{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T09:58:45Z","timestamp":1722938325154},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,7,19]],"date-time":"2008-07-19T00:00:00Z","timestamp":1216425600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2008,10]]},"DOI":"10.1007\/s10915-008-9208-6","type":"journal-article","created":{"date-parts":[[2008,7,18]],"date-time":"2008-07-18T10:45:53Z","timestamp":1216377953000},"page":"19-41","source":"Crossref","is-referenced-by-count":11,"title":["Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation"],"prefix":"10.1007","volume":"37","author":[{"given":"Matthew","family":"Dobson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mitchell","family":"Luskin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,7,19]]},"reference":[{"key":"9208_CR1","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1615\/IntJMultCompEng.v5.i5.40","volume":"5","author":"M. Arndt","year":"2007","unstructured":"Arndt, M., Luskin, M.: Goal-oriented atomistic-continuum adaptivity for the quasicontinuum approximation. Int. J. Multiscale Comput. Eng. 5, 407\u2013415 (2007)","journal-title":"Int. J. Multiscale Comput. Eng."},{"key":"9208_CR2","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1137\/070688559","volume":"7","author":"M. Arndt","year":"2008","unstructured":"Arndt, M., Luskin, M.: Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. SIAM J. Multiscale Model. Simul. 7, 147\u2013170 (2008)","journal-title":"SIAM J. Multiscale Model. Simul."},{"key":"9208_CR3","doi-asserted-by":"crossref","unstructured":"Arndt, M., Luskin, M.: Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Comput. Methods Appl. Mech. Eng. (2008, to appear)","DOI":"10.1016\/j.cma.2008.05.005"},{"issue":"160","key":"9208_CR4","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1090\/S0025-5718-1982-0669639-X","volume":"39","author":"R.E. Bank","year":"1982","unstructured":"Bank, R.E., Rose, D.J.: Analysis of a multilevel iterative method for nonlinear finite element equations. Math. Comput. 39(160), 453\u2013465 (1982)","journal-title":"Math. Comput."},{"issue":"4","key":"9208_CR5","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1051\/m2an:2005035","volume":"39","author":"X. Blanc","year":"2005","unstructured":"Blanc, X., Le Bris, C., Legoll, F.: Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics. M2AN Math. Model. Numer. Anal. 39(4), 797\u2013826 (2005)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"3","key":"9208_CR6","doi-asserted-by":"crossref","first-page":"R33","DOI":"10.1088\/0965-0393\/11\/3\/201","volume":"11","author":"W. Curtin","year":"2003","unstructured":"Curtin, W., Miller, R.: Atomistic\/continuum coupling in computational materials science. Model. Simul. Mater. Sci. Eng. 11(3), R33\u2013R68 (2003)","journal-title":"Model. Simul. Mater. Sci. Eng."},{"key":"9208_CR7","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1051\/m2an:2007058","volume":"42","author":"M. Dobson","year":"2008","unstructured":"Dobson, M., Luskin, M.: Analysis of a force-based quasicontinuum method. M2AN Math. Model. Numer. Anal. 42, 113\u2013139 (2008)","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"9208_CR8","unstructured":"Doedel, E.: Lecture notes on numerical analysis of bifucation problems, March 1997. Electronic Source: http:\/\/cmvl.cs.concordia.ca\/publications.html"},{"key":"9208_CR9","doi-asserted-by":"crossref","first-page":"214115","DOI":"10.1103\/PhysRevB.74.214115","volume":"74","author":"W. E","year":"2006","unstructured":"E, W., Lu, J., Yang, J.: Uniform accuracy of the quasicontinuum method. Phys. Rev. B 74, 214115 (2006)","journal-title":"Phys. Rev. B"},{"key":"9208_CR10","first-page":"18","volume-title":"Frontiers and Prospects of Contemporary Applied Mathematics","author":"W. E","year":"2005","unstructured":"E, W., Ming, P.: Analysis of the local quasicontinuum method. In: Frontiers and Prospects of Contemporary Applied Mathematics, pp. 18\u201332. World Scientific, Singapore (2005)"},{"key":"9208_CR11","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s00205-006-0031-7","volume":"183","author":"W. E","year":"2007","unstructured":"E, W., Ming, P.: Cauchy-born rule and the stabilitiy of crystalline solids: Static problems. Arch. Ration. Mech. Anal. 183, 241\u2013297 (2007)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"9208_CR12","series-title":"Publ. Math. Res. Center","first-page":"359","volume-title":"Applications of Bifurcation Theory","author":"H.B. Keller","year":"1977","unstructured":"Keller, H.B.: Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Applications of Bifurcation Theory. Proc. Advanced Sem., Univ. Wisconsin, Madison, WI, 1976. Publ. Math. Res. Center, vol. 38, pp. 359\u2013384. Academic Press, New York (1977)"},{"key":"9208_CR13","doi-asserted-by":"crossref","first-page":"1899","DOI":"10.1016\/S0022-5096(01)00034-5","volume":"49","author":"J. Knap","year":"2001","unstructured":"Knap, J., Ortiz, M.: An analysis of the quasicontinuum method. J. Mech. Phys. Solids 49, 1899\u20131923 (2001)","journal-title":"J. Mech. Phys. Solids"},{"issue":"242","key":"9208_CR14","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1090\/S0025-5718-02-01456-4","volume":"72","author":"P. Lin","year":"2003","unstructured":"Lin, P.: Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model. Math. Comput. 