{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T22:49:12Z","timestamp":1767912552313,"version":"3.49.0"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,3,16]],"date-time":"2018-03-16T00:00:00Z","timestamp":1521158400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["AdG247277"],"award-info":[{"award-number":["AdG247277"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003006","name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","doi-asserted-by":"publisher","award":["CH1-02 11-1."],"award-info":[{"award-number":["CH1-02 11-1."]}],"id":[{"id":"10.13039\/501100003006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1007\/s10444-018-9594-8","type":"journal-article","created":{"date-parts":[[2018,3,16]],"date-time":"2018-03-16T10:00:35Z","timestamp":1521194435000},"page":"1475-1518","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":43,"title":["Large deformation shape uncertainty quantification in acoustic scattering"],"prefix":"10.1007","volume":"44","author":[{"given":"R.","family":"Hiptmair","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0906-1179","authenticated-orcid":false,"given":"L.","family":"Scarabosio","sequence":"additional","affiliation":[]},{"given":"C.","family":"Schillings","sequence":"additional","affiliation":[]},{"given":"Ch.","family":"Schwab","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,3,16]]},"reference":[{"key":"9594_CR1","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.1016\/S1631-073X(02)02412-3","volume":"334","author":"G Allaire","year":"2002","unstructured":"Allaire, G., Jouve, F., Toader, A.-M.: A level-set method for shape optimization. C.R. Math. 334, 1125\u20131130 (2002)","journal-title":"C.R. Math."},{"key":"9594_CR2","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1137\/100786356","volume":"52","author":"I Babu\u0161ka","year":"2010","unstructured":"Babu\u0161ka, I., Nobile, F., Tempone, R.: A stochastic collocation method for elliptic partial differential equations with random input data. SIAM Rev. 52, 317\u2013355 (2010)","journal-title":"SIAM Rev."},{"key":"9594_CR3","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1006\/jcph.1994.1159","volume":"114","author":"J-P Berenger","year":"1994","unstructured":"Berenger, J.-P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185\u2013200 (1994)","journal-title":"J. Comput. Phys."},{"key":"9594_CR4","doi-asserted-by":"publisher","first-page":"4281","DOI":"10.1137\/090749256","volume":"31","author":"M Bieri","year":"2009","unstructured":"Bieri, M., Andreev, R., Schwab, C.: Sparse tensor discretization of elliptic SPDEs. SIAM J. Sci. Comput. 31, 4281\u20134304 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"9594_CR5","doi-asserted-by":"crossref","unstructured":"Brenner, S.C., Scott, R.: The mathematical theory of finite element methods, vol. 15 Springer Science & Business Media (2008)","DOI":"10.1007\/978-0-387-75934-0"},{"key":"9594_CR6","doi-asserted-by":"publisher","first-page":"4271","DOI":"10.1090\/S0002-9939-2012-11291-2","volume":"140","author":"J-P Calvi","year":"2012","unstructured":"Calvi, J.-P., Manh, P.: Lagrange interpolation at real projections of Leja sequences for the unit disk. Proc. Am. Math. Soc. 140, 4271\u20134284 (2012)","journal-title":"Proc. Am. Math. Soc."},{"key":"9594_CR7","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s00211-007-0086-x","volume":"107","author":"C Canuto","year":"2007","unstructured":"Canuto, C., Kozubek, T.: A fictitious domain approach to the numerical solution of PDEs in stochastic domains. Numerische mathematik 107, 257\u2013293 (2007)","journal-title":"Numerische mathematik"},{"key":"9594_CR8","doi-asserted-by":"publisher","first-page":"1173","DOI":"10.1016\/j.camwa.2016.01.005","volume":"71","author":"JE Castrillon-Candas","year":"2016","unstructured":"Castrillon-Candas, J.E., Nobile, F., Tempone, R. F.: Analytic regularity and collocation approximation for PDEs with random domain deformations. Comput. Math. Appl. 71, 1173\u20131197 (2016)","journal-title":"Comput. Math. Appl."},{"key":"9594_CR9","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s10208-013-9154-z","volume":"14","author":"A Chkifa","year":"2014","unstructured":"Chkifa, A., Cohen, A., Schwab, C.: High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Found. Comput. Math. 14, 601\u2013633 (2014)","journal-title":"Found. Comput. Math."