{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T01:47:19Z","timestamp":1768441639007,"version":"3.49.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T00:00:00Z","timestamp":1584316800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T00:00:00Z","timestamp":1584316800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"IITK-ISRO Space Technology Cell","award":["STC\/MATH\/2014100"],"award-info":[{"award-number":["STC\/MATH\/2014100"]}]},{"name":"NSF","award":["DMS-1720014"],"award-info":[{"award-number":["DMS-1720014"]}]},{"name":"TUBITAK","award":["1001-117F056"],"award-info":[{"award-number":["1001-117F056"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2020,4]]},"DOI":"10.1007\/s10915-020-01189-x","type":"journal-article","created":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T07:05:07Z","timestamp":1584342307000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems"],"prefix":"10.1007","volume":"83","author":[{"given":"Fatih","family":"Ecevit","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akash","family":"Anand","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yassine","family":"Boubendir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,3,16]]},"reference":[{"issue":"2","key":"1189_CR1","first-page":"165","volume":"318","author":"T Abboud","year":"1994","unstructured":"Abboud, T., N\u00e9d\u00e9lec, J.C., Zhou, B.: M\u00e9thode des \u00e9quations int\u00e9grales pour les hautes fr\u00e9quences. C. R. Acad. Sci. Paris S\u00e9r. I Math. 318(2), 165\u2013170 (1994)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"1189_CR2","unstructured":"Abboud, T., N\u00e9d\u00e9lec, J.C., Zhou, B.: Improvements of the integral equation method for high frequency problems. In: Proceedings of 3rd International Conference on Mathematical Aspects of Wave Propagation Problems (1995)"},{"issue":"5","key":"1189_CR3","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/S0955-7997(02)00161-3","volume":"27","author":"S Amini","year":"2003","unstructured":"Amini, S., Profit, A.: Multi-level fast multipole solution of the scattering problem. Eng. Anal. Bound. Elem. 27(5), 547\u2013564 (2003)","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"3","key":"1189_CR4","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s00211-009-0263-1","volume":"114","author":"A Anand","year":"2010","unstructured":"Anand, A., Boubendir, Y., Ecevit, F., Reitich, F.: Analysis of multiple scattering iterations for high-frequency scattering problems. II. The three-dimensional scalar case. Numer. Math. 114(3), 373\u2013427 (2010)","journal-title":"Numer. Math."},{"key":"1189_CR5","first-page":"169","volume-title":"Computational Methods for Acoustics Problems","author":"X Antoine","year":"2008","unstructured":"Antoine, X.: Advances in the on-surface radiation condition method: theory, numerics and applications. In: Magoul\u00e8s, F. (ed.) Computational Methods for Acoustics Problems, pp. 169\u2013194. Saxe-Coburg Publications, Stirlingshire (2008)"},{"issue":"1","key":"1189_CR6","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1093\/imanum\/drm001","volume":"28","author":"L Banjai","year":"2008","unstructured":"Banjai, L., Hackbusch, W.: Hierarchical matrix techniques for low- and high-frequency Helmholtz problems. IMA J. Numer. Anal. 28(1), 46\u201379 (2008)","journal-title":"IMA J. Numer. Anal."},{"key":"1189_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492910000012","volume":"19","author":"D Boffi","year":"2010","unstructured":"Boffi, D.: Finite element approximation of eigenvalue problems. Acta Numer. 19, 1\u2013120 (2010)","journal-title":"Acta Numer."},{"issue":"6","key":"1189_CR8","doi-asserted-by":"crossref","first-page":"B1130","DOI":"10.1137\/16M1080501","volume":"39","author":"Y Boubendir","year":"2017","unstructured":"Boubendir, Y., Ecevit, F., Reitich, F.: Acceleration of an iterative method for the evaluation of high-frequency multiple scattering effects. SIAM J. Sci. Comput. 