72(242), 657\u2013675 (2003) (electronic)","journal-title":"Math. Comput."},{"issue":"1","key":"9208_CR15","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/050636772","volume":"45","author":"P. Lin","year":"2007","unstructured":"Lin, P.: Convergence analysis of a quasi-continuum approximation for a two-dimensional material. SIAM J. Numer. Anal. 45(1), 313\u2013332 (2007)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9208_CR16","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.actamat.2003.09.011","volume":"52","author":"R. Miller","year":"2003","unstructured":"Miller, R., Shilkrot, L., Curtin, W.: A\u00a0coupled atomistic and discrete dislocation plasticity simulation of nano-indentation into single crystal thin films. Acta Mater. 52(2), 271\u2013284 (2003)","journal-title":"Acta Mater."},{"key":"9208_CR17","unstructured":"Miller, R., Tadmor, E.: The QC code. http:\/\/www.qcmethod.com\/"},{"issue":"3","key":"9208_CR18","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1023\/A:1026098010127","volume":"9","author":"R. Miller","year":"2002","unstructured":"Miller, R., Tadmor, E.: The quasicontinuum method: Overview, applications and current directions. J.\u00a0Comput. Aided Mater. Des. 9(3), 203\u2013239 (2002)","journal-title":"J.\u00a0Comput. Aided Mater. Des."},{"issue":"6","key":"9208_CR19","doi-asserted-by":"crossref","first-page":"2359","DOI":"10.1137\/050632488","volume":"28","author":"J.T. Oden","year":"2006","unstructured":"Oden, J.T., Prudhomme, S., Romkes, A., Bauman, P.: Multi-scale modeling of physical phenomena: Adaptive control of models. SIAM J. Sci. Comput. 28(6), 2359\u20132389 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"9208_CR20","unstructured":"Ortner, C., S\u00fcli, E.: A-posteriori analysis and adaptive algorithms for the quasicontinuum method in one dimension. Research Report NA-06\/13, Oxford University Computing Laboratory (2006)"},{"key":"9208_CR21","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1051\/m2an:2007057","volume":"42","author":"C. Ortner","year":"2008","unstructured":"Ortner, C., S\u00fcli, E.: Analysis of a quasicontinuum method in one dimension. M2AN 42, 57\u201391 (2008)","journal-title":"M2AN"},{"issue":"5\u20136","key":"9208_CR22","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1615\/IntJMultCompEng.v4.i5-6.60","volume":"4","author":"S. Prudhomme","year":"2006","unstructured":"Prudhomme, S., Bauman, P.T., Oden, J.T.: Error control for molecular statics problems. Int. J. Multiscale Comput. Eng. 4(5\u20136), 647\u2013662 (2006)","journal-title":"Int. J. Multiscale Comput. Eng."},{"issue":"8","key":"9208_CR23","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1103\/PhysRevLett.82.1704","volume":"82","author":"D. Rodney","year":"1999","unstructured":"Rodney, D., Phillips, R.: Structure and strength of dislocation junctions: An atomic level analysis. Phys. Rev. Lett. 82(8), 1704\u20131707 (1999)","journal-title":"Phys. Rev. Lett."},{"issue":"21","key":"9208_CR24","doi-asserted-by":"crossref","first-page":"214104","DOI":"10.1103\/PhysRevB.69.214104","volume":"69","author":"T. Shimokawa","year":"2004","unstructured":"Shimokawa, T., Mortensen, J., Schiotz, J., Jacobsen, K.: Matching conditions in the quasicontinuum method: Removal of the error introduced at the interface between the coarse-grained and fully atomistic regions. Phys. Rev. B 69(21), 214104 (2004)","journal-title":"Phys. Rev. B"},{"issue":"6","key":"9208_CR25","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1080\/01418619608243000","volume":"73","author":"E. Tadmor","year":"1996","unstructured":"Tadmor, E., Ortiz, M., Phillips, R.: Quasicontinuum analysis of defects in solids. Philos. Mag.\u00a0A 73(6), 1529\u20131563 (1996)","journal-title":"Philos. Mag.\u00a0A"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-008-9208-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-008-9208-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-008-9208-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T04:41:30Z","timestamp":1559450490000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-008-9208-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7,19]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,10]]}},"alternative-id":["9208"],"URL":"https:\/\/doi.org\/10.1007\/s10915-008-9208-6","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7,19]]}}}