},{"key":"9594_CR10","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1016\/j.matpur.2014.04.009","volume":"103","author":"A Chkifa","year":"2015","unstructured":"Chkifa, A.: Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. Journal de Math\u00e9,matiques Pures et Appliqu\u00e9es 103, 400\u2013428 (2015)","journal-title":"Journal de Math\u00e9,matiques Pures et Appliqu\u00e9es"},{"key":"9594_CR11","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1016\/j.jat.2012.11.005","volume":"166","author":"MA Chkifa","year":"2013","unstructured":"Chkifa, M.A.: On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection. J. Approx. Theory 166, 176\u2013200 (2013)","journal-title":"J. Approx. Theory"},{"key":"9594_CR12","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s10208-010-9072-2","volume":"10","author":"A Cohen","year":"2010","unstructured":"Cohen, A., DeVore, R., Schwab, C.: Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs. Found. Comput. Math. 10, 615\u2013646 (2010)","journal-title":"Found. Comput. Math."},{"key":"9594_CR13","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1142\/S0219530511001728","volume":"9","author":"A Cohen","year":"2011","unstructured":"Cohen, A.: Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs. Anal. Appl. 9, 11\u201347 (2011)","journal-title":"Anal. Appl."},{"key":"9594_CR14","unstructured":"Cohen, A., Schwab, C., Zech, J.: Shape Holomorphy of the stationary Navier-Stokes Equations, Report 2016-45, Seminar for Applied Mathematics, ETH Z\u00fcrich, Switzerland. to appear in SIAM J. Math. Analysis (2016)"},{"key":"9594_CR15","doi-asserted-by":"publisher","first-page":"2061","DOI":"10.1137\/S1064827596301406","volume":"19","author":"F Collino","year":"1998","unstructured":"Collino, F., Monk, P.: The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19, 2061\u20132090 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"9594_CR16","doi-asserted-by":"crossref","unstructured":"Colton, D., Kress, R.: Inverse acoustic and electromagnetic scattering theory, vol. 93 Springer Science & Business Media (2012)","DOI":"10.1007\/978-1-4614-4942-3"},{"key":"9594_CR17","doi-asserted-by":"publisher","first-page":"1285","DOI":"10.1051\/m2an\/2015012","volume":"49","author":"M Dambrine","year":"2015","unstructured":"Dambrine, M., Harbrecht, H., Puig, B.: Computing quantities of interest for random domains with second order shape sensitivity analysis, ESAIM. Math. Model. Numer. Anal. 49, 1285\u20131302 (2015)","journal-title":"Math. Model. Numer. Anal."},{"key":"9594_CR18","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1142\/S021820251750021X","volume":"27","author":"J Dick","year":"2017","unstructured":"Dick, J., Gantner, R.N., Le Gia, Q.T., Schwab, C.: Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Math. Models Methods Appl. Sci. 27, 953\u2013995 (2017)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"9594_CR19","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.cma.2013.11.015","volume":"270","author":"M Eigel","year":"2014","unstructured":"Eigel, M., Gittelson, C.J., Schwab, C., Zander, E.: Adaptive stochastic Galerkin FEM. Comput. Methods Appl. Mech. Eng. 270, 247\u2013269 (2014)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9594_CR20","doi-asserted-by":"crossref","unstructured":"Gantner, R.N.: A generic C++ library for multilevel Quasi-Monte Carlo. In: Proceedings of the Platform for Advanced Scientific Computing Conference, PASC \u201916, pp. 11:1\u201311:12. ACM, New York (2016)","DOI":"10.1145\/2929908.2929915"},{"key":"9594_CR21","unstructured":"Gantner, R.N., Peters, M.D.: Higher order Quasi-Monte Carlo for Bayesian shape inversion, Report 2016-45, Seminar for Applied Mathematics, ETH Z\u00fcrich, Switzerland (2016)"},{"key":"9594_CR22","first-page":"271","volume-title":"Springer Proceedings in Mathematics & Statistics","author":"Robert N. Gantner","year":"2016","unstructured":"Gantner R.N., Schwab, C.: Computational higher order Quasi-Monte Carlo integration. In: Cools R., Nuyens, D. