@article{2024-pureace,
title = { {Atomic Cluster Expansion without Self-Interaction}},
author = {Cheuk Hin Ho and Timon S. Gutleb and Christoph Ortner},
journal = {ArXiv e-prints},
volume = {2401.01550},
year = {2024},
url = {https://arxiv.org/abs/2401.01550},
pdf = {https://arxiv.org/pdf/2401.01550.pdf}
}
@article{2024-entropy-ml,
title = { {Surrogate models for vibrational entropy based on a spatial decomposition}},
author = {Tina Torabi and Yangshuai Wang and Christoph Ortner},
journal = {ArXiv e-prints},
volume = {2402.12744},
year = {2024},
url = {https://arxiv.org/abs/2402.12744},
pdf = {https://arxiv.org/pdf/2402.12744.pdf}
}
@article{2024-foundationmodel-v1,
title = { {A foundation model for atomistic materials chemistry}},
author = {Ilyes Batatia and Philipp Benner and Yuan Chiang and Alin M. Elena and Dávid P. Kovács and Janosh Riebesell et al},
note = {(62 authors not shown)},
journal = {ArXiv e-prints},
volume = {2401.00096},
year = {2024},
url = {https://arxiv.org/abs/2401.00096},
pdf = {https://arxiv.org/pdf/2401.00096.pdf}
}
@article{2023-mlipsgen_disloc,
title = { {A Theoretical Case Study of the Generalisation of Machine-learned Potentials}},
author = {Y. Wang and S. Patel and C. Ortner},
journal = {ArXiv e-prints},
volume = {2311.01664},
year = {2023},
url = {https://arxiv.org/abs/2311.01664},
pdf = {https://arxiv.org/pdf/2311.01664.pdf}
}
@article{2023-EMFNs-1,
title = { {Equivariant Matrix Function Neural Networks}},
author = {Ilyes Batatia and Lars L. Schaaf and Huajie Chen and Gábor Csányi and Christoph Ortner and Felix A. Faber},
journal = {ArXiv e-prints},
volume = {2310.10434},
year = {2023},
note = {accepted in ICLR 2024},
url = {https://arxiv.org/abs/2310.10434},
pdf = {https://arxiv.org/pdf/2310.10434.pdf}
}
@incollection{2023-tdl_review,
title = { {Thermodynamic Limits of Electronic Systems}},
author = {David Gontier and Jianfeng Lu and Christoph Ortner},
booktitle = {Density Functional Theory: Modeling, Mathematical Analysis, Computational Methods and Applications},
editor = {Eric Cances and Gero Friesecke},
publisher = {Springer},
year = {2023},
url = {https://arxiv.org/abs/2309.05118},
pdf = {https://arxiv.org/pdf/2309.05118.pdf}
}
@article{2023-acepotentials,
title = { {ACEpotentials.jl: A Julia Implementation of the Atomic Cluster Expansion}},
author = {William C. Witt and Cas van der Oord and Elena Gel\v{z}inyt\'{e} and Teemu J\"{a}rvinen and Andres Ross and James P. Darby and Cheuk Hin Ho and William J. Baldwin and Matthias Sachs and James Kermode and Noam Bernstein and G\'{a}bor Cs\'{a}nyi and Christoph Ortner},
journal = {J. Chem. Phys.},
volume = {159},
pages = {164101},
year = {2023},
url = {https://arxiv.org/abs/2309.03161},
pdf = {https://arxiv.org/pdf/2309.03161.pdf},
doi = {https://doi.org/10.1063/5.0158783}
}
@article{2023-acecommentary,
title = {On the Atomic Cluster Expansion: interatomic potentials and beyond},
author = {C. Ortner},
journal = {KIM REVIEW},
volume = {1},
year = {2023},
url = {https://kimreview.org/commentaries/10-25950-c7f24234/},
pdf = {https://kimreview.org/commentary-files/2023-08-01/kim-review-commentary-2023-08-01.pdf},
doi = {https://doi.org/10.25950/c7f24234}
}
@article{2023-bips-2,
