{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:00:57Z","timestamp":1776844857106,"version":"3.51.2"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,10,11]],"date-time":"2011-10-11T00:00:00Z","timestamp":1318291200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1007\/s10444-011-9194-3","type":"journal-article","created":{"date-parts":[[2011,10,10]],"date-time":"2011-10-10T14:57:33Z","timestamp":1318258653000},"page":"39-91","source":"Crossref","is-referenced-by-count":50,"title":["Multiple traces boundary integral formulation for Helmholtz transmission problems"],"prefix":"10.1007","volume":"37","author":[{"given":"R.","family":"Hiptmair","sequence":"first","affiliation":[]},{"given":"C.","family":"Jerez-Hanckes","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,10,11]]},"reference":[{"key":"9194_CR1","series-title":"Mathematics & Applications","volume-title":"An Introduction to Mathematics of Emerging Biomedical Imaging","author":"H Ammari","year":"2008","unstructured":"Ammari, H.: An Introduction to Mathematics of Emerging Biomedical Imaging. Mathematics & Applications, vol.\u00a062. Springer, Berlin (2008)"},{"key":"9194_CR2","volume-title":"Cours d\u2019analyse: Th\u00e9orie des distributions et analyse de Fourier. \u00c9ditions de l\u2019\u00c9cole Polytechnique","author":"JM Bony","year":"2001","unstructured":"Bony, J.M.: Cours d\u2019analyse: Th\u00e9orie des distributions et analyse de Fourier. \u00c9ditions de l\u2019\u00c9cole Polytechnique, Palaiseau, France (2001)"},{"issue":"1","key":"9194_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00211-004-0579-9","volume":"100","author":"A Buffa","year":"2005","unstructured":"Buffa, A., Hiptmair, R.: Regularized combined field integral equations. Numer. Math. 100(1), 1\u201319 (2005)","journal-title":"Numer. Math."},{"issue":"3","key":"9194_CR4","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s00211-002-0407-z","volume":"95","author":"A Buffa","year":"2003","unstructured":"Buffa, A., Hiptmair, R., von Petersdorff, T., Schwab, C.: Boundary element methods for Maxwell equations on Lipschitz domains. Numer. Math. 95(3), 459\u2013485 (2003)","journal-title":"Numer. Math."},{"issue":"7","key":"9194_CR5","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/S0764-4442(00)00225-1","volume":"330","author":"S Christiansen","year":"2000","unstructured":"Christiansen, S., N\u00e9d\u00e9lec, J.C.: Des pr\u00e9conditionneurs pour la r\u00e9solution num\u00e9rique des \u00e9quations int\u00e9grales de fronti\u00e9re de l\u2019acoustique. C. R. Acad. Sci. Paris, Ser. I Math 330(7), 617\u2013622 (2000)","journal-title":"C. R. Acad. Sci. Paris, Ser. I Math"},{"issue":"3","key":"9194_CR6","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1137\/0519043","volume":"19","author":"M Costabel","year":"1988","unstructured":"Costabel, M.: Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Math. Anal. 19(3), 613\u2013626 (1988)","journal-title":"SIAM J. Math. Anal."},{"issue":"3","key":"9194_CR7","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1051\/m2an:1999155","volume":"33","author":"M Costabel","year":"1999","unstructured":"Costabel, M., Dauge, M., Nicaise, S.: Singularities of Maxwell interface problems. M2AN 33(3), 627\u2013649 (1999)","journal-title":"M2AN"},{"key":"9194_CR8","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/0022-247X(85)90118-0","volume":"106","author":"M Costabel","year":"1985","unstructured":"Costabel, M., Stephan, E.: A direct bounary equation method for transmission problems. J. Math. Anal. Appl. 106, 367\u2013413 (1985)","journal-title":"J. Math. Anal. Appl."},{"key":"9194_CR9","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0086682","volume-title":"Elliptic Boundary Value Problems on Corner Domains","author":"M Dauge","year":"1988","unstructured":"Dauge, M.: Elliptic Boundary Value Problems on Corner Domains. Lecture Notes in Mathematics, vol. 1341. Springer, Berlin (1988)"},{"issue":"1","key":"9194_CR10","first-page":"124","volume":"2","author":"C Farhat","year":"1994","unstructured":"Farhat, C., Roux, F.X.: Implicit parallel processing in structural mechanics. Comput. Mech. Adv. 2(1), 124 (1994)","journal-title":"Comput. Mech. Adv."