{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T18:30:40Z","timestamp":1777573840923,"version":"3.51.4"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2004,11,15]],"date-time":"2004-11-15T00:00:00Z","timestamp":1100476800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[2005,5]]},"DOI":"10.1007\/s00607-004-0099-6","type":"journal-article","created":{"date-parts":[[2004,11,15]],"date-time":"2004-11-15T05:41:17Z","timestamp":1100497277000},"page":"225-247","source":"Crossref","is-referenced-by-count":107,"title":["Hierarchical LU Decomposition-based Preconditioners for BEM"],"prefix":"10.1007","volume":"74","author":[{"given":"M.","family":"Bebendorf","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2004,11,15]]},"reference":[{"key":"99_CR1","doi-asserted-by":"crossref","unstructured":"Bebendorf, M.: Approximation of boundary element matrices. Numer. Math. 86, 565\u2013589 (2000).","DOI":"10.1007\/PL00005410"},{"key":"99_CR2","unstructured":"Bebendorf, M.: Efficient Galerkin BEM using ACA (in preparation)."},{"key":"99_CR3","unstructured":"Bebendorf, M.: Efficient inversion of the galerkin matrix of general second-order elliptic operators with non-smooth coefficients. Math. Comp. (forthcoming)."},{"key":"99_CR4","doi-asserted-by":"crossref","unstructured":"Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of collocation matrices. Computing 70, 1\u201324 (2003).","DOI":"10.1007\/s00607-002-1469-6"},{"key":"99_CR5","doi-asserted-by":"crossref","unstructured":"Bebendorf, M., Hackbusch, W.: Existence of -matrix approximants to the inverse FE-matrix of elliptic operators with L\u221e-coefficients. Numer. Math. 95, 1\u201328 (2003).","DOI":"10.1007\/s00211-002-0445-6"},{"key":"99_CR6","unstructured":"Bebendorf, M., Kriemann, R.: Fast parallel solution of boundary element systems. Preprint 10\/2004, Max-Planck-Institute MIS, Leipzig CVS (forthcoming)."},{"key":"99_CR7","doi-asserted-by":"crossref","unstructured":"Beylkin, G., Coifman, R., Rokhlin, V.: Fast wavelet transforms and numerical algorithms. I. Comm. Pure Appl. Math. 44, 141\u2013183 (1991).","DOI":"10.1002\/cpa.3160440202"},{"key":"99_CR8","unstructured":"Chen, G., Zhou, J.: Boundary element methods. New York: Academic Press 1992."},{"key":"99_CR9","doi-asserted-by":"crossref","unstructured":"Dahmen, W., Pr\u00f6ssdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations. II. Matrix compression and fast solution. Adv. Comput. Math. 1, 259\u2013335 (1993).","DOI":"10.1007\/BF02072014"},{"key":"99_CR10","doi-asserted-by":"crossref","unstructured":"Dahmen, W., Pr\u00f6ssdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations. I. Stability and convergence. Math. Z. 215, 583\u2013620 (1994).","DOI":"10.1007\/BF02571732"},{"key":"99_CR11","doi-asserted-by":"crossref","unstructured":"Dahmen, W., Schneider, R.: Wavelets on Manifolds I: Construction and domain decomposition. SIAM J. Math. Anal. 31, 184\u2013230 (1999).","DOI":"10.1137\/S0036141098333451"},{"key":"99_CR12","doi-asserted-by":"crossref","unstructured":"Grasedyck, L., Hackbusch, W.: Construction and arithmetics of -matrices. Computing 70, 295\u2013334 (2003).","DOI":"10.1007\/s00607-003-0019-1"},{"key":"99_CR13","doi-asserted-by":"crossref","unstructured":"Grasedyck, L.: Adaptive recompression of -matrices for BEM. Preprint 17\/2004, Max-Planck-Institute MIS, Leipzig. Computing (this issue).","DOI":"10.1007\/s00607-004-0103-1"},{"key":"99_CR14","unstructured":"Greengard, L., Rokhlin, V.: A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica. Cambridge: Cambridge University Press, 1997, pp. 229\u2013269."