title = { {Retrieval of Boost Invariant Symbolic Observables via Feature Importance}},
author = {Jose M Munoz and Ilyes Batatia and Christoph Ortner and Francesco Romeo},
journal = {ArXiv e-prints},
volume = {2306.13496},
year = {2023},
note = {to appear in Journal Of Physics: Conference Series (ACAT2022 proceedings)},
url = {https://arxiv.org/abs/2306.13496},
pdf = {https://arxiv.org/pdf/2306.13496.pdf}
}
@article{2023-lie-mace,
title = {A General Framework for Equivariant Neural Networks on Reductive Lie Groups},
author = {I. Batatia and M. Geiger and J. Munoz and T. Smidt and L. Silberman and C. Ortner},
journal = {ArXiv e-prints},
volume = {2306.00091},
year = {2023},
note = {accepted in NEURIPS 2023},
url = {https://arxiv.org/abs/2306.00091},
pdf = {https://arxiv.org/pdf/2306.00091.pdf}
}
@article{2023-wf1d_vmc,
title = {A Multilevel Method for Many-Electron Schrödinger Equations Based on the Atomic Cluster Expansion},
author = {D. Zhou and H. Chen and C. Hin Ho and C. Ortner},
journal = {SIAM J. Sc. Comp.},
volume = {46},
year = {2024},
url = {https://arxiv.org/abs/2304.04260},
pdf = {https://arxiv.org/pdf/2304.04260.pdf},
doi = {10.1137/23M1565887}
}
@article{2022-ffbc,
title = {Higher Order Far-Field Boundary Conditions for Crystalline Defects},
author = {J. Braun and C. Ortner and Y. Wang and L. Zhang},
journal = {ArXiv e-prints},
volume = {2210.05573},
year = {2022},
url = {https://arxiv.org/abs/2210.05573},
pdf = {https://arxiv.org/pdf/2210.05573.pdf}
}
@article{2022-qmmm-apost-mlips,
title = {A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects},
author = {Y. Wang and J. R. Kermode and C. Ortner and L. Zhang},
journal = {ArXiv e-prints},
volume = {2210.04856},
year = {2022},
url = {https://arxiv.org/abs/2210.04856},
pdf = {https://arxiv.org/pdf/2210.04856.pdf}
}
@article{2022-HAL1,
title = {Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials},
author = {C. van der Oord and M. Sachs and D. P. Kov\'{a}cs and C. Ortner and Cs\'{a}nyi},
journal = {npj Computational Materials},
volume = {9},
year = {2023},
url = {https://arxiv.org/abs/2210.04225},
pdf = {https://arxiv.org/pdf/2210.04225.pdf},
doi = {s41524-023-01104-6}
}
@article{2022-Gautam,
title = {Exploiting Machine Learning in Multiscale Modelling of Materials},
author = {G. Anand and S. Ghosh and L. Zhang and A. Anupam and C. L. Freeman and C. Ortner and M. Eisenbach and J. R. Kermode},
journal = {J. Inst. Eng. India Ser. D},
volume = {},
year = {2022},
doi = {https://doi.org/10.1007/s40033-022-00424-z}
}
@article{2022-randomembedding,
title = {Tensor-reduced atomic density representations},
author = {J. P. Darby and D. P. Kov\'{a}cs and I. Batatia and M. A. Caro and G. L. W. Hart and C. Ortner and G. Cs\'{a}nyi},
journal = {Phys. Rev. Lett.},
volume = {131},
year = {2023},
url = {https://arxiv.org/abs/2210.01705},
pdf = {https://arxiv.org/pdf/2210.01705.pdf},
doi = {10.1103/PhysRevLett.131.028001}
}
@article{2022-generalisation1,
title = {A framework for a generalisation analysis of machine-learned interatomic potentials},
author = {C. Ortner and Y. Wang},
journal = {Multiscale Modeling & Simulation},
volume = {21},
year = {2023},
url = {https://arxiv.org/abs/2209.05366},
