{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T14:47:41Z","timestamp":1775746061007,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,6,8]],"date-time":"2013-06-08T00:00:00Z","timestamp":1370649600000},"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":[[2014,2]]},"DOI":"10.1007\/s10444-013-9306-3","type":"journal-article","created":{"date-parts":[[2013,6,7]],"date-time":"2013-06-07T01:02:04Z","timestamp":1370566924000},"page":"245-272","source":"Crossref","is-referenced-by-count":77,"title":["High-order accurate methods for Nystr\u00f6m discretization of integral equations on smooth curves in the plane"],"prefix":"10.1007","volume":"40","author":[{"given":"S.","family":"Hao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. H.","family":"Barnett","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. G.","family":"Martinsson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Young","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,6,8]]},"reference":[{"key":"9306_CR1","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1137\/S1064827597325141","volume":"20","author":"BK Alpert","year":"1999","unstructured":"Alpert, B.K.: Hybrid gauss-trapezoidal quadrature rules. SIAM J. Sci. Comput. 20, 1551\u20131584 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"9306_CR2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511626340","volume-title":"The Numerical Solution of Integral Equations of the Second Kind","author":"KE Atkinson","year":"1997","unstructured":"Atkinson, K.E.: The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, Cambridge (1997)"},{"key":"9306_CR3","doi-asserted-by":"crossref","unstructured":"Barnes, J., Hut, P.: A hierarchical O(N log N) force-calculation algorithm. Nature 324 (1986)","DOI":"10.1038\/324446a0"},{"key":"9306_CR4","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1016\/j.jcp.2011.11.015","volume":"231","author":"J Bremer","year":"2012","unstructured":"Bremer, J.: A fast direct solver for the integral equations of scattering theory on planar curves with corners. J. Comput. Phys. 231, 1879\u20131899 (2012)","journal-title":"J. Comput. Phys."},{"key":"9306_CR5","doi-asserted-by":"crossref","first-page":"2507","DOI":"10.1016\/j.jcp.2009.12.001","volume":"229","author":"J Bremer","year":"2010","unstructured":"Bremer, J., Rokhlin, V.: Efficient discretization of Laplace boundary integral equations on polygonal domains. J. Comput. Phys. 229, 2507\u20132525 (2010)","journal-title":"J. Comput. Phys."},{"key":"9306_CR6","doi-asserted-by":"crossref","first-page":"8259","DOI":"10.1016\/j.jcp.2010.06.040","volume":"229","author":"J Bremer","year":"2010","unstructured":"Bremer, J., Rokhlin, V., Sammis, I.: Universal quadratures for boundary integral equations on two-dimensional domains with corners. J. Comput. Phys. 229, 8259\u20138280 (2010)","journal-title":"J. Comput. Phys."},{"key":"9306_CR7","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1137\/S1052623498349796","volume":"9","author":"H Cheng","year":"1999","unstructured":"Cheng, H., Rokhlin, V., Yarvin, N.: Nonlinear optimization, quadrature, and interpolation. SIAM J. Optim. 9, 901\u2013923 (1999)","journal-title":"SIAM J. Optim."},{"key":"9306_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03537-5","volume-title":"Inverse Acoustic and Electromagnetic Scattering Theory, vol. 93 Applied Mathematical Sciences","author":"D Colton","year":"1998","unstructured":"Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, vol. 93, 2nd edn.Applied Mathematical Sciences. Springer-Verlag, Berlin (1998)","edition":"2"},{"key":"9306_CR9","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1137\/S0036144596305582","volume":"40","author":"TA Driscoll","year":"1998","unstructured":"Driscoll, T.A., Toh, K.-C., Trefethen, L.N.: From potential theory to matrix iteration in six steps. SIAM Rev. 40, 547\u2013578 (1998)","journal-title":"SIAM Rev."},{"key":"9306_CR10","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1002\/1096-987X(20010130)22:2<184::AID-JCC6>3.0.CO;2-7","volume":"22","author":"Z-H Duan","year":"2001","unstructured":"Duan, Z.-H., Krasny, R.: An adaptive treecode for computing nonbonded potential energy in classical molecular systems. J. Comput. Chem. 22, 184\u2013195 (2001)","journal-title":"J. Comput. Chem."},{"key":"9306_CR11","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","volume":"73","author":"L Greengard","year":"1987","unstructured":"Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73, 325\u2013348 (1987)","journal-title":"J. Comput. Phys."},{"key":"9306_CR12","unstructured":"Hao, S., Barnett, A., Martinsson, P.: Nystr\u00f6m Quadratures for BIEs with Weakly Singular Kernels on 1D Domains (2012). http:\/\/amath.colorado.edu\/faculty\/martinss\/Nystrom\/"},{"key":"9306_CR13","doi-asserted-by":"crossref","first-page":"8892","DOI":"10.1016\/j.jcp.2009.09.004","volume":"228","author":"J Helsing","year":"2009","unstructured":"Helsing, J.: Integral equation methods for elliptic problems with boundary conditions of mixed type. J. Comput. Phys. 228, 8892\u20138907 (2009)","journal-title":"J. Comput. Phys."