@misc{2026-dataaug,
title = {The High Cost of Data Augmentation for Learning Equivariant Models},
author = {Klintebäck, Henri and Ortner, Christoph and Silberman, Lior},
year = {2026},
url = {https://arxiv.org/abs/2602.03118},
pdf = {https://arxiv.org/pdf/2602.03118}
}
@misc{2026-mace-magnetic,
title = {Equivariant Many-body Message Passing Interatomic Potentials for Magnetic Materials},
author = {Ho, Cheuk Hin and van der Oord, Cas and Darby, James P. and Keane, Theo and Benson, Raz L. and Rebolledo Espinoza, Cristian and Kulkarni, Rutvij and Spinu, Elina and Papanikolaou, Michail and Tomsett, Richard and Forrest, Robert M. and Bean, Jonathan J. and Csányi, Gábor and Ortner, Christoph},
year = {2026},
url = {https://arxiv.org/abs/2604.08143},
pdf = {https://arxiv.org/pdf/2604.08143}
}
@article{2026-regulpriors,
title = {Regularity Priors for the Linear Atomic Cluster Expansion},
author = {Darby, James P. and Morrow, Joe D. and Bartók, Albert P. and Deringer, Volker L. and Csányi, Gábor and Ortner, Christoph},
year = {2026},
journal = {Mach. Learn.: Sci. Technol.},
volume = {7},
pages = {025063},
url = {https://arxiv.org/abs/2601.15072},
pdf = {https://arxiv.org/pdf/2601.15072},
doi = {10.1088/2632-2153/ae55fa}
}
@misc{2025-wssr,
title = {Stochastic Reconfiguration with Warm-Started SVD},
author = {Zhou, Dexuan and Chen, Huajie and Ho, Cheuk Hin and Liu, Xin and Ortner, Christoph},
year = {2025},
url = {https://arxiv.org/abs/2512.05749},
pdf = {https://arxiv.org/pdf/2512.05749}
}
@misc{2025-flexcalib,
title = {Flexible Uncertainty Calibration for Machine-Learned Interatomic Potentials},
author = {Ho, Cheuk Hin and Ortner, Christoph and Wang, Yangshuai},
year = {2025},
url = {https://arxiv.org/abs/2510.00721},
pdf = {https://arxiv.org/pdf/2510.00721}
}
@misc{2025-transferintegrals,
title = {Machine learning intermolecular transfer integrals with compact atomic cluster representations},
author = {Keeratikarn, Keerati and Ortner, Christoph and Frost, Jarvist Moore},
year = {2025},
url = {https://arxiv.org/abs/2511.06551},
pdf = {https://arxiv.org/pdf/2511.06551}
}
@article{2025-ace-tmg-1,
title = {An Atomic Cluster Expansion Potential for Twisted Multilayer Graphene},
author = {Wang, Yangshuai and Clark, Drake and Das, Sambit and Zhu, Ziyan and Massatt, Daniel and Gavini, Vikram and Luskin, Mitchell and Ortner, Christoph},
year = {2025},
journal = {Mach. Learn.: Sci. Technol.},
volume = {6},
pages = {18976},
url = {https://arxiv.org/abs/2506.15061},
pdf = {https://arxiv.org/pdf/2506.15061},
doi = {10.1088/2632-2153/ae1807}
}
@article{2025-sparse-ace-1,
title = {Scalable Data-Driven Basis Selection for Linear Machine Learning Interatomic Potentials},
author = {Torabi, Tina and Militzer, Matthias and Friedlander, Michael P. and Ortner, Christoph},
year = {2026},
journal = {Mach. Learn.: Sci. Technol.},
volume = {7},
pages = {10769},
url = {https://arxiv.org/abs/2504.16418},
pdf = {https://arxiv.org/pdf/2504.16418},
doi = {10.1088/2632-2153/ae49e2}
}
@misc{2025-xmace-1,
title = {Transferable Machine Learning Potential X-MACE for Excited States using Integrated DeepSets},
author = {Barrett, Rhyan and Ortner, Christoph and Westermayr, Julia},
year = {2025},
url = {https://arxiv.org/abs/2502.12870},
pdf = {https://arxiv.org/pdf/2502.12870}
}
@misc{2025-acecg-1,
title = {Many-Body Coarse-Grained Molecular Dynamics with the Atomic Cluster Expansion},
author = {Wang, Yangshuai and Csanyi, Gabor and Ortner, Christoph},
year = {2025},
url = {https://arxiv.org/abs/2502.04661},
pdf = {https://arxiv.org/pdf/2502.04661}
}
@misc{2025-locality-indirect,
title = {Nearsightedness in Materials with Indirect Band Gaps},
author = {Chen, Huajie and Feng, Juerong and Ortner, Christoph and Thomas, Jack},
year = {2025},
url = {https://arxiv.org/abs/2501.01188},
pdf = {https://arxiv.org/pdf/2501.01188}
}
@article{2024-diffmatrixfunc,
title = {Fast automatically differentiable matrix functions and applications in molecular simulations},
author = {Torabi, Tina and Gutleb, Timon S and Ortner, Christoph},
year = {2025},
journal = {Comput. Phys. Commun.},
volume = {317},
pages = {109832},
url = {https://arxiv.org/abs/2412.12598},
pdf = {https://arxiv.org/pdf/2412.12598},
doi = {10.1016/j.cpc.2025.109832}
}
@article{2024-jrglasses,
title = {Analysis of local structure of mechanical and thermal rearrangements in glasses with the atomic cluster expansion},
author = {Rottler, Joerg and Ortner, Christoph},
year = {2024},
journal = {J. Phys. Chem. B},
volume = {128},
pages = {11492-11499},
url = {https://arxiv.org/abs/2410.03216},
pdf = {https://arxiv.org/pdf/2410.03216},
doi = {10.1021/acs.jpcb.4c06079}
}
@article{2024-friction1,
title = {Machine Learning Configuration-Dependent Friction Tensors in Langevin Heatbaths},
author = {Sachs, Matthias and Stark, Wojciech G. and Maurer, Reinhard J and Ortner, Christoph},
year = {2025},
journal = {Mach. Learn.: Sci. Technol.},
volume = {6},
pages = {6670},
url = {https://arxiv.org/abs/2407.13935},
pdf = {https://arxiv.org/pdf/2407.13935},
doi = {10.1088/2632-2153/ada248}
}
@article{2024-esps1,
title = {Parameterizing Intersecting Surfaces via Invariants},
author = {Gutleb, Timon S and Barrett, Rhyan and Westermayr, Julia and Ortner, Christoph},
year = {2026},
journal = {Linear Algebra Appl.},
volume = {745},
pages = {54--85},
url = {https://arxiv.org/abs/2407.03731},
pdf = {https://arxiv.org/pdf/2407.03731},
doi = {10.1016/j.laa.2026.05.009}
}
@article{2024-selfconsistent1,
title = {Self-consistent Coulomb interactions for machine learning interatomic potentials},
author = {Thomas, Jack and Baldwin, William J. and Csányi, Gábor and Ortner, Christoph},
year = {2025},
journal = {Nonlinearity},
volume = {38},
pages = {095024},
url = {https://arxiv.org/abs/2406.10915},
pdf = {https://arxiv.org/pdf/2406.10915},
doi = {10.1088/1361-6544/ae0402}
}
@article{2024-pureace,
title = {Atomic Cluster Expansion without Self-Interaction},
author = {Ho, Cheuk Hin and Gutleb, Timon S and Ortner, Christoph},
year = {2024},
journal = {J. Comput. Phys.},
volume = {515},
pages = {113271},
url = {https://arxiv.org/abs/2401.01550},
pdf = {https://arxiv.org/pdf/2401.01550},
doi = {10.1016/j.jcp.2024.113271}
}
@article{2024-entropy-ml,
title = {Surrogate models for vibrational entropy based on a spatial decomposition},
author = {Torabi, Tina and Wang, Yangshuai and Ortner, Christoph},
year = {2025},
journal = {Multiscale Model. Simul.},
volume = {23},
pages = {514-544},
