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Jump to: China Scholarship Council (CSC) | Department of Energy | Deutsche Forschungsgemeinschaft (DFG) | EPSRC | Engineering and Physical Sciences Research Council (EPSRC) | European Research Council (ERC) | European Union (EU) | Fifth Framework Programme (European Commission) (FP5) | Fonds zur Förderung der Wissenschaftlichen Forschung (Austria) (FWF) | France. Agence nationale de la recherche (ANR) | Great Britain. Department of the Environment (DOE) | Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC) | Harvard University. Radcliffe Institute for Advanced Study | Hausdorff Institute of Mathematics (Bonn, Germany) | Institute for Mathematics and Its Applications (IMA) | Leverhulme Trust (LT) | NSF | National Research Foundation of Korea (NRF) | National Science Foundation (U.S.) (NSF) | National Science Foundation (U.S.). Partnerships for International Research and Education (PIRE) | National Science Foundation. Partnerships for International Research and Education (U.S.) (NSF PIRE) | Oxford Centre for Nonlinear PDE | PIRE | Seventh Framework Programme (European Commission) (FP7) | Sichuan da xue [Sichuan University] | Türkiye Bilimsel ve Teknolojik Araştırma Kurumu [Scientific and Technological Research Council of Turkey] (TÜBİTAK) | United States. Air Force. Office of Scientific Research (AFOSR) | United States. Army Research Office (ARO) | United States. Department of Energy | University of California, Los Angeles. Institute for Pure & Applied Mathematics | University of Minnesota | University of Minnesota Supercomputing Institute | University of Minnesota. Supercomputer Institute | University of Oxford | University of Warwick Mathematics and Statistics Doctoral Training Centre (MASDOC)
Number of items: 137.
China Scholarship Council (CSC)
Ortner, Christoph and Wang, Hoa (2013) A posteriori error control for a quasi-continuum approximation of a periodic chain. IMA Journal of Numerical Analysis, Volume 34 (Number 3). pp. 977-1001. doi:10.1093/imanum/drt011 ISSN 0272-4979.
Ortner, Christoph and Wang, Hao (2011) A priori error estimates for energy-based quasicontinuum approximations of a periodic chain. Mathematical Models and Methods in Applied Sciences, Volume 21 (Number 12). pp. 2491-2521. doi:10.1142/S0218202511005817 ISSN 0218-2025.
Department of Energy
Koten, Brian Van and Ortner, Christoph (2012) Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1203.5854v1).
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2011) Positive-definiteness of the blended force-based quasicontinuum method. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.2528v1).
Deutsche Forschungsgemeinschaft (DFG)
Mielke, Alexander, Ortner, Christoph and Şengül, Yasemin (2014) An approach to nonlinear viscoelasticity via metric gradient flows. SIAM Journal on Mathematical Analysis, Volume 46 (Number 2). pp. 1317-1347. doi:10.1137/130927632 ISSN 0036-1410.
Ortner, Christoph and Wollner, W. (2011) A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state. Numerische Mathematik, Volume 118 (Number 3). pp. 587-600. doi:10.1007/s00211-011-0360-9 ISSN 0029-599X.
Bartels, Sören, Müller, Rüdiger and Ortner, Christoph (2011) Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes. SIAM Journal on Numerical Analysis, Volume 49 (Number 1). pp. 110-134. doi:10.1137/090751530 ISSN 0036-1429.
Carstensen, Carsten and Ortner, Christoph (2010) Analysis of a class of penalty methods for computing singular minimizers. Computational Methods in Applied Mathematics, Volume 10 (Number 2). pp. 137-163. ISSN 1609-4840.
EPSRC
Ortner, Christoph and Shapeev, A. V. (2012) Interpolants of lattice functions for the analysis of atomistic/continuum multiscale methods. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1204.3705v1).
Ortner, Christoph and Theil, Florian (2012) Nonlinear elasticity from atomistic mechanics. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1202.3858v3).
Koten, Brian Van and Ortner, Christoph (2012) Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1203.5854v1).
