Hodapp, M.; Anciaux, G.; Curtin, W. A. Lattice Green function methods for atomistic/continuum coupling: theory and data-sparse implementation. (English) Zbl 1441.74010 Comput. Methods Appl. Mech. Eng. 348, 1039-1075 (2019). MSC: 74A25 82C22 PDF BibTeX XML Cite \textit{M. Hodapp} et al., Comput. Methods Appl. Mech. Eng. 348, 1039--1075 (2019; Zbl 1441.74010) Full Text: DOI
Alleman, Coleman N.; Foulk, James W. III; Mota, Alejandro; Lim, Hojun; Littlewood, David J. Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics. (English) Zbl 06876189 Comput. Mech. 61, No. 1-2, 207-218 (2018). MSC: 74 PDF BibTeX XML Cite \textit{C. N. Alleman} et al., Comput. Mech. 61, No. 1--2, 207--218 (2018; Zbl 06876189) Full Text: DOI
Mota, Alejandro; Tezaur, Irina; Alleman, Coleman The Schwarz alternating method in solid mechanics. (English) Zbl 1439.74450 Comput. Methods Appl. Mech. Eng. 319, 19-51 (2017); corrigendum ibid. 344, 1147-1148 (2019). MSC: 74S05 65N55 65N30 74A20 PDF BibTeX XML Cite \textit{A. Mota} et al., Comput. Methods Appl. Mech. Eng. 319, 19--51 (2017; Zbl 1439.74450) Full Text: DOI
Barajas-Solano, David A.; Tartakovsky, A. M. Hybrid multiscale finite volume method for advection-diffusion equations subject to heterogeneous reactive boundary conditions. (English) Zbl 1403.76056 Multiscale Model. Simul. 14, No. 4, 1341-1376 (2016). MSC: 76M12 76S05 65N08 35K51 35K57 PDF BibTeX XML Cite \textit{D. A. Barajas-Solano} and \textit{A. M. Tartakovsky}, Multiscale Model. Simul. 14, No. 4, 1341--1376 (2016; Zbl 1403.76056) Full Text: DOI
Yang, Qingcheng; To, Albert C. Multiresolution molecular mechanics: a unified and consistent framework for general finite element shape functions. (English) Zbl 1423.74038 Comput. Methods Appl. Mech. Eng. 283, 384-418 (2015). MSC: 74A25 74S05 PDF BibTeX XML Cite \textit{Q. Yang} and \textit{A. C. To}, Comput. Methods Appl. Mech. Eng. 283, 384--418 (2015; Zbl 1423.74038) Full Text: DOI
Chen, Jingrun; García-Cervera, Carlos J.; Li, Xiantao An atomistic/continuum coupling method using enriched bases. (English) Zbl 1317.65224 Multiscale Model. Simul. 13, No. 3, 766-789 (2015). MSC: 65N15 74G15 70E55 PDF BibTeX XML Cite \textit{J. Chen} et al., Multiscale Model. Simul. 13, No. 3, 766--789 (2015; Zbl 1317.65224) Full Text: DOI arXiv
Davydov, D.; Pelteret, J-P.; Steinmann, P. Comparison of several staggered atomistic-to-continuum concurrent coupling strategies. (English) Zbl 1423.74033 Comput. Methods Appl. Mech. Eng. 277, 260-280 (2014). MSC: 74A25 74G15 PDF BibTeX XML Cite \textit{D. Davydov} et al., Comput. Methods Appl. Mech. Eng. 277, 260--280 (2014; Zbl 1423.74033) Full Text: DOI
Tu, Fubin; Ling, Daosheng; Bu, Lingfang; Yang, Qingda Generalized bridging domain method for coupling finite elements with discrete elements. (English) Zbl 1423.74927 Comput. Methods Appl. Mech. Eng. 276, 509-533 (2014). MSC: 74S05 74H15 74E20 PDF BibTeX XML Cite \textit{F. Tu} et al., Comput. Methods Appl. Mech. Eng. 276, 509--533 (2014; Zbl 1423.74927) Full Text: DOI
Li, Xiantao Coarse-graining molecular dynamics models using an extended Galerkin projection method. (English) Zbl 1352.82021 Int. J. Numer. Methods Eng. 99, No. 3, 157-182 (2014). MSC: 82C80 65L60 74A25 82D25 PDF BibTeX XML Cite \textit{X. Li}, Int. J. Numer. Methods Eng. 99, No. 3, 157--182 (2014; Zbl 1352.82021) Full Text: DOI