url = {https://arxiv.org/abs/2402.12744},
pdf = {https://arxiv.org/pdf/2402.12744},
doi = {10.1137/24M165168X}
}
@article{2024-foundationmodel-v1,
title = {A foundation model for atomistic materials chemistry},
author = {Batatia, Ilyes and Benner, Philipp and Chiang, Yuan and Elena, Alin M. and Kovács, Dávid P. and Riebesell, Janosh and Advincula, Xavier R. and Asta, Mark and Avaylon, Matthew and Baldwin, William J. and Berger, Fabian and Bernstein, Noam and Bhowmik, Arghya and Bigi, Filippo and Blau, Samuel M. and Cărare, Vlad and Ceriotti, Michele and Chong, Sanggyu and Darby, James P. and De, Sandip and Della Pia, Flaviano and Deringer, Volker L. and Elijošius, Rokas and El-Machachi, Zakariya and Fako, Edvin and Falcioni, Fabio and Ferrari, Andrea C. and Gardner, John L. A. and Gawkowski, Mikołaj J. and Genreith-Schriever, Annalena and George, Janine and Goodall, Rhys E. A. and Grandel, Jonas and Grey, Clare P. and Grigorev, Petr and Han, Shuang and Handley, Will and Heenen, Hendrik H. and Hermansson, Kersti and Ho, Cheuk Hin and Hofmann, Stephan and Holm, Christian and Jaafar, Jad and Jakob, Konstantin S. and Jung, Hyunwook and Kapil, Venkat and Kaplan, Aaron D. and Karimitari, Nima and Kermode, James R. and Kourtis, Panagiotis and Kroupa, Namu and Kullgren, Jolla and Kuner, Matthew C. and Kuryla, Domantas and Liepuoniute, Guoda and Lin, Chen and Margraf, Johannes T. and Magdău, Ioan-Bogdan and Michaelides, Angelos and Moore, J. Harry and Naik, Aakash A. and Niblett, Samuel P. and Norwood, Sam Walton and O'Neill, Niamh and Ortner, Christoph and Persson, Kristin A. and Reuter, Karsten and Rosen, Andrew S. and Rosset, Louise A. M. and Schaaf, Lars L. and Schran, Christoph and Shi, Benjamin X. and Sivonxay, Eric and Stenczel, Tamás K. and Sutton, Christopher and Svahn, Viktor and Swinburne, Thomas D. and Tilly, Jules and van der Oord, Cas and Vargas, Santiago and Varga-Umbrich, Eszter and Vegge, Tejs and Vondrák, Martin and Wang, Yangshuai and Witt, William C. and Wolf, Thomas and Zills, Fabian and Csányi, Gábor},
year = {2026},
journal = {J. Chem. Phys.},
volume = {163},
pages = {184110},
url = {https://arxiv.org/abs/2401.00096},
pdf = {https://arxiv.org/pdf/2401.00096},
doi = {10.1063/5.0297006}
}
@article{2023-mlipsgen_disloc,
title = {A Theoretical Case Study of the Generalisation of Machine-learned Potentials},
author = {Wang, Yangshuai and Patel, Shashwat and Ortner, Christoph},
year = {2024},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {422},
pages = {116831},
url = {https://arxiv.org/abs/2311.01664},
pdf = {https://arxiv.org/pdf/2311.01664},
doi = {10.1016/j.cma.2024.116831}
}
@inproceedings{2023-EMFNs-1,
title = {Equivariant Matrix Function Neural Networks},
author = {Batatia, Ilyes and Schaaf, Lars Leon and Csanyi, Gabor and Ortner, Christoph and Faber, Felix Andreas},
year = {2024},
booktitle = {The Twelfth International Conference on Learning Representations}
}
@incollection{2023-tdl_review,
title = {Thermodynamic Limits of Electronic Systems},
author = {Gontier, David and Lu, Jianfeng and Ortner, Christoph},
year = {2023},
booktitle = {Density Functional Theory: Modeling, Mathematical Analysis, Computational Methods and Applications},
publisher = {Springer},
pages = {307-331},
url = {https://arxiv.org/abs/2309.05118},
pdf = {https://arxiv.org/pdf/2309.05118},
doi = {10.1007/978-3-031-22340-2_6}
}
@article{2023-acepotentials,
title = {ACEpotentials.jl: A Julia Implementation of the Atomic Cluster Expansion},
author = {Witt, William C. and van der Oord, Cas and Gelžinyté, Elena and Järvinen, Teemu and Ross, Andres and Darby, James P. and Ho, Cheuk Hin and Baldwin, William J. and Sachs, Matthias and Kermode, James and Bernstein, Noam and Csányi, Gábor and Ortner, Christoph},
year = {2023},
journal = {J. Chem. Phys.},
volume = {159},
pages = {164101},
url = {https://arxiv.org/abs/2309.03161},
pdf = {https://arxiv.org/pdf/2309.03161},
doi = {10.1063/5.0158783}
}
@article{2023-acecommentary,
title = {On the Atomic Cluster Expansion: interatomic potentials and beyond},
author = {Ortner, Christoph},
year = {2023},
journal = {KIM REVIEW},
volume = {1},
doi = {10.25950/c7f24234}
}
@misc{2023-bips-2,
title = {Retrieval of Boost Invariant Symbolic Observables via Feature Importance},
author = {Munoz, Jose M and Batatia, Ilyes and Ortner, Christoph and Romeo, Francesco},
year = {2023},
journal = {ArXiv e-prints},
url = {https://arxiv.org/abs/2306.13496},
pdf = {https://arxiv.org/pdf/2306.13496}
}
@inproceedings{2023-lie-mace,
title = {A general framework for equivariant neural networks on reductive lie groups},
author = {Batatia, Ilyes and Geiger, M. and Munoz, Jose and Smidt, T. and Silberman, L. and Ortner, Christoph},
year = {2024},
booktitle = {Proceedings of the 37th International Conference on Neural Information Processing Systems},
publisher = {Curran Associates Inc.},
pages = {55260-55284},
doi = {10.52202/075280-2412}
}
@article{2023-wf1d_vmc,
title = {A Multilevel Method for Many-Electron Schrödinger Equations Based on the Atomic Cluster Expansion},
author = {Zhou, Dexuan and Chen, Huajie and Ho, Cheuk Hin and Ortner, Christoph},
year = {2024},
journal = {SIAM J. Sci. Comput.},
volume = {46},
pages = {A105-A129},
url = {https://arxiv.org/abs/2304.04260},
pdf = {https://arxiv.org/pdf/2304.04260},
doi = {10.1137/23M1565887}
}
@article{2022-ffbc,
title = {Higher Order Far-Field Boundary Conditions for Crystalline Defects},
author = {Braun, Julian and Ortner, Christoph and Wang, Yangshuai and Zhang, Lei},
year = {2025},
journal = {SIAM J. Numer. Anal.},
volume = {63},
pages = {520-541},
url = {https://arxiv.org/abs/2210.05573},
pdf = {https://arxiv.org/pdf/2210.05573},
doi = {10.1137/24M165836X}
}
@article{2022-qmmm-apost-mlips,
title = {A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects},
author = {Wang, Yangshuai and Kermode, James R and Ortner, Christoph and Zhang, Lei},
year = {2024},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {428},
pages = {117097},
url = {https://arxiv.org/abs/2210.04856},
pdf = {https://arxiv.org/pdf/2210.04856},
doi = {10.1016/j.cma.2024.117097}
}
@article{2022-HAL1,
title = {Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials},
author = {van der Oord, Cas and Sachs, Matthias and Kovács, Dávid Péter and Ortner, Christoph and Csányi, Gábor},
year = {2023},
journal = {npj Computational Materials},
volume = {9},
pages = {168},
url = {https://arxiv.org/abs/2210.04225},
pdf = {https://arxiv.org/pdf/2210.04225},