},{"key":"9306_CR14","unstructured":"Helsing, J.: Solving Integral Equations on Piecewise Smooth Boundaries Using the RCIP Method: A Tutorial, p. 34. (2012,preprint) arXiv: 1207.6737v3"},{"key":"9306_CR15","unstructured":"Helsing, J., Karlsson, A.: An Accurate Boundary Value Problem Solver Applied to Scattering from Cylinders with Corners (2012). arXiv: 1211.2467"},{"key":"9306_CR16","doi-asserted-by":"crossref","first-page":"8820","DOI":"10.1016\/j.jcp.2008.06.022","volume":"227","author":"J Helsing","year":"2008","unstructured":"Helsing, J., Ojala, R.: Corner singularities for elliptic problems: integral equations, graded meshes, quadrature, and compressed inverse preconditioning. J. Comput. Phys. 227, 8820\u20138840 (2008)","journal-title":"J. Comput. Phys."},{"key":"9306_CR17","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1137\/S0036142995287847","volume":"34","author":"S Kapur","year":"1997","unstructured":"Kapur, S., Rokhlin, V.: High-order corrected trapezoidal quadrature rules for singular functions. SIAM J. Numer. Anal. 34, 1331\u20131356 (1997)","journal-title":"SIAM J. Numer. Anal."},{"key":"9306_CR18","doi-asserted-by":"crossref","unstructured":"Kl\u00f6ckner, A., Barnett, A.H., Greengard, L., O\u2019Neil, M.: Quadrature by Expansion: A New Method for the Evaluation of Layer Potentials. J. Comput. Phys. (2012). In press","DOI":"10.1016\/j.jcp.2013.06.027"},{"key":"9306_CR19","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/S0898-1221(00)00277-7","volume":"41","author":"P Kolm","year":"2001","unstructured":"Kolm, P., Rokhlin, V.: Numerical quadratures for singular and hypersingular integrals. Comput. Math. Appl. 41, 327\u2013352 (2001)","journal-title":"Comput. Math. Appl."},{"key":"9306_CR20","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/BF00044609","volume":"20","author":"R Kress","year":"1986","unstructured":"Kress, R.: On constant-alpha force-free fields in a torus. J. Eng. Math. 20, 323\u2013344 (1986)","journal-title":"J. Eng. Math."},{"key":"9306_CR21","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0895-7177(91)90068-I","volume":"15","author":"R Kress","year":"1991","unstructured":"Kress, R.: Boundary integral equations in time-harmonic acoustic scattering. Math. Comput. Model. 15, 229\u2013243 (1991)","journal-title":"Math. Comput. Model."},{"key":"9306_CR22","doi-asserted-by":"crossref","unstructured":"Kress, R.: Linear Integral Equations, vol. 82 of Applied Mathematical Sciences, 2nd edn. Springer (1999)","DOI":"10.1007\/978-1-4612-0559-3"},{"key":"9306_CR23","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF02391810","volume":"109","author":"E Martensen","year":"1963","unstructured":"Martensen, E.: \u00dcber eine methode zum r\u00e4umlichen neumannschen problem mit einer anwendung f\u00fcr torusartige berandungen. Acta Math. 109, 75\u2013135 (1963)","journal-title":"Acta Math."},{"key":"9306_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcp.2004.10.033","volume":"205","author":"P Martinsson","year":"2004","unstructured":"Martinsson, P., Rokhlin, V.: A fast direct solver for boundary integral equations in two dimensions. J. Comput. Phys. 205, 1\u201323 (2004)","journal-title":"J. Comput. Phys."},{"key":"9306_CR25","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/BF02547521","volume":"54","author":"E Nystr\u00f6m","year":"1930","unstructured":"Nystr\u00f6m, E.: \u00dcber die praktische Aufl\u00f6sung von Integralgleichungen mit Andwendungen aug Randwertaufgaben. Acta Math. 54, 185\u2013204 (1930)","journal-title":"Acta Math."},{"key":"9306_CR26","unstructured":"Ojala, R.: Towards an all-embracing elliptic solver in 2D. PhD thesis, Department of Mathematics, Lund University, Sweden (2011)"},{"key":"9306_CR27","doi-asserted-by":"crossref","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems. Society for industrial and applied mathematics, 2nd edn. (2003)","DOI":"10.1137\/1.9780898718003"},{"key":"9306_CR28","doi-asserted-by":"crossref","unstructured":"Trefethen, L.N.: Spectral Methods in MATLAB, vol. 10 of Software, Environments, and Tools, Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2000)","DOI":"10.1137\/1.9780898719598"},{"key":"9306_CR29","unstructured":"Trefethen, L.N.: Approximation Theory and Approximation Practice, SIAM (2012). http:\/\/www.maths.ox.ac.uk\/chebfun\/ATAP"},{"key":"9306_CR30","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.jcp.2003.11.021","volume":"196","author":"L Ying","year":"2004","unstructured":"Ying, L., Biros, G., Zorin, D.: A kernel-independent adaptive fast multipole method in two and three dimensions. J. Comput. Phys. 196, 591\u2013626 (2004)","journal-title":"J. Comput. Phys."},{"key":"9306_CR31","doi-asserted-by":"crossref","first-page":"4142","DOI":"10.1016\/j.jcp.2012.02.008","volume":"231","author":"PM Young","year":"2012","unstructured":"Young, P.M., Hao, S., Martinsson, P.G.: A high-order Nystr\u00f6m discretization scheme for boundary integral equations defined on rotationally symmetric surfaces. J. Comput. Phys. 231, 4142\u20134159 (2012)","journal-title":"J. Comput. Phys."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9306-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-013-9306-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9306-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,14]],"date-time":"2019-07-14T17:52:14Z","timestamp":1563126734000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-013-9306-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,8]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,2]]}},"alternative-id":["9306"],"URL":"https:\/\/doi.org\/10.1007\/s10444-013-9306-3","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6,8]]}}}