39(6), B1130\u2013B1155 (2017)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"1189_CR9","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1109\/TMAG.2005.844567","volume":"41","author":"O Bruno","year":"2005","unstructured":"Bruno, O., Geuzaine, C., Reitich, F.: On the O(1) solution of multiple-scattering problems. IEEE Trans. Magn. 41(5), 1488\u20131491 (2005)","journal-title":"IEEE Trans. Magn."},{"issue":"4","key":"1189_CR10","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1007\/s00211-013-0525-9","volume":"124","author":"OP Bruno","year":"2013","unstructured":"Bruno, O.P., Dom\u00ednguez, V., Sayas, F.J.: Convergence analysis of a high-order Nystr\u00f6m integral-equation method for surface scattering problems. Numer. Math. 124(4), 603\u2013645 (2013)","journal-title":"Numer. Math."},{"issue":"2","key":"1189_CR11","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.cam.2006.02.050","volume":"204","author":"OP Bruno","year":"2007","unstructured":"Bruno, O.P., Geuzaine, C.A.: An O(1) integration scheme for three-dimensional surface scattering problems. J. Comput. Appl. Math. 204(2), 463\u2013476 (2007)","journal-title":"J. Comput. Appl. Math."},{"issue":"1816","key":"1189_CR12","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1098\/rsta.2003.1338","volume":"362","author":"OP Bruno","year":"2004","unstructured":"Bruno, O.P., Geuzaine, C.A., Monro Jr., J.A., Reitich, F.: Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 362(1816), 629\u2013645 (2004)","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"issue":"1","key":"1189_CR13","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1006\/jcph.2001.6714","volume":"169","author":"OP Bruno","year":"2001","unstructured":"Bruno, O.P., Kunyansky, L.A.: A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications. J. Comput. Phys. 169(1), 80\u2013110 (2001)","journal-title":"J. Comput. Phys."},{"key":"1189_CR14","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1017\/S0962492912000037","volume":"21","author":"SN Chandler-Wilde","year":"2012","unstructured":"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, 89\u2013305 (2012)","journal-title":"Acta Numer."},{"issue":"4","key":"1189_CR15","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1007\/s00211-014-0648-7","volume":"129","author":"SN Chandler-Wilde","year":"2015","unstructured":"Chandler-Wilde, S.N., Hewett, D.P., Langdon, S., Twigger, A.: A high frequency boundary element method for scattering by a class of nonconvex obstacles. Numer. Math. 129(4), 647\u2013689 (2015)","journal-title":"Numer. Math."},{"issue":"2","key":"1189_CR16","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1137\/06065595X","volume":"45","author":"SN Chandler-Wilde","year":"2007","unstructured":"Chandler-Wilde, S.N., Langdon, S.: A Galerkin boundary element method for high frequency scattering by convex polygons. SIAM J. Numer. Anal. 45(2), 610\u2013640 (2007). (electronic)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1189_CR17","doi-asserted-by":"crossref","first-page":"573","DOI":"10.4208\/cicp.231209.040111s","volume":"11","author":"SN Chandler-Wilde","year":"2012","unstructured":"Chandler-Wilde, S.N., Langdon, S., Mokgolele, M.: A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions. Commun. Comput. Phys. 11(2), 573\u2013593 (2012)","journal-title":"Commun. Comput. Phys."},{"key":"1189_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02835-3","volume-title":"Inverse Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences","author":"D Colton","year":"1992","unstructured":"Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences, vol. 93. Springer, Berlin (1992)"},{"issue":"3","key":"1189_CR19","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s00466-009-0377-4","volume":"44","author":"RW Davies","year":"2009","unstructured":"Davies, R.W., Morgan, K., Hassan, O.: A high order hybrid finite element method applied to the solution of electromagnetic wave scattering problems in the time domain. Comput. Mech. 44(3), 321\u2013331 (2009)","journal-title":"Comput. Mech."