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2011) Positive-definiteness of the blended force-based quasicontinuum method. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.2528v1).
Langwallner, Bernhard, Ortner, Christoph and Süli, Endre (2011) Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.0746v1).
Jayawardana, K., Mordacq, C., Ortner, Christoph and Park, H. S. (2011) An analysis of surface relaxation in the surface cauchy-born model. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.0683v1).
Ortner, Christoph and Zhang, Lei (2011) Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces : a 2D model problem. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1110.0168v1).
Dobson, Matthew, Ortner, Christoph and Shapeev, A. V. (2010) The spectrum of the force-based quasicontinuum operator for a homogenous periodic chain. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1004.3435v1).
Engineering and Physical Sciences Research Council (EPSRC)
Chen, Huajie and Ortner, Christoph (2017) QM/MM methods for crystalline defects. Part 2 : Consistent energy and force-mixing. Multiscale Modeling & Simulation, 15 (1). pp. 184-214. doi:10.1137/15M1041250 ISSN 1540-3459.
Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V. and Van Koten, Brian (2016) Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134 (2). pp. 275-326. doi:10.1007/s00211-015-0772-z ISSN 0029-599X.
Gould, Nicholas, Ortner, Christoph and Packwood, David (2016) A dimer-type saddle search algorithm with preconditioning and linesearch. Mathematics of Computation, 85 . pp. 2939-2966. doi:10.1090/mcom/3096 ISSN 0025-5718.
Chen, Huajie and Ortner, Christoph (2016) QM/MM methods for crystalline defects. Part 1 : Locality of the tight binding model. Multiscale Modeling & Simulation, 14 (1). pp. 232-264. doi:10.1137/15M1022628 ISSN 1540-3459.
Ortner, Christoph and Zhang, Lei (2016) Atomistic/Continuum blending with ghost force correction. SIAM Journal Scientific Computing, 38 (1). A346-A375. doi:10.1137/15M1020241 ISSN 1064-8275 .
Ortner, Christoph, Shapeev, A. V. and Zhang, L. (2014) (In-)stability and stabilisation of QNL-type atomistic-to-continuum coupling methods. Multiscale Modeling & Simulation: a SIAM Interdisciplinary Journal , 12 (3). pp. 1258-1293. doi:10.1137/130933873 ISSN 1540-3459.
Hudson, Thomas and Ortner, Christoph (2014) Existence and stability of a screw dislocation under anti-plane deformation. Archive for Rational Mechanics and Analysis, 213 (3). pp. 887-929. doi:10.1007/s00205-014-0746-9 ISSN 0003-9527.
Li, Xingjie Helen, Luskin, Mitchell Barry, Ortner, Christoph and Shapeev, A. V. (2014) Theory-based benchmarking of the blended force-based quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 268 . pp. 763-781. doi:10.1016/j.cma.2013.10.007 ISSN 0045-7825.
Mielke, Alexander, Ortner, Christoph and Şengül, Yasemin (2014) An approach to nonlinear viscoelasticity via metric gradient flows. SIAM Journal on Mathematical Analysis, Volume 46 (Number 2). pp. 1317-1347. doi:10.1137/130927632 ISSN 0036-1410.
Ortner, Christoph and Wang, Hoa (2013) A posteriori error control for a quasi-continuum approximation of a periodic chain. IMA Journal of Numerical Analysis, Volume 34 (Number 3). pp. 977-1001. doi:10.1093/imanum/drt011 ISSN 0272-4979.
Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. doi:10.1017/S0962492913000068 ISSN 0962-4929.
Ortner, Christoph and Shapeev, A. V. (2013) Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice. Mathematics of Computation, Volume 82 (Number 284). pp. 2191-2236. doi:10.1090/S0025-5718-2013-02687-7 ISSN 0025-5718.
Ortner, Christoph and Theil, Florian (2013) Justification of the Cauchy-Born approximation of elastodynamics. Archive for Rational Mechanics and Analysis, Volume 207 (Number 3). pp. 1025-1073. doi:10.1007/s00205-012-0592-6 ISSN 0003-9527.