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, pp. 271\u2013288. Springer International Publishing, Cham (2016)"},{"key":"9594_CR23","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s00607-003-0015-5","volume":"71","author":"T Gerstner","year":"2003","unstructured":"Gerstner, T., Griebel, M.: Dimension\u2013adaptive tensor\u2013product quadrature. Computing 71, 65\u201387 (2003)","journal-title":"Computing"},{"key":"9594_CR24","unstructured":"Ghanem, R.G., Spanos, P.D.: Stochastic finite elements: a spectral approach Courier Corporation (2003)"},{"key":"9594_CR25","doi-asserted-by":"crossref","unstructured":"Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order, vol. 224 Springer Science & Business Media (2001)","DOI":"10.1007\/978-3-642-61798-0"},{"key":"9594_CR26","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1016\/j.jat.2016.02.006","volume":"207","author":"M Griebel","year":"2016","unstructured":"Griebel, M., Oettershagen, J.: On tensor product approximation of analytic functions. J. Appr. Theory 207, 348\u2013379 (2016)","journal-title":"J. Appr. Theory"},{"key":"9594_CR27","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1051\/m2an\/2013079","volume":"47","author":"H Harbrecht","year":"2013","unstructured":"Harbrecht, H., Li, J.: First order second moment analysis for stochastic interface problems based on low-rank approximation. ESAIM: Math. Model. Numer. Anal. 47, 1533\u20131552 (2013)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"key":"9594_CR28","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1007\/s00211-016-0791-4","volume":"134","author":"H Harbrecht","year":"2016","unstructured":"Harbrecht, H., Peters, M., Siebenmorgen, M.: Analysis of the domain mapping method for elliptic diffusion problems on random domains. Numer. Math. 134, 823\u2013856 (2016)","journal-title":"Numer. Math."},{"key":"9594_CR29","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s00211-008-0147-9","volume":"109","author":"H Harbrecht","year":"2008","unstructured":"Harbrecht, H., Schneider, R., Schwab, C.: Sparse second moment analysis for elliptic problems in stochastic domains. Numer. Math. 109, 385\u2013414 (2008)","journal-title":"Numer. Math."},{"key":"9594_CR30","unstructured":"Hiptmair, R., Sargheini, S.: Scatterers on the Substrate: Far field formulas, Report 2015-02, Seminar for Applied Mathematics, ETH Z\u00fcrich, Switzerland (2015)"},{"key":"9594_CR31","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371","volume-title":"Topics in matrix analysis","author":"RA Horn","year":"1991","unstructured":"Horn, R.A., Johnson, C.R.: Topics in matrix analysis. Cambridge University Press, Cambridge (1991)"},{"key":"9594_CR32","doi-asserted-by":"publisher","first-page":"2229","DOI":"10.1142\/S0218202517500439","volume":"27","author":"C Jerez-Hanckes","year":"2017","unstructured":"Jerez-Hanckes, C., Schwab, C., Zech, J.: Electromagnetic wave scattering by random surfaces: Shape holomorphy. Math. Mod. Meth. Appl. Sci. 27, 2229\u20132259 (2017)","journal-title":"Math. Mod. Meth. Appl. Sci."},{"key":"9594_CR33","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/BF02684334","volume":"60","author":"M Lassas","year":"1998","unstructured":"Lassas, M., Somersalo, E.: On the existence and convergence of the solution of PML equations. Computing 60, 229\u2013241 (1998)","journal-title":"Computing"},{"key":"9594_CR34","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.apnum.2009.08.005","volume":"60","author":"J Li","year":"2010","unstructured":"Li, J., Melenk, J.M., Wohlmuth, B., Zou, J.: Optimal a priori estimates for higher order finite elements for elliptic interface problems. Appl. Numer. Math. 60, 19\u201337 (2010)","journal-title":"Appl. Numer. Math."},{"key":"9594_CR35","doi-asserted-by":"publisher","first-page":"562","DOI":"10.1006\/jcph.2001.6749","volume":"170","author":"R Li","year":"2001","unstructured":"Li, R., Tang, T., Zhang, P.: Moving Mesh Methods in Multiple Dimensions Based on Harmonic Maps. J. Comput. Phys. 170, 562\u2013588 (2001)","journal-title":"J. Comput. Phys."},{"key":"9594_CR36","volume-title":"Strongly elliptic systems and boundary integral equations","author":"WCH McLean","year":"2000","unstructured":"McLean, W.C.H.: Strongly elliptic systems and boundary integral equations. Cambridge University Press, Cambridge (2000)"},{"key":"9594_CR37","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1137\/S0036142997315172","volume":"36","author":"P Monk","year":"1998","unstructured":"Monk, P., S\u00fcli, E.: The adaptive computation of far-field patterns by a posteriori error estimation of linear functionals. SIAM J. Numer. Anal. 36, 251\u2013274 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"9594_CR38","unstructured":"N\u00e9d\u00e9lec, J.