doi = {10.1038/s41524-023-01104-6}
}
@article{2022-Gautam,
title = {Exploiting Machine Learning in Multiscale Modelling of Materials},
author = {Anand, Gautam and Ghosh, S. and Zhang, Liwei and Anupam, A. and Freeman, C. L. and Ortner, Christoph and Eisenbach, M. and Kermode, James R},
year = {2023},
journal = {J. Inst. Eng. India Ser. D},
volume = {104},
pages = {867-877},
doi = {10.1007/s40033-022-00424-z}
}
@article{2022-randomembedding,
title = {Tensor-reduced atomic density representations},
author = {Darby, J. P. and Kovács, Dávid Péter and Batatia, Ilyes and Caro, M. A. and Hart, G. L. W. and Ortner, Christoph and Csányi, Gábor},
year = {2023},
journal = {Phys. Rev. Lett.},
volume = {131},
pages = {028001},
url = {https://arxiv.org/abs/2210.01705},
pdf = {https://arxiv.org/pdf/2210.01705},
doi = {10.1103/PhysRevLett.131.028001}
}
@article{2022-generalisation1,
title = {A framework for a generalisation analysis of machine-learned interatomic potentials},
author = {Ortner, Christoph and Wang, Yangshuai},
year = {2023},
journal = {Multiscale Model. Simul.},
volume = {21},
pages = {1053-1080},
url = {https://arxiv.org/abs/2209.05366},
pdf = {https://arxiv.org/pdf/2209.05366},
doi = {10.1137/22M152267X}
}
@article{2022-bip1,
title = {Boost Invariant Polynomials for Efficient Jet Tagging},
author = {Munoz, Jose M and Batatia, Ilyes and Ortner, Christoph},
year = {2022},
journal = {Mach. Learn.: Sci. Technol.},
volume = {3},
pages = {04LT05},
url = {https://arxiv.org/abs/2207.08272},
pdf = {https://arxiv.org/pdf/2207.08272},
doi = {10.1088/2632-2153/aca9ca}
}
@misc{2022-wave1,
title = {Atomic cluster expansion and wave function representations},
author = {Drautz, Ralf and Ortner, Christoph},
year = {2022},
url = {https://arxiv.org/abs/2206.11375},
pdf = {https://arxiv.org/pdf/2206.11375}
}
@inproceedings{2022-MACE,
title = {MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields},
author = {Batatia, Ilyes and Kovacs, David P and Simm, Gregor and Ortner, Christoph and Csanyi, Gabor},
year = {2022},
booktitle = {Advances in Neural Information Processing Systems},
volume = {35},
pages = {11423-11436},
url = {https://arxiv.org/abs/2206.07697},
pdf = {https://arxiv.org/pdf/2206.07697},
doi = {10.52202/068431-0830}
}
@article{2022-mlACE-1,
title = {Multilayer atomic cluster expansion for semi-local interactions},
author = {Bochkarev, Anton and Lysogorskiy, Yury and Ortner, Christoph and Csányi, Gábor and Drautz, Ralf},
year = {2022},
journal = {Phys. Rev. Res.},
volume = {4},
pages = {L042019},
url = {https://arxiv.org/abs/2205.08177},
pdf = {https://arxiv.org/pdf/2205.08177},
doi = {10.1103/PhysRevResearch.4.L042019}
}
@article{2022-acempnn-framework,
title = {The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials},
author = {Batatia, Ilyes and Batzner, Simon and Kovács, Dávid Péter and Musaelian, Albert and Simm, Gregor N. C. and Drautz, Ralf and Ortner, Christoph and Kozinsky, Boris and Csányi, Gábor},
year = {2025},
journal = {Nature Machine Intelligence},
volume = {7},
pages = {56-67},
url = {https://arxiv.org/abs/2205.06643},
pdf = {https://arxiv.org/pdf/2205.06643},
doi = {10.1038/s42256-024-00956-x}
}
@misc{2022-mepconv,
title = {Convergence of the Discrete Minimum Energy Path},
author = {Liu, Xuanyu and Chen, Huajie and Ortner, Christoph},
year = {2022},
url = {https://arxiv.org/abs/2204.07467},
pdf = {https://arxiv.org/pdf/2204.07467}
}
@article{2022-mepstab,
title = {Stability of the Minimum Energy Path},
author = {Liu, Xuanyu and Chen, Huajie and Ortner, Christoph},
year = {2024},
journal = {Numer. Math.},
volume = {156},
pages = {39-70},
url = {https://arxiv.org/abs/2204.00984},
pdf = {https://arxiv.org/pdf/2204.00984},
doi = {10.1007/s00211-023-01391-7}
}
@article{2022-commentfingerprints,
title = {Comment on ``Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions''},
author = {Pozdnyakov, S. N. and Willatt, M. J. and Bartok, A. P. and Ortner, Christoph and Csanyi, Gabor and Ceriotti, Michele},
year = {2022},
journal = {J. Chem. Phys.},
volume = {157},
pages = {177101},
doi = {10.1063/5.0088404}
}
@article{2022-recursive,
title = {Optimal Evaluation of Symmetry-Adapted $n$-Correlations Via Recursive Contraction of Sparse Symmetric Tensors},
author = {Kaliuzhnyi, Illia and Ortner, Christoph},
year = {2025},
journal = {J. Numer. Math.},
volume = {33},
pages = {87-104},
url = {https://arxiv.org/abs/2202.04140},
pdf = {https://arxiv.org/pdf/2202.04140},
doi = {10.1515/jnma-2024-0025}
}
@article{2021-acetb1,
title = {Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models},
author = {Zhang, Liwei and Onat, Berk and Dusson, Geneviève and McSloy, Adam and Anand, Gautam and Maurer, Reinhard J and Ortner, Christoph and Kermode, James R},
year = {2022},
journal = {npj Computational Materials},
volume = {8},
pages = {158},
url = {https://arxiv.org/abs/2111.13736},
pdf = {https://arxiv.org/pdf/2111.13736},
doi = {10.1038/s41524-022-00843-2}
}
@article{2021-acemolecules,
title = {Linear Atomic Cluster Expansion Force Fields for Organic Molecules: beyond RMSE},
author = {Kovacs, David P and van der Oord, Cas and Kucera, J. and Allen, Alice and Cole, D. and Ortner, Christoph and Csanyi, Gabor},
year = {2021},
journal = {J. Chem. Theory Comput.},
volume = {17},
pages = {7696-7711},
doi = {10.1021/acs.jctc.1c00647}
}
@article{2021-apxsym,
title = {Polynomial Approximation of Symmetric Functions},
author = {Bachmayr, Markus and Dusson, Geneviève and Ortner, Christoph and Thomas, Jack},
year = {2024},
journal = {Math. Comp.},
volume = {93},
pages = {811-839},
url = {https://arxiv.org/abs/2109.14771},
pdf = {https://arxiv.org/pdf/2109.14771},
doi = {10.1090/mcom/3868}
}
@article{2021-sensitivity,
title = {Local invertibility and sensitivity of atomic structure-feature mappings},
author = {Pozdnyakov, Sergey N. and Zhang, Liwei and Ortner, Christoph and Csanyi, Gabor and Ceriotti, Michele},
year = {2021},
journal = {Open Res Europe},
volume = {1},
pages = {126},
url = {https://arxiv.org/abs/2109.11440},
pdf = {https://arxiv.org/pdf/2109.11440},
doi = {10.12688/openreseurope.14156.1}
}
@article{2021-defectexpansion,
title = {Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect},
author = {Braun, Julian and Hudson, Thomas and Ortner, Christoph},
year = {2022},
journal = {Arch. Ration. Mech. Anal.},
volume = {245},
pages = {1437-1490},
url = {https://arxiv.org/abs/2108.04765},
pdf = {https://arxiv.org/pdf/2108.04765},
doi = {10.1007/s00205-022-01810-3}
}