Burke, Siobhan, Ortner, Christoph and Süli, Endre (2013) An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional. Mathematical Models and Methods in Applied Sciences, Volume 23 (Number 9). pp. 1663-1697. doi:10.1142/S021820251350019X ISSN 0218-2025.
Luskin, Mitchell Barry, Ortner, Christoph and Van Koten, B. (2013) Formulation and optimization of the energy-based blended quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 253 (Number 1). pp. 160-168. doi:10.1016/j.cma.2012.09.007 ISSN 0045-7825.
Jayawardana, Kavinda, Mordacq, Christelle, Ortner, Christoph and Park, Harold S. (2013) An analysis of the boundary layer in the 1D surface Cauchy–Born model. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (Number 1). pp. 109-123. doi:10.1051/m2an/2012021 ISSN 0764-583X.
Langwallner, Bernhard, Ortner, Christoph and Süli, Endre (2013) Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory. Multiscale Modeling & Simulation, Volume 11 (Number 1). pp. 59-91. doi:10.1137/110857787 ISSN 1540-3459.
Koten, Brian Van and Ortner, Christoph (2013) Symmetries of 2-lattices and second order accuracy of the Cauchy-Born model. Multiscale Modeling & Simulation, Volume 11 (Number 2). pp. 615-634. doi:10.1137/120870220 ISSN 1540-3459.
Ortner, Christoph and Zhang, L. (2012) Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces : a two-dimensional model problem. SIAM Journal on Numerical Analysis, Volume 50 (Number 6). pp. 2940-2965. doi:10.1137/110851791 ISSN 0036-1429.
Dobson, Matthew, Ortner, Christoph and Shapeev, A. V. (2012) The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 744-765. doi:10.1137/110825704 ISSN 1540-3459.
Ortner, Christoph (2012) The role of the patch test in 2D atomistic-to-continuum coupling methods. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 46 (Number 6). pp. 1275-1319. doi:10.1051/m2an/2012005 ISSN 0764-583X.
Hudson, Thomas and Ortner, Christoph (2012) On the stability of Bravais lattices and their Cauchy–Born approximations. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 46 (Number 1). pp. 81-110. doi:10.1051/m2an/2011014 ISSN 0764-583X.
Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331-368. ISBN 9783642219429
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. doi:10.1137/110859270 ISSN 1540-3459.
Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) A computational and theoretical investigation of the accuracy of quasicontinuum methods. In: Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, 1972-, (eds.) Numerical analysis of multiscale problems. Lecture notes in computational science and engineering, Volume 83 . Berlin: Springer, pp. 67-96. ISBN 9783642220609
Makridakis , C. , Ortner, Christoph and Süli, Endre (2011) A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Numerische Mathematik, Volume 119 (Number 1). pp. 83-121. doi:10.1007/s00211-011-0380-5 ISSN 0029-599X.
Ortner, Christoph (2011) Nonconforming finite-element discretization of convex variational problems. IMA Journal of Numerical Analysis, Volume 31 (Number 3). pp. 847-864. doi:10.1093/imanum/drq004 ISSN 0272-4979.
Ortner, Christoph and Wollner, W. (2011) A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state. Numerische Mathematik, Volume 118 (Number 3). pp. 587-600. doi:10.1007/s00211-011-0360-9 ISSN 0029-599X.
Ortner, Christoph and Praetorius, Dirk (2011) On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems. SIAM Journal on Numerical Analysis, Volume 49 (Number 1). pp. 346-367. doi:10.1137/090781073 ISSN 0036-1429.
Ortner, Christoph (2011) A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D. Mathematics of Computation, Volume 80 (Number 275). pp. 1265-1285. doi:10.1090/S0025-5718-2010-02453-6 ISSN 0025-5718.
Ortner, Christoph and Wang, Hao (2011) A priori error estimates for energy-based quasicontinuum approximations of a periodic chain. Mathematical Models and Methods in Applied Sciences, Volume 21 (Number 12). pp. 2491-2521. doi:10.1142/S0218202511005817 ISSN 0218-2025.