pdf = {https://arxiv.org/pdf/2209.05366.pdf},
doi = {10.1137/22M152267X}
}
@article{2022-bip1,
title = {Boost Invariant Polynomials for Efficient Jet Tagging},
author = {J. M Munoz and I. Batatia and C. Ortner},
journal = {Machine Learning: Science and Technology},
volume = {3},
year = {2022},
url = {https://arxiv.org/abs/2207.08272},
pdf = {https://arxiv.org/pdf/2207.08272.pdf},
doi = {10.1088/2632-2153/aca9ca}
}
@article{2022-wave1,
title = {Atomic cluster expansion and wave function representations},
author = {R. Drautz and C. Ortner},
journal = {ArXiv e-prints},
volume = {2206.11375},
year = {2022},
url = {https://arxiv.org/abs/2206.11375},
pdf = {https://arxiv.org/pdf/2206.11375.pdf}
}
@inproceedings{2022-MACE,
author = {Batatia, Ilyes and Kovacs, David P and Simm, Gregor and Ortner, Christoph and Csanyi, Gabor},
booktitle = {Advances in Neural Information Processing Systems},
editor = {S. Koyejo and S. Mohamed and A. Agarwal and D. Belgrave and K. Cho and A. Oh},
pages = {11423--11436},
publisher = {Curran Associates, Inc.},
title = {MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields},
url = {https://arxiv.org/abs/2206.07697},
pdf = {https://arxiv.org/pdf/2206.07697.pdf},
doi = {https://proceedings.neurips.cc/paper_files/paper/2022/file/4a36c3c51af11ed9f34615b81edb5bbc-Paper-Conference.pdf},
volume = {35},
year = {2022}
}
@article{2022-mlACE-1,
title = {Multilayer atomic cluster expansion for semi-local interactions},
author = {Anton Bochkarev and Yury Lysogorskiy and Christoph Ortner and Gábor Csányi and Ralf Drautz},
journal = {Phys. Rev. Res.},
volume = {4},
year = {2022},
url = {https://arxiv.org/abs/2205.08177},
pdf = {https://arxiv.org/pdf/2205.08177.pdf},
doi = {10.1103/PhysRevResearch.4.L042019}
}
@article{2022-acempnn-framework,
title = {The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials},
author = {Ilyes Batatia and Simon Batzner and Dávid Péter Kovács and Albert Musaelian and Gregor N. C. Simm and Ralf Drautz and Christoph Ortner and Boris Kozinsky and Gábor Csányi},
journal = {ArXiv e-prints},
volume = {2205.06643},
year = {2022},
note = {to appear in Nature Machine Intelligence},
url = {https://arxiv.org/abs/2205.06643},
pdf = {https://arxiv.org/pdf/2205.06643.pdf}
}
@article{2022-mepconv,
title = {Convergence of the Discrete Minimum Energy Path},
author = {Xuanyu Liu and Huajie Chen and Christoph Ortner},
journal = {ArXiv e-prints},
volume = {2204.07467},
year = {2022},
url = {https://arxiv.org/abs/2204.07467},
pdf = {https://arxiv.org/pdf/2204.07467.pdf}
}
@article{2022-mepstab,
title = {Stability of the Minimum Energy Path},
author = {Xuanyu Liu and Huajie Chen and Christoph Ortner},
journal = {Numer. Math.},
volume = {156},
year = {2024},
url = {https://arxiv.org/abs/2204.00984},
pdf = {https://arxiv.org/pdf/2204.00984.pdf},
doi = {https://doi.org/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 = {S. N. Pozdnyakov and M. J. Willatt and A. P. Bartok and C. Ortner and G. Csanyi and M. Ceriotti},
journal = {J. Chem. Phys.},
volume = {157},
pages = {177101},
year = {2022},
doi = {https://doi.org/10.1063/5.0088404}
}
@article{2022-recursive,