@article{2021-qmmm3,
title = {QM/MM Methods for Crystalline Defects. Part 3: Machine-Learned Interatomic Potentials},
author = {Chen, Huajie and Ortner, Christoph and Wang, Yangshuai},
year = {2023},
journal = {Multiscale Model. Simul.},
volume = {20},
pages = {1490-1518},
url = {https://arxiv.org/abs/2106.14559},
pdf = {https://arxiv.org/pdf/2106.14559},
doi = {10.1137/21M1441122}
}
@article{2021-tbmanybody,
title = {Body-Ordered Approximations of Atomic Properties},
author = {Thomas, Jack and Chen, Huajie and Ortner, Christoph},
year = {2022},
journal = {Arch. Ration. Mech. Anal.},
volume = {245},
pages = {1-60},
url = {https://arxiv.org/abs/2106.12572},
pdf = {https://arxiv.org/pdf/2106.12572},
doi = {10.1007/s00205-022-01809-w}
}
@article{2021-lavrentiev,
title = {Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap},
author = {Balci, Anna Kh and Ortner, Christoph and Storn, Johannes},
year = {2022},
journal = {Numer. Math.},
volume = {151},
pages = {779-805},
url = {https://arxiv.org/abs/2106.06837},
pdf = {https://arxiv.org/pdf/2106.06837},
doi = {10.1007/s00211-022-01303-1}
}
@article{2021-descriptors,
title = {Physics-inspired structural representations for molecules and materials},
author = {Musil, Felix and Grisafi, Andrea and Bartók, Albert P. and Ortner, Christoph and Csányi, Gábor and Ceriotti, Michele},
year = {2021},
journal = {Chem. Rev.},
volume = {121},
pages = {9759-9815},
url = {https://arxiv.org/abs/2101.04673},
pdf = {https://arxiv.org/pdf/2101.04673},
doi = {10.1021/acs.chemrev.1c00021}
}
@article{2020-apipsff,
title = {Atomic permutationally invariant polynomials for fitting molecular force fields},
author = {Allen, A. E. A. and Dusson, Geneviève and Ortner, Christoph and Csanyi, Gabor},
year = {2021},
journal = {Mach. Learn.: Sci. Technol.},
volume = {2},
pages = {025017},
doi = {10.1088/2632-2153/abd51e}
}
@article{2020-pace1,
title = {Performant implementation of the atomic cluster expansion (PACE): Application to copper and silicon},
author = {Lysogorskiy, Yury and van der Oord, Cas and Bochkarev, Anton and Menon, S. and Rinaldi, M. and Hammerschmidt, T. and Mrovec, M. and Thompson, A. and Csányi, Gábor and Ortner, Christoph and Drautz, Ralf},
year = {2021},
journal = {npj Computational Materials},
volume = {7},
pages = {97},
url = {https://arxiv.org/abs/2103.00814},
pdf = {https://arxiv.org/pdf/2103.00814},
doi = {10.1038/s41524-021-00559-9}
}
@article{2020-qmmmadaptfem,
title = {A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods},
author = {Wang, Yangshuai and Chen, Huajie and Liao, M. and Ortner, Christoph and Wang, Hao and Zhang, Lei},
year = {2021},
journal = {SIAM J. Sci. Comput.},
volume = {43},
pages = {A2785-A2808},
url = {https://arxiv.org/abs/2007.05260},
pdf = {https://arxiv.org/pdf/2007.05260},
doi = {10.1137/20M1353678}
}
@article{2020-sensitdesc,
title = {Sensitivity and Dimensionality of Atomic Environment Representations used for Machine Learning Interatomic Potentials},
author = {Onat, Berk and Ortner, Christoph and Kermode, James R},
year = {2020},
journal = {J. Chem. Phys.},
volume = {153},
pages = {144106},
url = {https://arxiv.org/abs/2006.01915},
pdf = {https://arxiv.org/pdf/2006.01915},
doi = {10.1063/5.0016005}
}
@article{2020-pointdeftbins,
title = {Point Defects in Tight Binding Models for Insulators},
author = {Ortner, Christoph and Thomas, Jack},
year = {2020},
journal = {Math. Models Methods Appl. Sci.},
volume = {30},
pages = {2753-2797},
url = {https://arxiv.org/abs/2004.05356},
pdf = {https://arxiv.org/pdf/2004.05356},
doi = {10.1142/S0218202520500542}
}
@article{2020-descriptors,
title = {Incompleteness of Atomic Structure Representations},
author = {Pozdnyakov, S. N. and Willatt, M. J. and Bartók, A. P. and Ortner, Christoph and Csányi, Gábor and Ceriotti, Michele},
year = {2020},
journal = {Phys. Rev. Lett.},
volume = {125},
pages = {166001},
url = {https://arxiv.org/abs/2001.11696},
pdf = {https://arxiv.org/pdf/2001.11696},
doi = {10.1103/PhysRevLett.125.166001}
}
@article{2019-ship1,
title = {Atomic Cluster Expansion: Completeness, Efficiency and Stability},
author = {Bachmayr, Markus and Csanyi, Gabor and Dusson, Geneviève and Drautz, Ralf and Etter, Simon and van der Oord, Cas and Ortner, Christoph},
year = {2022},
journal = {J. Comput. Phys.},
volume = {454},
pages = {110946},
url = {https://arxiv.org/abs/1911.03550},
pdf = {https://arxiv.org/pdf/1911.03550},
doi = {10.1016/j.jcp.2022.110946}
}
@article{2019-dislmulti,
title = {Elastic Far-Field Decay from Dislocations in Multilattices},
author = {Olson, Derek and Ortner, Christoph and Wang, Yangshuai and Zhang, Lei},
year = {2023},
journal = {Multiscale Model. Simul.},
volume = {21},
pages = {1379-1409},
url = {https://arxiv.org/abs/1910.12269},
pdf = {https://arxiv.org/pdf/1910.12269},
doi = {10.1137/22M1502021}
}
@article{2019-regapips1,
title = {Regularised Atomic Body-Ordered Permutation-Invariant Polynomials for the Construction of Interatomic Potentials},
author = {van der Oord, Cas and Dusson, Geneviève and Csanyi, Gabor and Ortner, Christoph},
year = {2020},
journal = {Mach. Learn.: Sci. Technol.},
volume = {1},
pages = {6660},
url = {https://arxiv.org/abs/1910.06010},
pdf = {https://arxiv.org/pdf/1910.06010},
doi = {10.1088/2632-2153/ab527c}
}
@article{2019-conductbilayer,
title = {Modeling and Computation of Kubo Conductivity for 2D Incommensurate Bilayers},
author = {Etter, Simon and Massat, D. and Luskin, Mitchell and Ortner, Christoph},
year = {2020},
journal = {Multiscale Model. Simul.},
volume = {18},
pages = {1525-1564},
url = {https://arxiv.org/abs/1907.01314},
pdf = {https://arxiv.org/pdf/1907.01314},
doi = {10.1137/19M1273499}
}
@article{2019-tbloc0T,
title = {Locality of Interatomic Forces in Tight Binding Models for Insulators},
author = {Chen, Huajie and Ortner, Christoph and Thomas, Jack},
year = {2020},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {54},
pages = {2295-2318},
url = {https://arxiv.org/abs/1906.11740},
pdf = {https://arxiv.org/pdf/1906.11740},
doi = {10.1051/m2an/2020020}
}
@article{2019-crackbif,
title = {Analysis of Cell Size Effects in Atomistic Crack Propagation},
author = {Buze, Maciej and Hudson, Thomas and Ortner, Christoph},
year = {2020},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {54},
pages = {1821 - 1847},
url = {https://arxiv.org/abs/1905.13328},
pdf = {https://arxiv.org/pdf/1905.13328},
doi = {10.1051/m2an/2020005}
}
@article{2018-uniform,