-C.: Acoustic and electromagnetic equations: integral representations for harmonic problems, vol. 144 Springer Science & Business Media (2001)"},{"key":"9594_CR39","doi-asserted-by":"publisher","first-page":"4663","DOI":"10.1016\/j.cma.2008.06.010","volume":"197","author":"A Nouy","year":"2008","unstructured":"Nouy, A., Clement, A., Schoefs, F., Mo\u00ebs, N.: An extended stochastic finite element method for solving stochastic partial differential equations on random domains. Comput. Methods Appl. Mech. Eng. 197, 4663\u20134682 (2008)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9594_CR40","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1006\/jcph.2000.6636","volume":"169","author":"RP Fedkiw","year":"2001","unstructured":"Osher S., Fedkiw, R.P.: Level set methods: An overview and some recent results. J. Comput. Phys. 169, 463\u2013502 (2001)","journal-title":"J. Comput. Phys."},{"key":"9594_CR41","first-page":"1","volume":"PP","author":"A Paganini","year":"2015","unstructured":"Paganini, A., Scarabosio, L., Hiptmair, R., Tsukerman, I.: Trefftz approximations: a new framework for nonreflecting boundary conditions. IEEE Trans. Magn. PP, 1\u20131 (2015)","journal-title":"IEEE Trans. Magn."},{"key":"9594_CR42","unstructured":"Scarabosio, L.: Shape uncertainty quantification for scattering transmission problems, PhD thesis, ETH Z\u00fcrich, 2016. Diss. No. 23574. http:\/\/e-collection.library.ethz.ch\/eserv\/eth:49652\/eth-49652-02.pdf"},{"key":"9594_CR43","doi-asserted-by":"publisher","first-page":"065011","DOI":"10.1088\/0266-5611\/29\/6\/065011","volume":"29","author":"C Schillings","year":"2013","unstructured":"Schillings, C., Schwab, C.: Sparse, adaptive Smolyak quadratures for Bayesian inverse problems. Inverse Prob. 29, 065011 (2013)","journal-title":"Inverse Prob."},{"key":"9594_CR44","doi-asserted-by":"publisher","first-page":"065007","DOI":"10.1088\/0266-5611\/30\/6\/065007","volume":"30","author":"C Schillings","year":"2014","unstructured":"Schillings, C., Schwab, C.: Sparsity in Bayesian inversion of parametric operator equations. Inverse Prob. 30, 065007 (2014)","journal-title":"Inverse Prob."},{"key":"9594_CR45","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1017\/S0962492911000055","volume":"20","author":"C Schwab","year":"2011","unstructured":"Schwab, C., Gittelson, C.J.: Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs. Acta Numer. 20, 291\u2013467 (2011)","journal-title":"Acta Numer."},{"key":"9594_CR46","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/j.jcp.2006.02.029","volume":"217","author":"DM Tartakovsky","year":"2006","unstructured":"Tartakovsky, D.M., Xiu, D.: Stochastic analysis of transport in tubes with rough walls. J. Comput. Phys. 217, 248\u2013259 (2006)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"9594_CR47","doi-asserted-by":"publisher","first-page":"897","DOI":"10.2307\/2371268","volume":"60","author":"N Wiener","year":"1938","unstructured":"Wiener, N.: The homogeneous chaos. Amer. J. Math. 60(4), 897\u2013936 (1938)","journal-title":"Amer. J. Math."},{"key":"9594_CR48","doi-asserted-by":"publisher","first-page":"1118","DOI":"10.1137\/040615201","volume":"27","author":"D Xiu","year":"2005","unstructured":"Xiu, D., Hesthaven, J.S.: High-order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 27, 1118\u20131139 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"9594_CR49","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1137\/040613160","volume":"28","author":"D Xiu","year":"2006","unstructured":"Xiu, D., Tartakovsky, D.M.: Numerical methods for differential equations in random domains. SIAM J. Sci. Comput. 28, 1167\u20131185 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"9594_CR50","unstructured":"Zech, J., Schwab, C.: Convergence rates of high dimensional Smolyak quadrature, Report 2017-27, Seminar for Applied Mathematics, ETH Z\u00fcrich, Switzerland (2017)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-018-9594-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-018-9594-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-018-9594-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T10:35:15Z","timestamp":1603967715000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-018-9594-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,16]]},"references-count":50,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["9594"],"URL":"https:\/\/doi.org\/10.1007\/s10444-018-9594-8","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,16]]},"assertion":[{"value":"2 February 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}