{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T02:26:32Z","timestamp":1775183192458,"version":"3.50.1"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2007,2,6]],"date-time":"2007-02-06T00:00:00Z","timestamp":1170720000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2007,2,28]]},"DOI":"10.1007\/s11075-007-9063-9","type":"journal-article","created":{"date-parts":[[2007,2,5]],"date-time":"2007-02-05T10:21:05Z","timestamp":1170670865000},"page":"309-330","source":"Crossref","is-referenced-by-count":18,"title":["Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials"],"prefix":"10.1007","volume":"43","author":[{"given":"Vita","family":"Rutka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Wiegmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,2,6]]},"reference":[{"key":"9063_CR1","volume-title":"Mechanics of Composite Materials","author":"J. Aboudi","year":"1991","unstructured":"Aboudi, J.: Mechanics of Composite Materials. Elsevier, Amsterdam, The Netherlands (1991)"},{"key":"9063_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9286-6","volume-title":"Shape Optimization by the Homogenization Method","author":"G. Allaire","year":"2002","unstructured":"Allaire, G.: Shape Optimization by the Homogenization Method. Springer, Berlin Heidelberg New York (2002)"},{"key":"9063_CR3","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1137\/0731054","volume":"31","author":"R.J. LeVeque","year":"1994","unstructured":"LeVeque, R.J., Li, Z.: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31, 1019\u20131044 (1994)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9063_CR4","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1137\/S0036142995291329","volume":"35","author":"Z. Li","year":"1998","unstructured":"Li, Z.: A fast iterative algorithm for elliptic interface problems. SIAM J. Numer.\u00a0Anal. 35(1), 230\u2013254 (1998)","journal-title":"SIAM J. Numer.\u00a0Anal."},{"issue":"2","key":"9063_CR5","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1137\/0721021","volume":"21","author":"A. Mayo","year":"1984","unstructured":"Mayo, A.: The fast solution of Poisson\u2019s and the biharmonic equations on irregular regions. SIAM J. Numer.\u00a0Anal. 21(2), 285\u2013299 (1984)","journal-title":"SIAM J. Numer.\u00a0Anal."},{"key":"9063_CR6","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S.J. Osher","year":"1988","unstructured":"Osher, S.J., Sethian, J.A.: Fronts propagating with curvature dependent speed: algorithms based on the Hamilton\u2013Jacobi formulation. J. Comput.\u00a0Phys. 79, 12\u201349 (1988)","journal-title":"J. Comput.\u00a0Phys."},{"key":"9063_CR7","unstructured":"Rutka, V.: A fast numerical method for the computation of effective elastic moduli of 3D fibrous microstructures. Master\u2019s thesis, University of Kaiserslautern (2001)"},{"key":"9063_CR8","unstructured":"Rutka, V.: Immersed interface methods for elliptic boundary value problems. Ph.D. thesis, TU Kaiserslautern (2005)"},{"key":"9063_CR9","unstructured":"Rutka, V., Wiegmann, A., Andr\u00e4, H.: EJIIM for calculation of effective elastic moduli in 3D linear elasticity. Technical Report\u00a093, Fraunhofer ITWM Kaiserslautern (2006)"},{"issue":"2","key":"9063_CR10","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1006\/jcph.2000.6581","volume":"163","author":"J.A. Sethian","year":"2000","unstructured":"Sethian, J.A., Wiegmann, A.: Structural boundary design via level set and explicit jump immersed interface methods. J. Comput. Phys. 163(2), 489\u2013528 (2000)","journal-title":"J. Comput. Phys."},{"key":"9063_CR11","doi-asserted-by":"crossref","unstructured":"Wiegmann, A.: Fast Poisson, fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds. Technical Report LBNL-43565, Lawrence Berkeley National Laboratory, MS 50A-1148, One Cyclotron Rd, Berkeley CA 94720 (1999)","DOI":"10.2172\/982430"},{"issue":"3","key":"9063_CR12","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1137\/S0036142997328664","volume":"37","author":"A. Wiegmann","year":"2000","unstructured":"Wiegmann, A., Bube, K.P.: The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions. SIAM J. Numer. Anal. 37(3), 827\u2013862 (2000)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"9063_CR13","first-page":"783","volume":"10","author":"X. Yang","year":"2003","unstructured":"Yang, X., Li, B., Li, Z.: The immersed interface method for elasticity problems with interfaces. Dyn. Contin., Discrete Impuls. Syst. 10(5), 783\u2013808 (2003)","journal-title":"Dyn. Contin., Discrete Impuls. Syst."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9063-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-007-9063-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9063-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:08Z","timestamp":1559351288000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-007-9063-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,6]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,2,28]]}},"alternative-id":["9063"],"URL":"https:\/\/doi.org\/10.1007\/s11075-007-9063-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,2,6]]}}}