title = {Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect},
author = {Braun, Julian and Ortner, Christoph},
year = {2020},
journal = {SIAM J. Numer. Anal.},
volume = {58},
pages = {279-297},
url = {https://arxiv.org/abs/1811.08741},
pdf = {https://arxiv.org/pdf/1811.08741},
doi = {10.1137/18M122830X}
}
@article{2018-entropy,
title = {Thermodynamic Limit of the Transition Rate of a Crystalline Defect},
author = {Braun, Julian and Duong, M. H. and Ortner, Christoph},
year = {2020},
journal = {Arch. Ration. Mech. Anal.},
volume = {238},
pages = {1413-1474},
url = {https://arxiv.org/abs/1810.11643},
pdf = {https://arxiv.org/pdf/1810.11643},
doi = {10.1007/s00205-020-01568-6}
}
@article{2018-antiplanecrack,
title = {Analysis of an atomistic model for anti-plane fracture},
author = {Buze, Maciej and Hudson, Thomas and Ortner, Christoph},
year = {2019},
journal = {Math. Models Methods Appl. Sci.},
volume = {29},
pages = {2469-2521},
url = {https://arxiv.org/abs/1810.05501},
pdf = {https://arxiv.org/pdf/1810.05501},
doi = {10.1142/S0218202519500520}
}
@article{2018-preconstring,
title = {A preconditioning scheme for minimum energy path finding methods},
author = {Makri, Stela and Ortner, Christoph and Kermode, James R},
year = {2019},
journal = {J. Chem. Phys.},
volume = {150},
pages = {094109},
url = {https://arxiv.org/abs/1810.02705},
pdf = {https://arxiv.org/pdf/1810.02705},
doi = {10.1063/1.5064465}
}
@article{2018-ffprecon,
title = {Preconditioners for the geometry optimisation and saddle point search of molecular systems},
author = {Mones, Letif and Ortner, Christoph and Csanyi, Gabor},
year = {2018},
journal = {Scientific Reports},
volume = {8},
pages = {13991},
url = {https://arxiv.org/abs/1804.01590},
pdf = {https://arxiv.org/pdf/1804.01590},
doi = {10.1038/s41598-018-32105-x}
}
@article{2017-bcscrew,
title = {The Effect of Crystal Symmetries on the Locality of Screw Dislocation Cores},
author = {Braun, Julian and Buze, Maciej and Ortner, Christoph},
year = {2019},
journal = {SIAM J. Math. Anal.},
volume = {51},
pages = {1108-1136},
url = {https://arxiv.org/abs/1710.07708},
pdf = {https://arxiv.org/pdf/1710.07708},
doi = {10.1137/17M1157520}
}
@misc{2017-bem,
title = {Coupling Atomistic, Elasticity and Boundary Element Models},
author = {Dedner, A. S. and Ortner, Christoph and Wu, Huan},
year = {2017},
url = {https://arxiv.org/abs/1709.05977},
pdf = {https://arxiv.org/pdf/1709.05977}
}
@article{2017-defects,
title = {Geometry Equilibration of Crystalline Defects in Quantum and Atomistic Descriptions},
author = {Chen, Huajie and Nazar, Faizan Q and Ortner, Christoph},
year = {2019},
journal = {Math. Models Methods Appl. Sci.},
volume = {29},
pages = {419-492},
url = {https://arxiv.org/abs/1709.02770},
pdf = {https://arxiv.org/pdf/1709.02770},
doi = {10.1142/S0218202519500131}
}
@article{2017-momentumspace,
title = {Incommensurate Heterostructures in Momentum Space},
author = {Massat, D. and Carr, S. and Luskin, Mitchell and Ortner, Christoph},
year = {2018},
journal = {Multiscale Model. Simul.},
volume = {16},
pages = {429-451},
url = {https://arxiv.org/abs/1708.02320},
pdf = {https://arxiv.org/pdf/1708.02320},
doi = {10.1137/17M1141035}
}
@article{2017-ljstacking,
title = {Polytypism in the ground state structure of the Lennard-Jonesium},
author = {Pártay, L. B. and Ortner, Christoph and Bartók, A. P. and Pickard, C. J. and Csányi, Gábor},
year = {2017},
journal = {Phys. Chem. Chem. Phys.},
volume = {19},
pages = {19369-19376},
url = {https://arxiv.org/abs/1705.01751},
pdf = {https://arxiv.org/pdf/1705.01751},
doi = {10.1039/C7CP02923C}
}
@article{2016-pmd1,
title = {Some Remarks on Preconditioning Molecular Dynamics},
author = {Alrachid, H. and Mones, Letif and Ortner, Christoph},
year = {2018},
journal = {SMAI J. Comp. Math.},
volume = {4},
pages = {57--80},
url = {https://arxiv.org/abs/1612.05435},
pdf = {https://arxiv.org/pdf/1612.05435},
doi = {10.5802/smai-jcm.29}
}
@article{2016-multibqcf,
title = {Force-Based Atomistic/Continuum Blending for Multilattices},
author = {Olson, D. and Li, Xingjie Helen and Ortner, Christoph and Van Koten, Brian},
year = {2018},
journal = {Numer. Math.},
volume = {140},
pages = {703-754},
url = {https://arxiv.org/abs/1611.05935},
pdf = {https://arxiv.org/pdf/1611.05935},
doi = {10.1007/s00211-018-0979-x}
}
@article{2016-multipt,
title = {Regularity and Locality of Point Defects in Multilattices},
author = {Olson, D. and Ortner, Christoph},
year = {2017},
journal = {Appl. Math. Res. Express},
volume = {1-41},
url = {https://arxiv.org/abs/1608.08930},
pdf = {https://arxiv.org/pdf/1608.08930},
doi = {10.1093/amrx/abw012}
}
@article{2016-realspace,
title = {Electronic Density of States for Incommensurate Layers},
author = {Massatt, Daniel and Luskin, Mitchell and Ortner, Christoph},
year = {2017},
journal = {Multiscale Model. Simul.},
volume = {15},
pages = {476-499},
url = {https://arxiv.org/abs/1608.01968},
pdf = {https://arxiv.org/pdf/1608.01968},
doi = {10.1137/16M1088363}
}
@article{2016-dimercycling,
title = {Convergence and Cycling in Walker-type Saddle Search Algorithms},
author = {Levitt, A. and Ortner, Christoph},
year = {2017},
journal = {SIAM J. Numer. Anal.},
volume = {55},
pages = {2204-2227},
url = {https://arxiv.org/abs/1607.08875},
pdf = {https://arxiv.org/pdf/1607.08875},
doi = {10.1137/16M1087199}
}
@article{2016-tblimit,
title = {Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding},
author = {Chen, Huajie and Lu, Jianfeng and Ortner, Christoph},
year = {2018},
journal = {Arch. Ration. Mech. Anal.},
volume = {230},
pages = {701-733},
url = {https://arxiv.org/abs/1607.06850},
pdf = {https://arxiv.org/pdf/1607.06850},
doi = {10.1007/s00205-018-1256-y}
}
@article{2016-qcp2,
title = {Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements},
author = {Dedner, A. and Wu, Huan and Ortner, Christoph},
year = {2017},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {51},
pages = {2263-2288},
url = {https://arxiv.org/abs/1607.05936},
pdf = {https://arxiv.org/pdf/1607.05936},
doi = {10.1051/m2an/2017013}
}
@article{2016-scbpc,
title = {Analysis of a Predictor-Corrector Method for Computationally
Efficient Modeling of Surface Effects in 1D},
author = {Binder, A. J. and Luskin, Mitchell and Ortner, Christoph},
year = {2017},
journal = {Multiscale Model. Simul.},
volume = {15},
pages = {892-919},
url = {https://arxiv.org/abs/1605.05750},
pdf = {https://arxiv.org/pdf/1605.05750},
doi = {10.1137/16M1065884}
}
@article{2016-defectFE1d,