Langwallner, Bernhard, Ortner, Christoph and Süli, Endre (2010) Existence and convergence results for the Galerkin approximation of an electronic density functional. Mathematical Models and Methods in Applied Sciences, Volume 20 (Number 12). pp. 2237-2265. doi:10.1142/S021820251000491X ISSN 0218-2025.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Volume 58 (Number 10). pp. 1741-1757. doi:10.1016/j.jmps.2010.06.011 ISSN 0022-5096.
Burke, Siobhan, Ortner, Christoph and Süli, Endre (2010) An adaptive finite element approximation of a variational model of brittle fracture. SIAM Journal on Numerical Analysis, Volume 48 (Number 3). pp. 980-1012. doi:10.1137/080741033 ISSN 0036-1429.
Larsen, Christopher J., Ortner, Christoph and Süli, Endre (2010) Existence of solutions to a regularized model of dynamic fracture. Mathematical Models and Methods in Applied Sciences, Volume 20 (Number 7). pp. 1021-1048. doi:10.1142/S0218202510004520 ISSN 0218-2025.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, Volume 197 (Number 1). pp. 179-202. doi:10.1007/s00205-009-0276-z ISSN 0003-9527.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Volume 8 (Number 3). pp. 782-802. doi:10.1137/090767005 ISSN 1540-3459.
Carstensen, Carsten and Ortner, Christoph (2010) Analysis of a class of penalty methods for computing singular minimizers. Computational Methods in Applied Mathematics, Volume 10 (Number 2). pp. 137-163. ISSN 1609-4840.
Luskin, Mitchell Barry and Ortner, Christoph (2009) An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 4). pp. 3070-3086. doi:10.1137/080743391 ISSN 0036-1429.
European Research Council (ERC)
Olson, Derek and Ortner, Christoph (2017) Regularity and locality of point defects in multilattices. Applied Mathematics Research eXpress, 2017 (2). pp. 297-337. doi:10.1093/amrx/abw012 ISSN 1687-1200.
Chen, Huajie and Ortner, Christoph (2017) QM/MM methods for crystalline defects. Part 2 : Consistent energy and force-mixing. Multiscale Modeling & Simulation, 15 (1). pp. 184-214. doi:10.1137/15M1041250 ISSN 1540-3459.
Massatt, D., Luskin, M. and Ortner, Christoph (2017) Electronic density of states for incommensurate layers. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 15 (1). pp. 476-499. doi:10.1137/16M1088363 ISSN 1540-3459.
Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V. and Van Koten, Brian (2016) Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134 (2). pp. 275-326. doi:10.1007/s00211-015-0772-z ISSN 0029-599X.
Chen, Huajie and Ortner, Christoph (2016) QM/MM methods for crystalline defects. Part 1 : Locality of the tight binding model. Multiscale Modeling & Simulation, 14 (1). pp. 232-264. doi:10.1137/15M1022628 ISSN 1540-3459.
Mielke, Alexander, Ortner, Christoph and Şengül, Yasemin (2014) An approach to nonlinear viscoelasticity via metric gradient flows. SIAM Journal on Mathematical Analysis, Volume 46 (Number 2). pp. 1317-1347. doi:10.1137/130927632 ISSN 0036-1410.
European Union (EU)
Ortner, Christoph and Süli, Endre (2007) Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. SIAM Journal on Numerical Analysis, Volume 45 (Number 4). pp. 1370-1397. doi:10.1137/06067119X ISSN 0036-1429.
Fifth Framework Programme (European Commission) (FP5)
Negri, Matteo and Ortner, Christoph (2008) Quasi-static crack propagation by Griffith's criterion. Mathematical Models and Methods in Applied Sciences, Volume 18 (Number 11). pp. 1895-1925. doi:10.1142/S0218202508003236 ISSN 0218-2025.