},{"issue":"2","key":"9194_CR11","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1137\/050641545","volume":"45","author":"F Fr\u00fchauf","year":"2007","unstructured":"Fr\u00fchauf, F., Gebauer, B., Scherzer, O.: Detecting interfaces in a parabolic-elliptic problem from surface measurements. SIAM J. Numer. Anal. 45(2), 810\u2013836 (2007)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9194_CR12","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1006\/jmaa.2001.7537","volume":"262","author":"GN Gatica","year":"2001","unstructured":"Gatica, G.N., Hsiao, G.C., Mellado, M.E.: A domain decomposition method based on BEM and FEM for linear exterior boundary value problems. J. Math. Anal. Appl. 262(1), 70\u201386 (2001)","journal-title":"J. Math. Anal. Appl."},{"key":"9194_CR13","doi-asserted-by":"crossref","unstructured":"Haase, G., Heise, B., Kuhn, M., Langer, U.: Adaptive domain decomposition methods for finite and boundary element equations. In: Wendland, W. (ed.) Boundary Element Topics. Proceedings of the Final Conference of the Priority Research Programme \u201cBoundary Element Methods\u201d 1989\u20131995 of the German Research Foundation, 2\u20134 Oct 1995 in Stuttgart, Germany, pp. 121\u2013147. Springer, Berlin (1997)","DOI":"10.1007\/978-3-642-60791-2_7"},{"issue":"31","key":"9194_CR14","doi-asserted-by":"crossref","first-page":"7410","DOI":"10.1364\/AO.37.007410","volume":"37","author":"M Hammer","year":"1998","unstructured":"Hammer, M., Schweitzer, D., Michel, B., Thamm, E., Kolb, A.: Single scattering by red blood cells. Appl. Opt. 37(31), 7410\u20137418 (1998)","journal-title":"Appl. Opt."},{"issue":"1","key":"9194_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1163\/156939389X00016","volume":"3","author":"R Harrington","year":"1989","unstructured":"Harrington, R.: Boundary integral formulations for homogeneous material bodies. J. Electromagn. Waves Appl. 3(1), 1\u201315 (1989)","journal-title":"J. Electromagn. Waves Appl."},{"issue":"6","key":"9194_CR16","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1137\/S0036141094271259","volume":"27","author":"C Hazard","year":"1996","unstructured":"Hazard, C., Lenoir, M.: On the solution of time-harmonic scattering problems for Maxwell\u2019s equations. SIAM J. Math. Anal. 27(6), 1597\u20131630 (1996)","journal-title":"SIAM J. Math. Anal."},{"issue":"5","key":"9194_CR17","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.camwa.2006.10.008","volume":"52","author":"R Hiptmair","year":"2006","unstructured":"Hiptmair, R.: Operator preconditioning. Comput. Math. Appl. 52(5), 699\u2013706 (2006)","journal-title":"Comput. Math. Appl."},{"key":"9194_CR18","doi-asserted-by":"crossref","unstructured":"Hiptmair, R., Jerez-Hanckes, C.: Multiple traces boundary integral formulation for Helmholtz transmission problems. Tech. Rep.\u00a035, SAM ETH Zurich (2010)","DOI":"10.1007\/s10444-011-9194-3"},{"key":"9194_CR19","doi-asserted-by":"crossref","first-page":"2107","DOI":"10.1137\/050639958","volume":"44","author":"R Hiptmair","year":"2006","unstructured":"Hiptmair, R., Meury, P.: Stabilized FEM-BEM coupling for Helmholtz transmission problems. SIAM J. Numer. Anal. 44, 2107\u20132130 (2006)","journal-title":"SIAM J. Numer. Anal."},{"key":"9194_CR20","unstructured":"Hsiao, G., Wendland, W.: Domain decomposition in boundary element methods. In: Glowinski, R., Kuznetsov, Y., Meurant, G., P\u00e9riaux, J., Widlund, O. (eds.) Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, pp. 41\u201349. SIAM Philadelphia (1991)"},{"issue":"10\u201311","key":"9194_CR21","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1016\/j.apnum.2006.03.030","volume":"56","author":"GC Hsiao","year":"2006","unstructured":"Hsiao, G.C.: Boundary element methods\u2014An overview. Appl. Numer. Math. 56(10\u201311), 1356\u20131369 (2006)","journal-title":"Appl. Numer. Math."},{"issue":"1\u20132","key":"9194_CR22","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/S0377-0427(00)00488-X","volume":"125","author":"GC Hsiao","year":"2000","unstructured":"Hsiao, G.C., Steinbach, O., Wendland, W.L.: Domain decomposition methods via boundary integral equations. J. Comp. Appl. Math. 125(1\u20132), 521\u2013537 (2000)","journal-title":"J. Comp. Appl. Math."},{"key":"9194_CR23","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-68545-6","volume-title":"Boundary integral equations","author":"GC Hsiao","year":"2008","unstructured":"Hsiao, G.C., Wendland, W.L.: Boundary integral equations. Applied Mathematical Sciences, vol. 164. Springer, Berlin (2008)"},{"key":"9194_CR24","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1006\/jfan.1995.1067","volume":"130","author":"D Jerison","year":"1995","unstructured":"Jerison, D., Kenig, C.: The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130, 161\u2013219 (1995)","journal-title":"J. Funct. Anal."