title = {Optimal Evaluation of Symmetry-Adapted $n$-Correlations Via Recursive Contraction of Sparse Symmetric Tensors},
author = {Illia Kaliuzhnyi and Christoph Ortner},
journal = {J. Numer. Math.},
volume = {online},
year = {2024},
url = {https://arxiv.org/abs/2202.04140},
pdf = {https://arxiv.org/pdf/2202.04140.pdf},
doi = {https://doi.org/10.1515/jnma-2024-0025}
}
@article{2021-acetb1,
title = {Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models},
author = {Liwei Zhang and Berk Onat and Genevieve Dusson and Gautam Anand and Reinhard J Maurer and Christoph Ortner and James R Kermode},
journal = {npj Computational Materials},
volume = {8},
year = {2022},
doi = {https://doi.org/10.1038/s41524-022-00843-2},
url = {https://arxiv.org/abs/2111.13736},
pdf = {https://arxiv.org/pdf/2111.13736.pdf}
}
@article{2021-acemolecules,
title = {Linear Atomic Cluster Expansion Force Fields for Organic Molecules: beyond RMSE},
author = {D. P. Kovacs and C. van der Oord and J. Kucera and A. Allen and D. Cole and C. Ortner and G. Csanyi},
journal = {J. Chem. Theory Comput.},
volume = {17},
year = {2021},
doi = {https://doi.org/10.1021/acs.jctc.1c00647},
url = {https://chemrxiv.org/engage/chemrxiv/article-details/60dc704cf7373f0c3843a874},
pdf = {https://chemrxiv.org/engage/api-gateway/chemrxiv/assets/orp/resource/item/60dc704cf7373f0c3843a874/original/linear-atomic-cluster-expansion-force-fields-for-organic-molecules-beyond-rmse.pdf}
}
@article{2021-apxsym,
title = {Polynomial Approximation of Symmetric Functions},
author = {Markus Bachmayr and Geneviève Dusson and Christoph Ortner and Jack Thomas},
journal = {Math. Comp.},
volume = {93},
year = {2024},
pages = {811-839},
doi = {https://doi.org/10.1090/mcom/3868},
url = {https://arxiv.org/abs/2109.14771},
pdf = {https://arxiv.org/pdf/2109.14771.pdf}
}
@article{2021-sensitivity,
title = {Local invertibility and sensitivity of atomic structure-feature mappings},
author = {Sergey N. Pozdnyakov and Liwei Zhang and Christoph Ortner and Gabor Csanyi and Michele Ceriotti},
journal = {Open Res Europe},
volume = {1},
number = {126},
year = {2021},
doi = {https://doi.org/10.12688/openreseurope.14156.1},
url = {https://arxiv.org/abs/2109.11440},
pdf = {https://arxiv.org/pdf/2109.11440.pdf}
}
@article{2021-defectexpansion,
title = {Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect},
author = {Julian Braun, Thomas Hudson, Christoph Ortner},
journal = {Arch. Ration. Mech. Anal.},
volume = {246},
year = {2022},
doi = {10.1007/s00205-022-01810-3},
url = {https://arxiv.org/abs/2108.04765},
pdf = {https://arxiv.org/pdf/2108.04765.pdf}
}
@article{2021-qmmm3,
title = {QM/MM Methods for Crystalline Defects. Part 3: Machine-Learned Interatomic Potentials},
author = {Huajie Chen, Christoph Ortner, Yangshuai Wang},
journal = {SIAM Multiscale Model. Simul.},
volume = {20},
year = {2022},
url = {https://arxiv.org/abs/2106.14559},
pdf = {https://arxiv.org/pdf/2106.14559.pdf},
doi = {10.1137/21M1441122}
}
@article{2021-tbmanybody,
title = {Rigorous body-order approximations of an electronic structure potential energy landscape},
author = {Jack Thomas and Huajie Chen and Christoph Ortner},
journal = {Arch. Ration. Mech. Anal.},
volume = {246},
year = {2022},