title = {On assessing the accuracy of defect free energy computations},
author = {Dobson, Matthew and Duong, M. H. and Ortner, Christoph},
year = {2018},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {52},
pages = {1315-1352},
url = {https://arxiv.org/abs/1602.08643},
pdf = {https://arxiv.org/pdf/1602.08643},
doi = {10.1051/m2an/2017052}
}
@article{2016-precon1,
title = {A universal preconditioner for simulating condensed phase materials},
author = {Packwood, David and Kermode, James R and Mones, Letif and Bernstein, Noam and Woolley, J. and Gould, N. I. M. and Ortner, Christoph and Csanyi, Gabor},
year = {2016},
journal = {J. Chem. Phys.},
volume = {144},
pages = {164109},
url = {https://arxiv.org/abs/1604.02570},
pdf = {https://arxiv.org/pdf/1604.02570},
doi = {10.1063/1.4947024}
}
@article{2015-tfw,
title = {Locality of the Thomas-Fermi-von Weizsäcker Equations},
author = {Nazar, Faizan Q and Ortner, Christoph},
year = {2017},
journal = {Arch. Ration. Mech. Anal.},
volume = {224},
pages = {817-870},
url = {https://arxiv.org/abs/1509.06753},
pdf = {https://arxiv.org/pdf/1509.06753},
doi = {10.1007/s00205-017-1075-6}
}
@article{2015-qmtb2,
title = {QM/MM Methods for Crystalline Defects. Part 2: Consistent energy
and force-mixing},
author = {Chen, Huajie and Ortner, Christoph},
year = {2017},
journal = {Multiscale Model. Simul.},
volume = {15},
pages = {184-214},
url = {https://arxiv.org/abs/1509.06627},
pdf = {https://arxiv.org/pdf/1509.06627},
doi = {10.1137/15M1041250}
}
@article{2015-qmtb1,
title = {QM/MM Methods for Crystalline Defects. Part 1: Locality of the Tight
Binding Model},
author = {Chen, Huajie and Ortner, Christoph},
year = {2016},
journal = {Multiscale Model. Simul.},
volume = {14},
pages = {232-264},
url = {https://arxiv.org/abs/1505.05541},
pdf = {https://arxiv.org/pdf/1505.05541},
doi = {10.1137/15M1022628}
}
@article{2014-dimer,
title = {A dimer-type saddle search algorithm with preconditioning and linesearch},
author = {Gould, N. and Ortner, Christoph and Packwood, David},
year = {2016},
journal = {Math. Comp.},
volume = {85},
pages = {2939-2966},
url = {https://arxiv.org/abs/1407.2817},
pdf = {https://arxiv.org/pdf/1407.2817},
doi = {10.1090/mcom/3096}
}
@article{2014-bgfc,
title = {Atomistic/Continuum Blending with Ghost Force Correction},
author = {Ortner, Christoph and Zhang, Lei},
year = {2016},
journal = {SIAM J. Sci. Comput.},
volume = {38},
pages = {A346-A375},
url = {https://arxiv.org/abs/1407.0053},
pdf = {https://arxiv.org/pdf/1407.0053},
doi = {10.1137/15M1020241}
}
@article{2014-bqce,
title = {Analysis of blended atomistic/continuum hybrid methods},
author = {Li, Xingjie Helen and Ortner, Christoph and Shapeev, A. and Van Koten, Brian},
year = {2016},
journal = {Numer. Math.},
volume = {134},
pages = {275-326},
url = {https://arxiv.org/abs/1404.4878},
pdf = {https://arxiv.org/pdf/1404.4878},
doi = {10.1007/s00211-015-0772-z}
}
@article{2014-dislift,
title = {Analysis of stable screw dislocation configurations in an anti-plane lattice model},
author = {Hudson, Thomas and Ortner, Christoph},
year = {2015},
journal = {SIAM J. Math. Anal.},
volume = {47},
pages = {291-320},
url = {https://arxiv.org/abs/1403.0518},
pdf = {https://arxiv.org/pdf/1403.0518},
doi = {10.1137/140964436}
}
@article{2013-grac.bench,
title = {Energy-Based Atomistic-to-Continuum Coupling Without Ghost Forces},
author = {Ortner, Christoph and Zhang, Lei},
year = {2014},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {279},
pages = {29-45},
url = {https://arxiv.org/abs/1312.6814},
pdf = {https://arxiv.org/pdf/1312.6814}
}
@article{2013-stab.ac,
title = {(In-)Stability and Stabilisation of QNL-Type
Atomistic-to-Continuum Coupling Methods},
author = {Ortner, Christoph and Shapeev, A. and Zhang, Lei},
year = {2014},
journal = {Multiscale Model. Simul.},
volume = {12},
pages = {1258--1293},
url = {https://arxiv.org/abs/1308.3894},
pdf = {https://arxiv.org/pdf/1308.3894}
}
@article{2013-visc,
title = {An approach to nonlinear viscoleasticity via metric gradient flows},
author = {Mielke, A. and Ortner, Christoph and Sengul, Y.},
year = {2014},
journal = {SIAM J. Math. Anal.},
volume = {46},
pages = {1317--1347}
}
@article{2013-defects,
title = {Analysis of Boundary Conditions for Crystal Defect Atomistic
Simulations},
author = {Ehrlacher, V. and Ortner, Christoph and Shapeev, A. V.},
year = {2016},
journal = {Arch. Ration. Mech. Anal.},
volume = {222},
pages = {1217-1268},
url = {https://arxiv.org/abs/1306.5334},
pdf = {https://arxiv.org/pdf/1306.5334},
doi = {10.1007/s00205-016-1019-6}
}
@article{2013-disl,
title = {Existence and stability of a screw dislocation under
anti-plane deformation},
author = {Hudson, Thomas and Ortner, Christoph},
year = {2014},
journal = {Arch. Ration. Mech. Anal.},
volume = {213},
pages = {887-929},
url = {https://arxiv.org/abs/1304.2500},
pdf = {https://arxiv.org/pdf/1304.2500},
doi = {10.1007/s00205-014-0746-9}
}
@article{2013-CMAME-bqcfcomp,
title = {Theory-based Benchmarking of the Blended Force-Based
Quasicontinuum Method},
author = {Li, Xingjie Helen and Luskin, Mitchell and Ortner, Christoph and Shapeev, A.},
year = {2014},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {268},
pages = {763-781},
url = {https://arxiv.org/abs/1304.1368},
pdf = {https://arxiv.org/pdf/1304.1368},
doi = {10.1016/j.cma.2013.10.007}
}
@article{2013-atc.acta,
title = {Atomistic-to-continuum coupling},
author = {Luskin, Mitchell and Ortner, Christoph},
year = {2013},
journal = {Acta Numerica},
volume = {22},
pages = {397-508},
doi = {10.1017/s0962492913000068}
}
@article{2012-ac.aposteriori.1d,
title = {A posteriori error control for a quasicontinuum approximation of a periodic chain},
author = {Ortner, Christoph and Wang, Hao},
year = {2014},
journal = {IMA J. Numer. Anal.},
volume = {34},
pages = {977-1001},
url = {https://arxiv.org/abs/1211.3346},
pdf = {https://arxiv.org/pdf/1211.3346},
doi = {10.1093/imanum/drt011}
}
@misc{2012-lattint,
title = {Interpolants of Lattice Functions for the Analysis of
Atomistic/Continuum Multiscale Methods},
author = {Ortner, Christoph and Shapeev, A.},
year = {2012},
url = {https://arxiv.org/abs/1204.3705},
pdf = {https://arxiv.org/pdf/1204.3705}
}
@article{2012-multi1,
title = {Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model},
author = {Van Koten, Brian and Ortner, Christoph},
year = {2013},
journal = {Multiscale Model. Simul.},
volume = {11},
pages = {615-634},
url = {https://arxiv.org/abs/1203.5854},