},{"key":"9194_CR25","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/B978-0-12-068650-6.50026-5","volume-title":"The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972)","author":"RB Kellogg","year":"1972","unstructured":"Kellogg, R.B.: Higher order singularities for interface problems. In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972), pp. 589\u2013602. Academic, New York (1972)"},{"key":"9194_CR26","first-page":"948","volume-title":"Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), vol.\u00a01","author":"CE Kenig","year":"1987","unstructured":"Kenig, C.E.: Carleman estimates, uniform Sobolev inequalities for second-order differential operators, and unique continuation theorems. In: Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), vol.\u00a01, pp. 948\u2013960. Amer. Math. Soc., Providence, RI (1987)"},{"key":"9194_CR27","first-page":"227","volume":"16","author":"V Kondrat\u2019ev","year":"1967","unstructured":"Kondrat\u2019ev, V.: Boundary value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16, 227\u2013313 (1967)","journal-title":"Trans. Moscow Math. Soc."},{"issue":"6","key":"9194_CR28","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1063\/1.523808","volume":"19","author":"R Kre\u00df","year":"1978","unstructured":"Kre\u00df, R., Roach, G.F.: Transmission problems for the Helmholtz equation. J. Math. Phys. 19(6), 1433\u20131437 (1978)","journal-title":"J. Math. Phys."},{"issue":"11","key":"9194_CR29","doi-asserted-by":"crossref","first-page":"2814","DOI":"10.1016\/j.apnum.2008.12.030","volume":"59","author":"AR Laliena","year":"2009","unstructured":"Laliena, A.R., Rap\u00fan, M.L., Sayas, F.J.: Symmetric boundary integral formulations for Helmholtz transmission problems. Appl. Numer. Math. 59(11), 2814\u20132823 (2009)","journal-title":"Appl. Numer. Math."},{"issue":"3","key":"9194_CR30","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s00607-003-0018-2","volume":"71","author":"U Langer","year":"2003","unstructured":"Langer, U., Steinbach, O.: Boundary element tearing and interconnecting methods. Computing 71(3), 205\u2013228 (2003)","journal-title":"Computing"},{"key":"9194_CR31","volume-title":"\u00c9quations diff\u00e9rentielles op\u00e9rationnelles et probl\u00e8mes aux limites. Die Grundlehren der mathematischen Wissenschaften, Bd. 111","author":"JL Lions","year":"1961","unstructured":"Lions, J.L.: \u00c9quations diff\u00e9rentielles op\u00e9rationnelles et probl\u00e8mes aux limites. Die Grundlehren der mathematischen Wissenschaften, Bd. 111. Springer, Berlin (1961)"},{"key":"9194_CR32","volume-title":"Probl\u00e8mes aux Limites Non Homog\u00e8nes, vol.\u00a01","author":"JL Lions","year":"1968","unstructured":"Lions, J.L., Magenes, E.: Probl\u00e8mes aux Limites Non Homog\u00e8nes, vol.\u00a01. Dunod, Paris, France (1968)"},{"issue":"1","key":"9194_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/nla.716","volume":"18","author":"K Mardal","year":"2010","unstructured":"Mardal, K., Winther, R.: Preconditioning discretizations of systems of partial differential equations. Numer. Linear. Algebr. 18(1), 1\u201340 (2010)","journal-title":"Numer. Linear. Algebr."},{"key":"9194_CR34","volume-title":"Strongly Elliptic Systems and Boundary Integral Equations","author":"W McLean","year":"2000","unstructured":"McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, UK (2000)"},{"issue":"4","key":"9194_CR35","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1018944530343","volume":"11","author":"W McLean","year":"1999","unstructured":"McLean, W., Steinbach, O.: Boundary element preconditioners for a hypersingular integral equation on an interval. Adv. Comput. Math. 11(4), 271\u2013286 (1999)","journal-title":"Adv. Comput. Math."},{"key":"9194_CR36","unstructured":"Meury, P.: Stable finite element boundary element Galerkin schemes for acoustic and electromagnetic scattering. ETH Dissertation No. 17320, ETH Z\u00fcrich, Z\u00fcrich, Switzerland (2007)"},{"key":"9194_CR37","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1002\/cpa.3160070304","volume":"7","author":"C M\u00fcller","year":"1954","unstructured":"M\u00fcller, C.: On the behavior of the solutions of the differential equation \u0394U\u2009=\u2009F(x,U) in the neighborhood of a point. Comm. Pure Appl. Math. 7, 505\u2013515 (1954)","journal-title":"Comm. Pure Appl. Math."},{"key":"9194_CR38","series-title":"Expositions in Mathematics","doi-asserted-by":"crossref","DOI":"10.1515\/9783110848915","volume-title":"Elliptic Problems in Domains with Piecewise Smooth Boundaries","author":"S Nazarov","year":"1994","unstructured":"Nazarov, S., Plamenevskii, B.: Elliptic Problems in Domains with Piecewise Smooth Boundaries, Expositions in Mathematics, vol.