},{"key":"99_CR15","unstructured":"Hackbusch, W.: Theorie und Numerik elliptischer Differentialgleichungen. Stuttgart: Teubner 1996 \u2013 English translation: Elliptic differential equations. Theory and numerical treatment. Berlin: Springer 1992."},{"key":"99_CR16","doi-asserted-by":"crossref","unstructured":"Hackbusch, W.: A sparse matrix arithmetic based on -matrices. I. Introduction to -matrices. Computing 62, 89\u2013108 (1999).","DOI":"10.1007\/s006070050015"},{"key":"99_CR17","doi-asserted-by":"crossref","unstructured":"Hackbusch, W., Khoromskij, B. N.: A sparse -matrix arithmetic. II. Application to multi-dimensional problems. Computing 64, 21\u201347 (2000).","DOI":"10.1007\/PL00021408"},{"key":"99_CR18","unstructured":"Hackbusch, W., Khoromskij, B., Kriemann, R.: Hierarchical matrices based on a weak admissibility criterion. Preprint 2\/2003, Max-Planck-Institute MIS, Leipzig."},{"key":"99_CR19","doi-asserted-by":"crossref","unstructured":"Hackbusch, W., Nowak, Z. P.: On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54, 463\u2013491 (1989).","DOI":"10.1007\/BF01396324"},{"key":"99_CR20","unstructured":"Higham, N.: Accuracy and stability of numerical algorithms. SIAM 1996."},{"key":"99_CR21","doi-asserted-by":"crossref","unstructured":"Kurz, S., Rain, O., Rjasanow, S.: The adaptive cross approximation technique for the 3-D boundary element method. IEEE Trans. on Magnetics 38, 421\u2013424 (2002).","DOI":"10.1109\/20.996112"},{"key":"99_CR22","doi-asserted-by":"crossref","unstructured":"Langer, U., Pusch, D., Reitzinger, S.: Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods. Int. J. Numer. Meth. Engng. 58, 1937\u20131953 (2003).","DOI":"10.1002\/nme.839"},{"key":"99_CR23","unstructured":"Lintner, M.: L\u00f6sung der 2-D Wellengleichung mittels hierarchischer Matrizen. Technische Universit\u00e4t M\u00fcnchen 2002."},{"key":"99_CR24","doi-asserted-by":"crossref","unstructured":"Rjasanow, S.: Effective algorithms with circulant-block matrices. Linear Algebra Appl. 202, 55\u201369 (1994).","DOI":"10.1016\/0024-3795(94)90184-8"},{"key":"99_CR25","doi-asserted-by":"crossref","unstructured":"Sch\u00f6berl, J.: NETGEN \u2013 An advancing front 2D\/3D-mesh generator based on abstract rules. Comput. Visual. Sci. 1, 41\u201352 (1997).","DOI":"10.1007\/s007910050004"},{"key":"99_CR26","doi-asserted-by":"crossref","unstructured":"Steinbach, O., Wendland, W.: The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9, 191\u2013216 (1998).","DOI":"10.1023\/A:1018937506719"},{"key":"99_CR27","doi-asserted-by":"crossref","unstructured":"Taylor, M. E.: Pseudodifferential operators. Princeton: Princeton University Press 1981.","DOI":"10.1515\/9781400886104"},{"key":"99_CR28","doi-asserted-by":"crossref","unstructured":"Tyrtyshnikov, E.: Mosaic-skeleton approximations. Calcolo 33, 47\u201357 (1998).","DOI":"10.1007\/BF02575706"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-004-0099-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00607-004-0099-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00607-004-0099-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,30]],"date-time":"2023-04-30T07:03:12Z","timestamp":1682838192000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00607-004-0099-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11,15]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2005,5]]}},"alternative-id":["99"],"URL":"https:\/\/doi.org\/10.1007\/s00607-004-0099-6","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,11,15]]}}}