Fonds zur Förderung der Wissenschaftlichen Forschung (Austria) (FWF)
Ferraz-Leite, S., Ortner, Christoph and Praetorius, Dirk (2008) Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators. Numerische Mathematik, Volume 116 (Number 2). pp. 291-316. doi:10.1007/s00211-010-0292-9 ISSN 0029-599X.
France. Agence nationale de la recherche (ANR)
Dobson, Matthew, Ortner, Christoph and Shapeev, A. V. (2012) The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 744-765. doi:10.1137/110825704 ISSN 1540-3459.
Great Britain. Department of the Environment (DOE)
Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. doi:10.1017/S0962492913000068 ISSN 0962-4929.
Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC)
Ortner, Christoph and Zhang, Lei (2016) Atomistic/Continuum blending with ghost force correction. SIAM Journal Scientific Computing, 38 (1). A346-A375. doi:10.1137/15M1020241 ISSN 1064-8275 .
Harvard University. Radcliffe Institute for Advanced Study
Massatt, D., Luskin, M. and Ortner, Christoph (2017) Electronic density of states for incommensurate layers. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 15 (1). pp. 476-499. doi:10.1137/16M1088363 ISSN 1540-3459.
Hausdorff Institute of Mathematics (Bonn, Germany)
Carstensen, Carsten and Ortner, Christoph (2010) Analysis of a class of penalty methods for computing singular minimizers. Computational Methods in Applied Mathematics, Volume 10 (Number 2). pp. 137-163. ISSN 1609-4840.
Institute for Mathematics and Its Applications (IMA)
Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331-368. ISBN 9783642219429
Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) A computational and theoretical investigation of the accuracy of quasicontinuum methods. In: Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, 1972-, (eds.) Numerical analysis of multiscale problems. Lecture notes in computational science and engineering, Volume 83 . Berlin: Springer, pp. 67-96. ISBN 9783642220609
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Volume 58 (Number 10). pp. 1741-1757. doi:10.1016/j.jmps.2010.06.011 ISSN 0022-5096.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, Volume 197 (Number 1). pp. 179-202. doi:10.1007/s00205-009-0276-z ISSN 0003-9527.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Volume 8 (Number 3). pp. 782-802. doi:10.1137/090767005 ISSN 1540-3459.
Luskin, Mitchell Barry and Ortner, Christoph (2009) An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 4). pp. 3070-3086. doi:10.1137/080743391 ISSN 0036-1429.
Leverhulme Trust (LT)
Chen, Huajie and Ortner, Christoph (2017) QM/MM methods for crystalline defects. Part 2 : Consistent energy and force-mixing. Multiscale Modeling & Simulation, 15 (1). pp. 184-214. doi:10.1137/15M1041250 ISSN 1540-3459.
Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V. and Van Koten, Brian (2016) Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134 (2). pp. 275-326. doi:10.1007/s00211-015-0772-z ISSN 0029-599X.
Chen, Huajie and Ortner, Christoph (2016) QM/MM methods for crystalline defects. Part 1 : Locality of the tight binding model. Multiscale Modeling & Simulation, 14 (1). pp. 232-264. doi:10.1137/15M1022628 ISSN 1540-3459.
Mielke, Alexander, Ortner, Christoph and Şengül, Yasemin (2014) An approach to nonlinear viscoelasticity via metric gradient flows. SIAM Journal on Mathematical Analysis, Volume 46 (Number 2). pp. 1317-1347. doi:10.1137/130927632 ISSN 0036-1410.
NSF
Jayawardana, K., Mordacq, C., Ortner, Christoph and Park, H. S. (2011) An analysis of surface relaxation in the surface cauchy-born model. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.0683v1).
Dobson, Matthew, Ortner, Christoph and Shapeev, A. V. (2010) The spectrum of the force-based quasicontinuum operator for a homogenous periodic chain. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1004.3435v1).
National Research Foundation of Korea (NRF)
Carstensen, Carsten and Ortner, Christoph (2010) Analysis of a class of penalty methods for computing singular minimizers. Computational Methods in Applied Mathematics, Volume 10 (Number 2). pp. 137-163. ISSN 1609-4840.