\u00a013. Walter de Gruyter, Berlin (1994)"},{"key":"9194_CR39","series-title":"Applied Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4393-7","volume-title":"Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems","author":"JC N\u00e9d\u00e9lec","year":"2001","unstructured":"N\u00e9d\u00e9lec, J.C.: Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems. Applied Mathematical Sciences, vol.\u00a044. Springer, Berlin (2001)"},{"key":"9194_CR40","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1002\/mma.1670170602","volume":"17","author":"S Nicaise","year":"1994","unstructured":"Nicaise, S., S\u00e4ndig, A.M.: General interface problems I\/II. Math. Methods Appl. Sci. 17, 395\u2013450 (1994)","journal-title":"Math. Methods Appl. Sci."},{"key":"9194_CR41","series-title":"Texts in Applied Mathematics","volume-title":"Numerical Mathematics","author":"A Quarteroni","year":"2000","unstructured":"Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Texts in Applied Mathematics, vol.\u00a037. Springer, New York (2000)"},{"key":"9194_CR42","volume-title":"Numerical Techniques in Electromagnetics","author":"M Sadiku","year":"1996","unstructured":"Sadiku, M.: Numerical Techniques in Electromagnetics, 2nd edn. CRC Press LLC, New York (1996)","edition":"2"},{"key":"9194_CR43","series-title":"Springer Series in Computational Mathematics","volume-title":"Boundary Element Methods","author":"S Sauter","year":"2010","unstructured":"Sauter, S., Schwab, C.: Boundary Element Methods, Springer Series in Computational Mathematics, vol. 39. Springer, Heidelberg (2010)"},{"key":"9194_CR44","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1090\/S0025-5718-1974-0373326-0","volume":"28","author":"A Schatz","year":"1974","unstructured":"Schatz, A.: An observation concerning Ritz\u2013Galerkin methods with indefinite bilinear forms. Math. Comput. 28, 959\u2013962 (1974)","journal-title":"Math. Comput."},{"key":"9194_CR45","volume-title":"Partial Differential Equations in Physics. Pure and Applied Mathematics","author":"A Sommerfeld","year":"1949","unstructured":"Sommerfeld, A.: Partial Differential Equations in Physics. Pure and Applied Mathematics. Academic, New York (1949)"},{"key":"9194_CR46","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-68805-3","volume-title":"Numerical approximation methods for elliptic boundary value problems","author":"O Steinbach","year":"2008","unstructured":"Steinbach, O.: Numerical approximation methods for elliptic boundary value problems. Springer, New York (2008)"},{"key":"9194_CR47","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1023\/A:1018937506719","volume":"9","author":"O Steinbach","year":"1998","unstructured":"Steinbach, O., Wendland, W.: The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9, 191\u2013216 (1998)","journal-title":"Adv. Comput. Math."},{"key":"9194_CR48","doi-asserted-by":"crossref","unstructured":"Steinbach, O., Windisch, M.: Robust boundary element domain decomposition solvers in acoustics. Tech. Rep.\u00a09, Institut f\u00fcr Numerische Mathematik, TU Graz (2009)","DOI":"10.1007\/978-3-642-11304-8_31"},{"key":"9194_CR49","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1002\/mma.1670110203","volume":"11","author":"T Petersdorff von","year":"1989","unstructured":"von Petersdorff, T.: Boundary integral equations for mixed Dirichlet, Neumann and transmission problems. Math. Methods Appl. Sci. 11, 185\u2013213 (1989)","journal-title":"Math. Methods Appl. Sci."},{"key":"9194_CR50","volume-title":"Numerical Analysis for Electromagnetic Integral Equations","author":"K Warnick","year":"2008","unstructured":"Warnick, K.: Numerical Analysis for Electromagnetic Integral Equations. Artech House, Norwood, MA (2008)"},{"key":"9194_CR51","doi-asserted-by":"crossref","DOI":"10.1118\/1.1589017","volume-title":"Introduction to Biomedical Imaging","author":"A Webb","year":"2003","unstructured":"Webb, A.: Introduction to Biomedical Imaging. Wiley, New York (2003)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9194-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-011-9194-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9194-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,9]],"date-time":"2021-12-09T22:25:39Z","timestamp":1639088739000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-011-9194-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,11]]},"references-count":51,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["9194"],"URL":"https:\/\/doi.org\/10.1007\/s10444-011-9194-3","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,10,11]]}}}