url = {https://arxiv.org/abs/2106.12572},
pdf = {https://arxiv.org/pdf/2106.12572.pdf},
doi = {https://doi.org/10.1007/s00205-022-01809-w}
}
@article{2021-lavrentiev,
title = {Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap},
author = {Anna Kh Balci and Christoph Ortner and Johannes Storn},
journal = {Numer. Math.},
volume = {151},
year = {2022},
doi = {https://doi.org/10.1007/s00211-022-01303-1},
url = {https://arxiv.org/abs/2106.06837},
pdf = {https://arxiv.org/pdf/2106.06837.pdf}
}
@article{2021-descriptors,
title = {Physics-inspired structural representations for molecules and materials},
author = {Felix Musil and Andrea Grisafi and Albert P. Bartók and Christoph Ortner and Gábor Csányi and Michele Ceriotti},
journal = {Chem. Rev.},
volume = {121},
year = {2021},
url = {https://arxiv.org/abs/2101.04673},
pdf = {https://arxiv.org/pdf/2101.04673.pdf},
doi = {https://doi.org/10.1021/acs.chemrev.1c00021}
}
@article{2020-apipsff,
title = {Atomic permutationally invariant polynomials for fitting molecular force fields},
author = {A. E. A. Allen and G. Dusson and C. Ortner and G. Csanyi},
journal = {Mach. Learn.: Sci. Technol.},
year = {2021},
volume = {2},
pages = {025017},
url = {https://arxiv.org/pdf/2010.12200},
pdf = {https://arxiv.org/pdf/2010.12200.pdf},
doi = {https://doi.org/10.1088/2632-2153/abd51e}
}
@article{2020-pace1,
title = {Performant implementation of the atomic cluster expansion (PACE): Application to copper and silicon},
author = {Y. Lysogorskiy and C. van der Oord and A. Bochkarev and S. Menon and M. Rinaldi and T. Hammerschmidt and M. Mrovec and A. Thompson and G. Csányi and C. Ortner and R. Drautz},
journal = {npj Computational Materials},
volume = {7},
year = {2021},
url = {https://arxiv.org/abs/2103.00814},
pdf = {https://arxiv.org/pdf/2103.00814.pdf},
doi = {https://doi.org/10.1038/s41524-021-00559-9}
}
@article{2020-qmmmadaptfem,
title = {A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods},
author = {Y. Wang and H. Chen and M. Liao and C. Ortner and H. Wang and
L. Zhang},
journal = {SIAM J. Sci. Comput.},
volume = {43},
year = {2021},
url = {https://arxiv.org/abs/2007.05260},
pdf = {https://arxiv.org/pdf/2007.05260.pdf},
doi = {https://doi.org/10.1137/20M1353678}
}
@article{2020-sensitdesc,
title = {Sensitivity and Dimensionality of Atomic Environment Representations used for Machine Learning Interatomic Potentials},
author = {B. Onat and C. Ortner and James R. Kermode},
journal = {J. Chem. Phys.},
volume = {153},
year = {2020},
url = {https://arxiv.org/abs/2006.01915},
pdf = {https://arxiv.org/pdf/2006.01915.pdf},
doi = {https://doi.org/10.1063/5.0016005}
}
@article{2020-pointdeftbins,
title = {Point Defects in Tight Binding Models for Insulators},
author = {C. Ortner and J. Thomas},
journal = {Math. Models Meth. Appl. Sc.},
volume = {30},
number = {14},
year = {2020},
url = {https://arxiv.org/abs/2004.05356},
pdf = {https://arxiv.org/pdf/2004.05356.pdf},
doi = {https://doi.org/10.1142/S0218202520500542}
}
@article{2020-descriptors,
title = {On the Completeness of Atomic Structure Representations},
author = {S. N. Pozdnyakov and M. J. Willatt and A. P. Bart\'{o}k and C. Ortner and G\'{a}bor Cs\'{a}nyi and Michele Ceriotti},