pdf = {https://arxiv.org/pdf/1203.5854},
doi = {10.1137/120870220}
}
@article{2012-ARMA-cb,
title = {Justification of the Cauchy--Born Approximation of Elastodynamics},
author = {Ortner, Christoph and Theil, F.},
year = {2013},
journal = {Arch. Ration. Mech. Anal.},
volume = {207},
pages = {1025-1073},
url = {https://arxiv.org/abs/1202.3858},
pdf = {https://arxiv.org/pdf/1202.3858},
doi = {10.1007/s00205-012-0592-6}
}
@misc{2012-ARXIV-ellRd,
title = {A note on linear elliptic systems on $\R^d$},
author = {Ortner, Christoph and Süli, Endre},
year = {2012},
url = {https://arxiv.org/abs/1202.3970},
pdf = {https://arxiv.org/pdf/1202.3970}
}
@article{2012-encyclopedia,
title = {Atomistic-to-continuum coupling},
author = {Luskin, Mitchell and Ortner, Christoph},
year = {2013},
journal = {Springer Encyclopedia for Applied and Computational Mathematics}
}
@article{2012-MMS-bqcf.stab,
title = {Positive Definiteness of the Blended Force-Based Quasicontinuum Method},
author = {Li, Xingjie Helen and Luskin, Mitchell and Ortner, Christoph},
year = {2012},
journal = {Multiscale Model. Simul.},
volume = {10},
pages = {1023-1045},
url = {https://arxiv.org/abs/1112.2528},
pdf = {https://arxiv.org/pdf/1112.2528},
doi = {10.1137/110859270}
}
@article{2012-CMAME-optbqce,
title = {Formulation and optimization of the energy-based blended
quasicontinuum method},
author = {Luskin, Mitchell and Ortner, Christoph and Van Koten, Brian},
year = {2013},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {253},
pages = {160-168},
url = {https://arxiv.org/abs/1112.2377},
pdf = {https://arxiv.org/pdf/1112.2377},
doi = {10.1016/j.cma.2012.09.007}
}
@article{2012-MMS-ac.dft.1d,
title = {Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory},
author = {Langwallner, Bernhard and Ortner, Christoph and Süli, Endre},
year = {2013},
journal = {Multiscale Model. Simul.},
volume = {11},
pages = {59-91},
url = {https://arxiv.org/abs/1112.0746},
pdf = {https://arxiv.org/pdf/1112.0746},
doi = {10.1137/110857787}
}
@article{2013-ac.scb.1d,
title = {An Analysis of the Boundary Layer in the 1D Surface Cauchy--Born Model},
author = {Jayawardana, K. and Mordacq, C. and Ortner, Christoph and Park, H. S.},
year = {2013},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {47},
pages = {109-123},
doi = {10.1051/m2an/2012021}
}
@article{2012-SINUM-ac.2dcorners,
title = {Construction and sharp consistency estimates for
atomistic/continuum coupling methods with general
interfaces: a 2D model problem},
author = {Ortner, Christoph and Zhang, Lei},
year = {2012},
journal = {SIAM J. Numer. Anal.},
volume = {50},
pages = {2940-2965},
url = {https://arxiv.org/abs/1110.0168},
pdf = {https://arxiv.org/pdf/1110.0168},
doi = {10.1137/110851791}
}
@article{2012-MATHCOMP-qce.pair,
title = {Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice},
author = {Ortner, Christoph and Shapeev, A. V.},
year = {2013},
journal = {Math. Comp.},
volume = {82},
pages = {2191-2236},
url = {https://arxiv.org/abs/1104.0311},
pdf = {https://arxiv.org/pdf/1104.0311},
doi = {10.1090/S0025-5718-2013-02687-7}
}
@article{2012-M2AN-qc.patch.2d,
title = {The role of the patch test in 2D atomistic-to-continuum coupling methods},
author = {Ortner, Christoph},
year = {2012},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {46},
pages = {1275-1319},
doi = {10.1051/m2an/2012005}
}
@incollection{2012-SLN-DurhamSympProc,
title = {A computational and theoretical investigation of the
accuracy of quasicontinuum methods},
author = {Van Koten, Brian and Li, Xingjie Helen and Luskin, Mitch and Ortner, Christoph},
year = {2012},
booktitle = {Numerical Analysis of Multiscale Problems},
publisher = {Springer Lecture Notes in Computational Science and Engineering 83},
pages = {67-96},
doi = {10.1007/978-3-642-22061-6_3}
}
@article{2012-MMS-qcf.spectrum,
title = {The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain},
author = {Dobson, Matthew and Ortner, Christoph and Shapeev, A. V.},
year = {2012},
journal = {Multiscale Model. Simul.},
volume = {10},
pages = {744-765},
url = {https://arxiv.org/abs/1004.3435},
pdf = {https://arxiv.org/pdf/1004.3435},
doi = {10.1137/110825704}
}
@article{2011-M3AS-qc.coarse,
title = {A Priori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain},
author = {Ortner, Christoph and Wang, Hao},
year = {2011},
journal = {Math. Models Methods Appl. Sci.},
volume = {21},
pages = {2491--2521},
doi = {10.1142/S0218202511005817}
}
@article{2012-IJMCE-sac,
title = {Stress-based atomistic/continuum coupling: a new variant of the quasicontinuum approximation},
author = {Makridakis, Charalambos and Ortner, Christoph and Süli, Endre},
year = {2012},
journal = {Int. J. Multiscale Comput. Eng.},
volume = {10}
}
@incollection{2012-stat.qcf,
title = {Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation},
author = {Luskin, Mitchell and Ortner, Christoph},
year = {2012},
booktitle = {Numerical Analysis and Multiscale Computations},
publisher = {Springer Lect. Notes Comput. Sci. Eng. Springer 82},
pages = {331-368},
url = {https://arxiv.org/abs/1104.1774},
pdf = {https://arxiv.org/pdf/1104.1774},
doi = {10.1007/978-3-642-21943-6_14}
}
@misc{2012-viscoelastic,
title = {Existence of solutions of partially degenerate visco-elastic problems, and applications to modelling muscular contraction and cardiac electro-mechanical activity},
author = {Pathmanathan, Pras and Ortner, Christoph and Kay, David},
year = {2012}
}
@article{2012-M3AS-genat,
title = {An adaptive finite element approximation of a generalised Ambrosio--Tortorelli functional},
author = {Burke, Siobhan and Ortner, Christoph and Suli, Endre},
year = {2013},
journal = {Math. Models Methods Appl. Sci.},
volume = {23},
pages = {1663-1697},
doi = {10.1142/S021820251350019X}
}
@article{2012-M2AN-CBstab,
title = {On the stability of Bravais lattices and their Cauchy--Born approximations},
author = {Hudson, Thomas and Ortner, Christoph},
year = {2012},
journal = {M2AN Math. Model. Numer. Anal.},
volume = {46},
pages = {81-110},
doi = {10.1051/m2an/2011014}
}
@article{2011-NUMMATH-qcf1d,
title = {A priori error analysis of two force-based atomistic/continuum models of a periodic chain},
author = {Makridakis, Charalambos and Ortner, Christoph and Süli, Endre},
year = {2011},
journal = {Numer. Math.},
volume = {119},
pages = {83--121},
doi = {10.1007/s00211-011-0380-5}
}
@article{2011-NUMMATH-GradConstr,
title = {A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state},