},{"key":"1189_CR20","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.cam.2013.11.012","volume":"261","author":"V Dom\u00ednguez","year":"2014","unstructured":"Dom\u00ednguez, V.: Filon\u2013Clenshaw\u2013Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities. J. Comput. Appl. Math. 261, 299\u2013319 (2014)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"1189_CR21","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s00211-007-0071-4","volume":"106","author":"V Dom\u00ednguez","year":"2007","unstructured":"Dom\u00ednguez, V., Graham, I.G., Smyshlyaev, V.P.: A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Numer. Math. 106(3), 471\u2013510 (2007)","journal-title":"Numer. Math."},{"issue":"2","key":"1189_CR22","doi-asserted-by":"crossref","first-page":"407","DOI":"10.3906\/mat-1609-40","volume":"42","author":"F Ecevit","year":"2018","unstructured":"Ecevit, F.: Frequency independent solvability of surface scattering problems. Turk. J. Math. 42(2), 407\u2013422 (2018)","journal-title":"Turk. J. Math."},{"issue":"2","key":"1189_CR23","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1093\/imanum\/drx079","volume":"39","author":"F Ecevit","year":"2019","unstructured":"Ecevit, F., Eruslu, H.H.: A Galerkin BEM for high-frequency scattering problems based on frequency-dependent changes of variables. IMA J. Numer. Anal. 39(2), 893\u2013923 (2019)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"1189_CR24","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s00211-016-0800-7","volume":"135","author":"F Ecevit","year":"2017","unstructured":"Ecevit, F., \u00d6zen, H.\u00c7.: Frequency-adapted galerkin boundary element methods for convex scattering problems. Numer. Math. 135(1), 27\u201371 (2017)","journal-title":"Numer. Math."},{"issue":"2","key":"1189_CR25","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s00211-009-0249-z","volume":"114","author":"F Ecevit","year":"2009","unstructured":"Ecevit, F., Reitich, F.: Analysis of multiple scattering iterations for high-frequency scattering problems. I. The two-dimensional case. Numer. Math. 114(2), 271\u2013354 (2009)","journal-title":"Numer. Math."},{"issue":"139","key":"1189_CR26","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1090\/S0025-5718-1977-0436612-4","volume":"31","author":"B Engquist","year":"1977","unstructured":"Engquist, B., Majda, A.: Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31(139), 629\u2013651 (1977)","journal-title":"Math. Comput."},{"key":"1189_CR27","unstructured":"Gibbs, A., Chandler-Wilde, S., Langdon, S., Moiola, A.: A high frequency boundary element method for scattering by a class of multiple obstacles (2019). arXiv:1903.04449"},{"issue":"1","key":"1189_CR28","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.cam.2005.11.024","volume":"198","author":"E Giladi","year":"2007","unstructured":"Giladi, E.: Asymptotically derived boundary elements for the Helmholtz equation in high frequencies. J. Comput. Appl. Math. 198(1), 52\u201374 (2007)","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"1189_CR29","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.wavemoti.2003.12.004","volume":"39","author":"D Givoli","year":"2004","unstructured":"Givoli, D.: High-order local non-reflecting boundary conditions: a review. Wave Motion 39(4), 319\u2013326 (2004). New computational methods for wave propagation","journal-title":"Wave Motion"},{"issue":"1","key":"1189_CR30","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.jcp.2006.06.007","volume":"221","author":"MJ Grote","year":"2007","unstructured":"Grote, M.J., Kirsch, C.: Nonreflecting boundary condition for time-dependent multiple scattering. J. Comput. Phys. 221(1), 41\u201362 (2007)","journal-title":"J. Comput. Phys."},{"issue":"8","key":"1189_CR31","doi-asserted-by":"crossref","first-page":"3135","DOI":"10.1016\/j.jcp.2011.01.017","volume":"230","author":"MJ Grote","year":"2011","unstructured":"Grote, M.J., Sim, I.: Local nonreflecting boundary condition for time-dependent multiple scattering. J. Comput. Phys. 230(8), 3135\u20133154 (2011)","journal-title":"J. Comput. Phys."