburg, S. Six boundary elements per wavelength: is that enough? J. Comp. Acous. 10 (2002), no. 01, 25-51. doi: 10.1142/S0218396X02001401
    • (2002) J. Comp. Acous. , vol.10 , Issue.1 , pp. 25-51
    • Marburg, S.1
  • 39
    • 84918688551 scopus 로고
    • On the steady problem of small oscillations of a fluid in the presence of a submerged body
    • Maź ya, V. G. On the steady problem of small oscillations of a fluid in the presence of a submerged body. Proc. Semin. Sobolev 2 (1977), 57-79.
    • (1977) Proc. Semin. Sobolev , vol.2 , pp. 57-79
    • Maź ya, V.G.1
  • 42
    • 0000498121 scopus 로고
    • Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle
    • Melrose, R. B.; Taylor, M. E. Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Adv. in Math. 55 (1985), no. 3, 242-315. doi: 10.1016/0001-8708(85)90093-3
    • (1985) Adv. in Math. , vol.55 , Issue.3 , pp. 242-315
    • Melrose, R.B.1    Taylor, M.E.2
  • 44
    • 84901342997 scopus 로고    scopus 로고
    • Is the Helmholtz equation really sign-indefinite?
    • Moiola, A.; Spence, E. A. Is the Helmholtz equation really sign-indefinite? SIAM Rev. 56 (2014), no. 2, 274-312. doi: 10.1137/120901301
    • (2014) SIAM Rev , vol.56 , Issue.2 , pp. 274-312
    • Moiola, A.1    Spence, E.A.2
  • 45
    • 84980087895 scopus 로고
    • The decay of solutions of the exterior initial-boundary value problem for the wave equation
    • Morawetz, C. S. The decay of solutions of the exterior initial-boundary value problem for the wave equation. Comm. Pure Appl. Math. 14 (1961), no. 3, 561-568. doi: 10.1002/cpa.3160140327
    • (1961) Comm. Pure Appl. Math. , vol.14 , Issue.3 , pp. 561-568
    • Morawetz, C.S.1
  • 46
    • 84980131041 scopus 로고
    • Decay for solutions of the exterior problem for the wave equation
    • Morawetz, C. S. Decay for solutions of the exterior problem for the wave equation. Comm. Pure Appl. Math. 28 (1975), no. 2, 229-264. doi: 10.1002/cpa.3160280204
    • (1975) Comm. Pure Appl. Math. , vol.28 , Issue.2 , pp. 229-264
    • Morawetz, C.S.1
  • 47
    • 84981760477 scopus 로고
    • An inequality for the reduced wave operator and the justification of geometrical optics
    • Morawetz, C. S.; Ludwig, D. An inequality for the reduced wave operator and the justification of geometrical optics. Comm. Pure Appl. Math. 21 (1968), no. 2, 187-203. doi: 10.1002/cpa.3160210206
    • (1968) Comm. Pure Appl. Math. , vol.21 , Issue.2 , pp. 187-203
    • Morawetz, C.S.1    Ludwig, D.2
  • 48
    • 84980140132 scopus 로고
    • Decay of solutions of the wave equation outside nontrapping obstacles
    • Morawetz, C. S.; Ralston, J. V.; Strauss, W. A. Decay of solutions of the wave equation outside nontrapping obstacles. Comm. Pure Appl. Math. 30 (1977), no. 4, 447-508. doi: 10.1002/cpa.3160300405
    • (1977) Comm. Pure Appl. Math. , vol.30 , Issue.4 , pp. 447-508
    • Morawetz, C.S.1    Ralston, J.V.2    Strauss, W.A.3
  • 49
    • 0003890212 scopus 로고
    • Les méthodes directes en théorie des équations elliptiques
    • Paris; Academia, Éditeurs, Prague
    • Nečas, J. Les méthodes directes en théorie des équations elliptiques. Masson et Cie, Éditeurs, Paris; Academia, Éditeurs, Prague (1967), 351 pp.
    • (1967) Masson et Cie, Éditeurs , pp. 351
    • Nečas, J.1
  • 50
    • 0012415109 scopus 로고    scopus 로고
    • Acoustic and electromagnetic equations. Integral representations for harmonic problems
    • Springer, New York
    • Nédélec, J. C. Acoustic and electromagnetic equations. Integral representations for harmonic problems. Applied Mathematical Sciences, 144. Springer, New York, 2001.
    • (2001) Applied Mathematical Sciences , vol.144
    • Nédélec, J.C.1
  • 52
    • 0000494186 scopus 로고
    • Darstellung der Eigenwerte von Δ u+λ u = 0 durch ein Randintegral
    • Rellich, F. Darstellung der Eigenwerte von Δ u+λ u = 0 durch ein Randintegral. Math. Z. 46 (1940), 635-636. doi: 10.1007/BF01181459
    • (1940) Math. Z. , vol.46 , pp. 635-636
    • Rellich, F.1
  • 56
    • 84939898317 scopus 로고    scopus 로고
    • Bounds on acoustic layer potentials via oscillatory integral techniques
    • Spence, E. A. Bounds on acoustic layer potentials via oscillatory integral techniques. BIT. Numerical Mathematics (2014), doi: 10.1007/s10543-014-0506-0.
    • (2014) BIT. Numerical Mathematics
    • Spence, E.A.1
  • 57
    • 84975082584 scopus 로고    scopus 로고
    • Wavenumber-explicit bounds in time-harmonic acoustic scattering
    • Spence, E. A. Wavenumber-explicit bounds in time-harmonic acoustic scattering. SIAM J. Math. Anal. 46 (2014), no. 4, 2987-3024. doi: 10.1137/130932855
    • (2014) SIAM J. Math. Anal. , vol.46 , Issue.4 , pp. 2987-3024
    • Spence, E.A.1
  • 58
    • 79960108069 scopus 로고    scopus 로고
    • A new frequency-uniform coercive boundary integral equation for acoustic scattering
    • Spence, E. A.; Chandler-Wilde, S. N.; Graham, I. G.; Smyshlyaev, V. P. A new frequency-uniform coercive boundary integral equation for acoustic scattering. Comm. Pure Appl. Math. 64 (2011), no. 10, 1384-1415. doi: 10.1002/cpa.20378
    • (2011) Comm. Pure Appl. Math. , vol.64 , Issue.10 , pp. 1384-1415
    • Spence, E.A.1    Chandler-Wilde, S.N.2    Graham, I.G.3    Smyshlyaev, V.P.4
  • 60
    • 0035888632 scopus 로고    scopus 로고
    • Neumann's method for second-order elliptic systems in domains with non-smooth boundaries
    • Steinbach, O.; Wendland, W. L. On C. Neumann's method for second-order elliptic systems in domains with non-smooth boundaries. J. Math. Anal. Appl. 262 (2001), no. 2, 733-748. doi: 10.1006/jmaa.2001.7615
    • (2001) J. Math. Anal. Appl. , vol.262 , Issue.2 , pp. 733-748
    • Steinbach, O.1    Wendland, W.L.2    On, C.3
  • 61
    • 84980193941 scopus 로고
    • Dispersal of waves vanishing on the boundary of an exterior domain
    • Strauss, W. A. Dispersal of waves vanishing on the boundary of an exterior domain. Comm. Pure Appl. Math. 28 (1975), no. 2, 265-278. doi: 10.1002/cpa.3160280205
    • (1975) Comm. Pure Appl. Math. , vol.28 , Issue.2 , pp. 265-278
    • Strauss, W.A.1


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