National Science Foundation (U.S.) (NSF)
Massatt, D., Luskin, M. and Ortner, Christoph (2017) Electronic density of states for incommensurate layers. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 15 (1). pp. 476-499. doi:10.1137/16M1088363 ISSN 1540-3459.
Li, Xingjie Helen, Luskin, Mitchell Barry, Ortner, Christoph and Shapeev, A. V. (2014) Theory-based benchmarking of the blended force-based quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 268 . pp. 763-781. doi:10.1016/j.cma.2013.10.007 ISSN 0045-7825.
Luskin, Mitchell Barry, Ortner, Christoph and Van Koten, B. (2013) Formulation and optimization of the energy-based blended quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 253 (Number 1). pp. 160-168. doi:10.1016/j.cma.2012.09.007 ISSN 0045-7825.
Jayawardana, Kavinda, Mordacq, Christelle, Ortner, Christoph and Park, Harold S. (2013) An analysis of the boundary layer in the 1D surface Cauchy–Born model. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (Number 1). pp. 109-123. doi:10.1051/m2an/2012021 ISSN 0764-583X.
Koten, Brian Van and Ortner, Christoph (2013) Symmetries of 2-lattices and second order accuracy of the Cauchy-Born model. Multiscale Modeling & Simulation, Volume 11 (Number 2). pp. 615-634. doi:10.1137/120870220 ISSN 1540-3459.
Dobson, Matthew, Ortner, Christoph and Shapeev, A. V. (2012) The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 744-765. doi:10.1137/110825704 ISSN 1540-3459.
Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331-368. ISBN 9783642219429
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. doi:10.1137/110859270 ISSN 1540-3459.
Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) A computational and theoretical investigation of the accuracy of quasicontinuum methods. In: Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, 1972-, (eds.) Numerical analysis of multiscale problems. Lecture notes in computational science and engineering, Volume 83 . Berlin: Springer, pp. 67-96. ISBN 9783642220609
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Volume 58 (Number 10). pp. 1741-1757. doi:10.1016/j.jmps.2010.06.011 ISSN 0022-5096.
Larsen, Christopher J., Ortner, Christoph and Süli, Endre (2010) Existence of solutions to a regularized model of dynamic fracture. Mathematical Models and Methods in Applied Sciences, Volume 20 (Number 7). pp. 1021-1048. doi:10.1142/S0218202510004520 ISSN 0218-2025.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, Volume 197 (Number 1). pp. 179-202. doi:10.1007/s00205-009-0276-z ISSN 0003-9527.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Volume 8 (Number 3). pp. 782-802. doi:10.1137/090767005 ISSN 1540-3459.
Luskin, Mitchell Barry and Ortner, Christoph (2009) An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 4). pp. 3070-3086. doi:10.1137/080743391 ISSN 0036-1429.
National Science Foundation (U.S.). Partnerships for International Research and Education (PIRE)
Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. doi:10.1017/S0962492913000068 ISSN 0962-4929.
National Science Foundation. Partnerships for International Research and Education (U.S.) (NSF PIRE)
Olson, Derek and Ortner, Christoph (2017) Regularity and locality of point defects in multilattices. Applied Mathematics Research eXpress, 2017 (2). pp. 297-337. doi:10.1093/amrx/abw012 ISSN 1687-1200.
Oxford Centre for Nonlinear PDE
Jayawardana, Kavinda, Mordacq, Christelle, Ortner, Christoph and Park, Harold S. (2013) An analysis of the boundary layer in the 1D surface Cauchy–Born model. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (Number 1). pp. 109-123. doi:10.1051/m2an/2012021 ISSN 0764-583X.
PIRE
Koten, Brian Van and Ortner, Christoph (2012) Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1203.5854v1).
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2011) Positive-definiteness of the blended force-based quasicontinuum method. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1112.2528v1).
Seventh Framework Programme (European Commission) (FP7)
Makridakis , C. , Ortner, Christoph and Süli, Endre (2011) A priori error analysis of two force-based atomistic/continuum models of a periodic chain. Numerische Mathematik, Volume 119 (Number 1). pp. 83-121. doi:10.1007/s00211-011-0380-5 ISSN 0029-599X.