},{"key":"1189_CR32","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.wavemoti.2017.12.008","volume":"78","author":"S Groth","year":"2018","unstructured":"Groth, S., Hewett, D., Langdon, S.: A hybrid numerical-asymptotic boundary element method for high frequency scattering by penetrable convex polygons. Wave Motion 78, 32\u201353 (2018)","journal-title":"Wave Motion"},{"issue":"2","key":"1189_CR33","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1093\/imamat\/hxt040","volume":"80","author":"SP Groth","year":"2013","unstructured":"Groth, S.P., Hewett, D.P., Langdon, S.: Hybrid numerical-asymptotic approximation for high-frequency scattering by penetrable convex polygons. IMA J. Appl. Math. 80(2), 324\u2013353 (2013)","journal-title":"IMA J. Appl. Math."},{"issue":"5","key":"1189_CR34","first-page":"395","volume":"5","author":"J Hesthaven","year":"2004","unstructured":"Hesthaven, J., Warburton, T.: High-order accurate methods for time-domain electromagnetics. CMES Comput. Model. Eng. Sci. 5(5), 395\u2013407 (2004)","journal-title":"CMES Comput. Model. Eng. Sci."},{"issue":"5","key":"1189_CR35","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1017\/S0956792515000315","volume":"26","author":"DP Hewett","year":"2015","unstructured":"Hewett, D.P.: Shadow boundary effects in hybrid numerical-asymptotic methods for high-frequency scattering. Eur. J. Appl. Math. 26(5), 773\u2013793 (2015)","journal-title":"Eur. J. Appl. Math."},{"issue":"4","key":"1189_CR36","doi-asserted-by":"crossref","first-page":"1698","DOI":"10.1093\/imanum\/dru043","volume":"35","author":"DP Hewett","year":"2014","unstructured":"Hewett, D.P., Langdon, S., Chandler-Wilde, S.N.: A frequency-independent boundary element method for scattering by two-dimensional screens and apertures. IMA J. Numer. Anal. 35(4), 1698\u20131728 (2014)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"1189_CR37","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1137\/110856812","volume":"51","author":"DP Hewett","year":"2013","unstructured":"Hewett, D.P., Langdon, S., Melenk, J.M.: A high frequency $hp$ boundary element method for scattering by convex polygons. SIAM J. Numer. Anal. 51(1), 629\u2013653 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"1189_CR38","doi-asserted-by":"crossref","first-page":"2305","DOI":"10.1137\/060651525","volume":"29","author":"D Huybrechs","year":"2007","unstructured":"Huybrechs, D., Vandewalle, S.: A sparse discretization for integral equation formulations of high frequency scattering problems. SIAM J. Sci. Comput. 29(6), 2305\u20132328 (2007)","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"1189_CR39","doi-asserted-by":"crossref","first-page":"2020","DOI":"10.1016\/j.cam.2009.08.053","volume":"234","author":"S Langdon","year":"2010","unstructured":"Langdon, S., Mokgolele, M., Chandler-Wilde, S.: High frequency scattering by convex curvilinear polygons. J. Comput. Appl. Math. 234(6), 2020\u20132026 (2010)","journal-title":"J. Comput. Appl. Math."},{"issue":"10","key":"1189_CR40","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1002\/cpa.20378","volume":"64","author":"EA Spence","year":"2011","unstructured":"Spence, E.A., Chandler-Wilde, S.N., Graham, I.G., Smyshlyaev, V.P.: A new frequency-uniform coercive boundary integral equation for acoustic scattering. Commun. Pure Appl. Math. 64(10), 1384\u20131415 (2011)","journal-title":"Commun. Pure Appl. Math."},{"issue":"10","key":"1189_CR41","doi-asserted-by":"crossref","first-page":"3411","DOI":"10.1109\/TAP.2010.2055809","volume":"58","author":"MS Tong","year":"2010","unstructured":"Tong, M.S., Chew, W.C.: Multilevel fast multipole acceleration in the Nystr\u00f6m discretization of surface electromagnetic integral equations for composite objects. IEEE Trans. Antennas Propag. 58(10), 3411\u20133416 (2010)","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01189-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-020-01189-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01189-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T00:23:44Z","timestamp":1615854224000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-020-01189-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,16]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["1189"],"URL":"https:\/\/doi.org\/10.1007\/s10915-020-01189-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,16]]},"assertion":[{"value":"15 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"1"}}