author = {Ortner, Christoph and Wollner, Winnifried},
year = {2011},
journal = {Numer. Math.},
publisher = {Springer Berlin / Heidelberg},
volume = {118},
pages = {587-600},
doi = {10.1007/s00211-011-0360-9}
}
@article{2011-CMAME-qcf.iter,
title = {Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem},
author = {Dobson, Matthew and Luskin, Mitch and Ortner, Christoph},
year = {2011},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {200},
pages = {2697-2709},
doi = {doi:10.1016/j.cma.2010.07.008}
}
@article{2011-IMAJNA-lavrentiev_nc,
title = {Nonconforming finite-element discretization of convex variational problems},
author = {Ortner, Christoph},
year = {2011},
journal = {IMA J. Numer. Anal.},
volume = {31},
pages = {847-864},
doi = {10.1093/imanum/drq004}
}
@article{2011-MCOM-qnl1d,
title = {A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D},
author = {Ortner, Christoph},
year = {2011},
journal = {Math. Comp.},
volume = {80},
pages = {1265--1285},
doi = {10.1090/S0025-5718-2010-02453-6}
}
@article{2011-SINUM_ANCFEM,
title = {On the convergence of adaptive nonconforming finite element methods for a class of convex variational problems},
author = {Ortner, Christoph and Praetorius, Dirk},
year = {2011},
journal = {SIAM J. Numer. Anal.},
volume = {49},
pages = {346--367},
doi = {10.1137/090781073}
}
@article{2011-SINUM-allencahn,
title = {Robust a priori and a posteriori error analysis for the
approximation of Allen-Cahn and Ginzburg-Landau
equations past topological changes},
author = {Bartels, Soren and Muller, Rudiger and Ortner, Christoph},
year = {2011},
journal = {SIAM J. Numer. Anal.},
volume = {49},
pages = {110--134},
doi = {10.1137/090751530}
}
@incollection{2011-Ch-frac,
title = {Adaptive finite element approximation of the Francfort-Marigo model of brittle fracture},
author = {Burke, Siobhan and Ortner, Christoph and Suli, Endre},
year = {2011},
booktitle = {Approximation and computation},
publisher = {Springer},
volume = {42},
pages = {297-310},
doi = {10.1007/978-1-4419-6594-3_19}
}
@article{2010-CMAM-PenaltyMethod,
title = {Analysis of a class of penalty methods for computing singular minimizers},
author = {Carstensen, C. and Ortner, Christoph},
year = {2010},
journal = {Comput. Methods Appl. Math.},
volume = {10},
pages = {137-163},
doi = {10.2478/cmam-2010-0008}
}
@article{2010-M3AS-tfwd,
title = {Existence and convergence results for the Galerkin approximation of an electronic density functional},
author = {Langwallner, Bernhard and Ortner, Christoph and Suli, Endre},
year = {2010},
journal = {Math. Models Methods Appl. Sci.},
volume = {20},
pages = {2237--2265},
doi = {10.1142/S021820251000491X}
}
@article{2010-JMPS-qce.stab,
title = {Accuracy of quasicontinuum approximations near instabilities},
author = {Dobson, Matthew and Luskin, Mitchell and Ortner, Christoph},
year = {2010},
journal = {J. Mech. Phys. Solids},
volume = {58},
pages = {1741--1757},
doi = {10.1016/j.jmps.2010.06.011}
}
@article{2010-NUMMATH-ABEM,
title = {Convergence of simple adaptive Galerkin schemes based on h-h/2 error estimators},
author = {Ferraz-Leite, S. and Ortner, Christoph and Praetorius, Dirk},
year = {2010},
journal = {Numer. Math.},
volume = {116},
pages = {291--316},
doi = {10.1007/s00211-010-0292-9}
}
@article{2010-SINUM-afemat,
title = {An adaptive finite element approximation of a variational
model of brittle fracture},
author = {Burke, Siobhan and Ortner, Christoph and Suli, Endre},
year = {2010},
journal = {SIAM J. Numer. Anal.},
volume = {48},
pages = {980--1012},
doi = {10.1137/080741033}
}
@article{2010-M3AS-dynafracat,
title = {Existence of solutions to a regularized model of dynamic
fracture},
author = {Larsen, Christopher J. and Ortner, Christoph and Suli, Endre},
year = {2010},
journal = {Math. Models Methods Appl. Sci.},
volume = {20},
pages = {1021--1048},
doi = {10.1142/S0218202510004520}
}
@article{2010-ARMA-QCF,
title = {Stability, instability, and error of the force-based
quasicontinuum approximation},
author = {Dobson, Matthew and Luskin, Mitchell and Ortner, Christoph},
year = {2010},
journal = {Arch. Ration. Mech. Anal.},
volume = {197},
pages = {179--202},
doi = {10.1007/s00205-009-0276-z}
}
@article{2010-MMS-SharpStabQCF,
title = {Sharp stability estimates for the force-based quasicontinuum
approximation of homogeneous tensile deformation},
author = {Dobson, Matthew and Luskin, Mitchell and Ortner, Christoph},
year = {2010},
journal = {Multiscale Model. Simul.},
volume = {8},
pages = {782--802},
doi = {10.1137/090767005}
}
@article{2009-IMAJNA-DGFEM,
title = {Compact embeddings of broken Sobolev spaces and
applications},
author = {Buffa, Annalisa and Ortner, Christoph},
year = {2009},
journal = {IMA J. Numer. Anal.},
volume = {29},
pages = {827--855},
doi = {10.1093/imanum/drn038}
}
@article{2009-SINUM-QCCluster,
title = {An analysis of node-based cluster summation rules in the
quasicontinuum method},
author = {Luskin, Mitchell and Ortner, Christoph},
year = {2009},
journal = {SIAM J. Numer. Anal.},
volume = {47},
pages = {3070--3086},
doi = {10.1137/080743391}
}
@article{2009-SINUM-ApostEx,
title = {A posteriori existence in numerical computations},
author = {Ortner, Christoph},
year = {2009},
journal = {SIAM J. Numer. Anal.},
volume = {47},
pages = {2550--2577},
doi = {10.1137/060668183}
}
@article{2008-M3AS-Griffith,
title = {Quasi-static crack propagation by Griffith's criterion},
author = {Negri, Matteo and Ortner, Christoph},
year = {2008},
journal = {Math. Models Methods Appl. Sci.},
volume = {18},
pages = {1895--1925},
doi = {10.1142/S0218202508003236}
}
@article{2008-M2AN-QC1D,
title = {Analysis of a quasicontinuum method in one dimension},
author = {Ortner, Christoph and Suli, Endre},
year = {2008},
journal = {M2AN Math. Model. Numer. Anal.},
volume = {42},
pages = {57--91},
doi = {10.1051/m2an:2007057}
}
@article{2007-SINUM-DGFEM,
title = {Discontinuous Galerkin finite element approximation of
nonlinear second-order elliptic and hyperbolic systems},
author = {Ortner, Christoph and Suli, Endre},
year = {2007},
journal = {SIAM J. Numer. Anal.},
volume = {45},
pages = {1370--1397},
doi = {10.1137/06067119X}
}
@article{2006-SIMA-GFlow,
title = {Gradient flows as a selection procedure for equilibria of
nonconvex energies},
author = {Ortner, Christoph},
year = {2006},
journal = {SIAM J. Math. Anal.},
volume = {38},
pages = {1214--1234},
doi = {10.1137/050643982}
}
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