Sichuan da xue [Sichuan University]
Ortner, Christoph and Wang, Hoa (2013) A posteriori error control for a quasi-continuum approximation of a periodic chain. IMA Journal of Numerical Analysis, Volume 34 (Number 3). pp. 977-1001. doi:10.1093/imanum/drt011 ISSN 0272-4979.
Türkiye Bilimsel ve Teknolojik Araştırma Kurumu [Scientific and Technological Research Council of Turkey] (TÜBİTAK)
Mielke, Alexander, Ortner, Christoph and Şengül, Yasemin (2014) An approach to nonlinear viscoelasticity via metric gradient flows. SIAM Journal on Mathematical Analysis, Volume 46 (Number 2). pp. 1317-1347. doi:10.1137/130927632 ISSN 0036-1410.
United States. Air Force. Office of Scientific Research (AFOSR)
Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V. and Van Koten, Brian (2016) Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134 (2). pp. 275-326. doi:10.1007/s00211-015-0772-z ISSN 0029-599X.
Ortner, Christoph, Shapeev, A. V. and Zhang, L. (2014) (In-)stability and stabilisation of QNL-type atomistic-to-continuum coupling methods. Multiscale Modeling & Simulation: a SIAM Interdisciplinary Journal , 12 (3). pp. 1258-1293. doi:10.1137/130933873 ISSN 1540-3459.
Li, Xingjie Helen, Luskin, Mitchell Barry, Ortner, Christoph and Shapeev, A. V. (2014) Theory-based benchmarking of the blended force-based quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 268 . pp. 763-781. doi:10.1016/j.cma.2013.10.007 ISSN 0045-7825.
Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. doi:10.1017/S0962492913000068 ISSN 0962-4929.
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. doi:10.1137/110859270 ISSN 1540-3459.
United States. Army Research Office (ARO)
Massatt, D., Luskin, M. and Ortner, Christoph (2017) Electronic density of states for incommensurate layers. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 15 (1). pp. 476-499. doi:10.1137/16M1088363 ISSN 1540-3459.
United States. Department of Energy
Li, Xingjie Helen, Luskin, Mitchell Barry, Ortner, Christoph and Shapeev, A. V. (2014) Theory-based benchmarking of the blended force-based quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 268 . pp. 763-781. doi:10.1016/j.cma.2013.10.007 ISSN 0045-7825.
Luskin, Mitchell Barry, Ortner, Christoph and Van Koten, B. (2013) Formulation and optimization of the energy-based blended quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 253 (Number 1). pp. 160-168. doi:10.1016/j.cma.2012.09.007 ISSN 0045-7825.
Koten, Brian Van and Ortner, Christoph (2013) Symmetries of 2-lattices and second order accuracy of the Cauchy-Born model. Multiscale Modeling & Simulation, Volume 11 (Number 2). pp. 615-634. doi:10.1137/120870220 ISSN 1540-3459.
Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331-368. ISBN 9783642219429
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. doi:10.1137/110859270 ISSN 1540-3459.
Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) A computational and theoretical investigation of the accuracy of quasicontinuum methods. In: Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, 1972-, (eds.) Numerical analysis of multiscale problems. Lecture notes in computational science and engineering, Volume 83 . Berlin: Springer, pp. 67-96. ISBN 9783642220609
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Volume 58 (Number 10). pp. 1741-1757. doi:10.1016/j.jmps.2010.06.011 ISSN 0022-5096.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, Volume 197 (Number 1). pp. 179-202. doi:10.1007/s00205-009-0276-z ISSN 0003-9527.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Volume 8 (Number 3). pp. 782-802. doi:10.1137/090767005 ISSN 1540-3459.
Luskin, Mitchell Barry and Ortner, Christoph (2009) An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 4). pp. 3070-3086. doi:10.1137/080743391 ISSN 0036-1429.