Yang, Qingcheng; Biyikli, Emre; To, Albert C. Multiresolution molecular mechanics: convergence and error structure analysis. (English) Zbl 1296.74132 Comput. Methods Appl. Mech. Eng. 269, 20-45 (2014). MSC: 74S05 PDF BibTeX XML Cite \textit{Q. Yang} et al., Comput. Methods Appl. Mech. Eng. 269, 20--45 (2014; Zbl 1296.74132) Full Text: DOI
Biyikli, Emre; Yang, Qingcheng; To, Albert C. Multiresolution molecular mechanics: dynamics. (English) Zbl 1296.74005 Comput. Methods Appl. Mech. Eng. 274, 42-55 (2014). MSC: 74A25 PDF BibTeX XML Cite \textit{E. Biyikli} et al., Comput. Methods Appl. Mech. Eng. 274, 42--55 (2014; Zbl 1296.74005) Full Text: DOI
Yang, Qingcheng; Biyikli, Emre; To, Albert C. Multiresolution molecular mechanics: statics. (English) Zbl 1296.74006 Comput. Methods Appl. Mech. Eng. 258, 26-38 (2013). MSC: 74A25 PDF BibTeX XML Cite \textit{Q. Yang} et al., Comput. Methods Appl. Mech. Eng. 258, 26--38 (2013; Zbl 1296.74006) Full Text: DOI
Thirunavukkarasu, Senganal; Guddati, Murthy N. A domain decomposition method for concurrent coupling of multiscale models. (English) Zbl 1352.65327 Int. J. Numer. Methods Eng. 92, No. 11, 918-939 (2012). MSC: 65M55 PDF BibTeX XML Cite \textit{S. Thirunavukkarasu} and \textit{M. N. Guddati}, Int. J. Numer. Methods Eng. 92, No. 11, 918--939 (2012; Zbl 1352.65327) Full Text: DOI
Li, Xiantao An atomistic-based boundary element method for the reduction of molecular statics models. (English) Zbl 1253.74121 Comput. Methods Appl. Mech. Eng. 225-228, 1-13 (2012). MSC: 74S15 74A25 74E15 PDF BibTeX XML Cite \textit{X. Li}, Comput. Methods Appl. Mech. Eng. 225--228, 1--13 (2012; Zbl 1253.74121) Full Text: DOI
Makridakis, Charalambos; Ortner, Christoph; Süli, Endre A priori error analysis of two force-based atomistic/continuum models of a periodic chain. (English) Zbl 1225.82070 Numer. Math. 119, No. 1, 83-121 (2011). MSC: 82D25 65N12 65N15 70C20 PDF BibTeX XML Cite \textit{C. Makridakis} et al., Numer. Math. 119, No. 1, 83--121 (2011; Zbl 1225.82070) Full Text: DOI
Kobayashi, Ryo; Nakamura, Takahide; Ogata, Shuji A simple dynamical scale-coupling method for concurrent simulation of hybridized atomistic/coarse-grained-particle system. (English) Zbl 1193.74167 Int. J. Numer. Methods Eng. 83, No. 2, 249-268 (2010). MSC: 74S30 74A25 82B21 PDF BibTeX XML Cite \textit{R. Kobayashi} et al., Int. J. Numer. Methods Eng. 83, No. 2, 249--268 (2010; Zbl 1193.74167) Full Text: DOI
Dobson, Matthew; Luskin, Mitchell An analysis of the effect of ghost force oscillation on quasicontinuum error. (English) Zbl 1165.81414 ESAIM, Math. Model. Numer. Anal. 43, No. 3, 591 (2009). MSC: 81V70 82B30 65Z05 70C20 PDF BibTeX XML Cite \textit{M. Dobson} and \textit{M. Luskin}, ESAIM, Math. Model. Numer. Anal. 43, No. 3, 591 (2009; Zbl 1165.81414) Full Text: DOI EuDML arXiv
Arndt, Marcel; Luskin, Mitchell Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. (English) Zbl 1194.74012 Comput. Methods Appl. Mech. Eng. 197, No. 49-50, 4298-4306 (2008). MSC: 74A25 74S30 82B21 65Z05 70C20 70G75 PDF BibTeX XML Cite \textit{M. Arndt} and \textit{M. Luskin}, Comput. Methods Appl. Mech. Eng. 197, No. 49--50, 4298--4306 (2008; Zbl 1194.74012) Full Text: DOI arXiv