University of California, Los Angeles. Institute for Pure & Applied Mathematics
Luskin, Mitchell Barry and Ortner, Christoph (2013) Atomistic-to-continuum coupling. Acta Numerica, Volume 22 . pp. 397-508. doi:10.1017/S0962492913000068 ISSN 0962-4929.
University of Minnesota
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Volume 58 (Number 10). pp. 1741-1757. doi:10.1016/j.jmps.2010.06.011 ISSN 0022-5096.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, Volume 197 (Number 1). pp. 179-202. doi:10.1007/s00205-009-0276-z ISSN 0003-9527.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Volume 8 (Number 3). pp. 782-802. doi:10.1137/090767005 ISSN 1540-3459.
University of Minnesota Supercomputing Institute
Koten, Brian Van and Ortner, Christoph (2012) Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1203.5854v1).
University of Minnesota. Supercomputer Institute
Luskin, Mitchell Barry, Ortner, Christoph and Van Koten, B. (2013) Formulation and optimization of the energy-based blended quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, Volume 253 (Number 1). pp. 160-168. doi:10.1016/j.cma.2012.09.007 ISSN 0045-7825.
Koten, Brian Van and Ortner, Christoph (2013) Symmetries of 2-lattices and second order accuracy of the Cauchy-Born model. Multiscale Modeling & Simulation, Volume 11 (Number 2). pp. 615-634. doi:10.1137/120870220 ISSN 1540-3459.
Luskin, Mitchell Barry and Ortner, Christoph (2012) Linear stationary iterative methods for the force-based quasicontinuum approximation. In: Engquist, Björn, 1945- and Runborg, Olof and Tsai, Yen-Hsi R., (eds.) Numerical Analysis of Multiscale Computations. Lecture notes in computational science and engineering, Volume 82 . Berlin: Springer, pp. 331-368. ISBN 9783642219429
Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) Positive definiteness of the blended force-based quasicontinuum method. Multiscale Modeling & Simulation, Volume 10 (Number 3). pp. 1023-1045. doi:10.1137/110859270 ISSN 1540-3459.
Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) A computational and theoretical investigation of the accuracy of quasicontinuum methods. In: Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, 1972-, (eds.) Numerical analysis of multiscale problems. Lecture notes in computational science and engineering, Volume 83 . Berlin: Springer, pp. 67-96. ISBN 9783642220609
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, Volume 58 (Number 10). pp. 1741-1757. doi:10.1016/j.jmps.2010.06.011 ISSN 0022-5096.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, Volume 197 (Number 1). pp. 179-202. doi:10.1007/s00205-009-0276-z ISSN 0003-9527.
Dobson, Matthew, Luskin, Mitchell Barry and Ortner, Christoph (2010) Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation. Multiscale Modeling & Simulation, Volume 8 (Number 3). pp. 782-802. doi:10.1137/090767005 ISSN 1540-3459.
Luskin, Mitchell Barry and Ortner, Christoph (2009) An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 4). pp. 3070-3086. doi:10.1137/080743391 ISSN 0036-1429.
University of Oxford
Ortner, Christoph and Wang, Hoa (2013) A posteriori error control for a quasi-continuum approximation of a periodic chain. IMA Journal of Numerical Analysis, Volume 34 (Number 3). pp. 977-1001. doi:10.1093/imanum/drt011 ISSN 0272-4979.
Ortner, Christoph and Wang, Hao (2011) A priori error estimates for energy-based quasicontinuum approximations of a periodic chain. Mathematical Models and Methods in Applied Sciences, Volume 21 (Number 12). pp. 2491-2521. doi:10.1142/S0218202511005817 ISSN 0218-2025.
University of Warwick Mathematics and Statistics Doctoral Training Centre (MASDOC)
Dedner, Andreas, Ortner, Christoph and Wu, H. (2017) Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. ESAIM: Mathematical Modelling and Numerical Analysis, 51 (6). pp. 2263-2288. doi:10.1051/m2an/2017013 ISSN 0764-583X.
This list was generated on Thu Mar 28 18:09:13 2024 GMT.