journal = {Phys. Rev. Lett.},
volume = {125},
pages = {166001},
year = {2020},
url = {https://arxiv.org/abs/2001.11696},
pdf = {https://arxiv.org/pdf/2001.11696.pdf},
doi = {https://doi.org/10.1103/PhysRevLett.125.166001}
}
@article{2019-ship1,
title = {Atomic Cluster Expansion: Completeness, Efficiency and Stability},
author = {M. Bachmayr and G. Csanyi and G. Dusson and R. Drautz and S. Etter and C. van der Oord and C. Ortner},
journal = {J. Comp. Phys.},
volume = {454},
year = {2022},
doi = {https://doi.org/10.1016/j.jcp.2022.110946},
url = {https://arxiv.org/abs/1911.03550},
pdf = {https://arxiv.org/pdf/1911.03550.pdf}
}
@article{2019-dislmulti,
title = {Theoretical Study of Elastic Far-Field Decay from Dislocations in Multilattices},
author = {D. Olson and C. Ortner},
journal = {Multiscale Modeling & Simulation},
volume = {21},
year = {2023},
url = {https://arxiv.org/abs/1910.12269},
pdf = {https://arxiv.org/pdf/1910.12269.pdf},
doi = {10.1137/22M1502021}
}
@article{2019-regapips1,
title = {Regularised Atomic Body-Ordered Permutation-Invariant Polynomials for the Construction of Interatomic Potentials},
author = {C. van der Oord and G. Dusson and G. Csanyi and C. Ortner},
journal = {Mach. Learn.: Sci. Technol.},
volume = {1},
year = {2020},
url = {https://arxiv.org/abs/1910.06010},
pdf = {https://arxiv.org/pdf/1910.06010.pdf},
doi = {10.1088/2632-2153/ab527c}
}
@article{2019-conductbilayer,
title = {Modeling and Computation of Kubo Conductivity for 2D Incommensurate Bilayers},
author = {S. Etter and D. Massat and M. Luskin and C. Ortner},
journal = {Multiscale Model. Simul.},
volume = {18},
year = {2020},
url = {https://arxiv.org/abs/1907.01314},
pdf = {https://arxiv.org/pdf/1907.01314.pdf},
doi = {https://doi.org/10.1137/19M1273499}
}
@article{2019-tbloc0T,
title = {Locality of Interatomic Forces in Tight Binding Models for Insulators},
author = {H. Chen and C. Ortner and J. Thomas},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {54},
year = {2020},
url = {https://arxiv.org/abs/1906.11740},
pdf = {https://arxiv.org/pdf/1906.11740.pdf},
doi = {https://doi.org/10.1051/m2an/2020020}
}
@article{2019-crackbif,
title = {Analysis of Cell Size Effects in Atomistic Crack Propagation},
author = {M. Buze and T. Hudson and C. Ortner},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {54},
year = {2020},
pages = {1821 - 1847},
url = {https://arxiv.org/abs/1905.13328},
pdf = {https://arxiv.org/pdf/1905.13328.pdf},
doi = {https://doi.org/10.1051/m2an/2020005}
}
@article{2018-uniform,
title = {Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect},
author = {J. Braun and C. Ortner},
journal = {SIAM J. Numer. Anal.},
volume = {58},
year = {2020},
url = {https://arxiv.org/abs/1811.08741},
pdf = {https://arxiv.org/pdf/1811.08741.pdf},
doi = {10.1137/18M122830X}
}
@article{2018-entropy,
title = {Thermodynamic Limit of the Transition Rate of a Crystalline Defect},
author = {J. Braun and M. H. Duong and C. Ortner},
journal = {Arch. Ration. Mech. Anal.},
volume = {238},
year = {2020},
url = {https://arxiv.org/abs/1810.11643},
pdf = {https://arxiv.org/pdf/1810.11643.pdf},
doi = {10.1007/s00205-020-01568-6}
}
@article{2018-antiplanecrack,
title = {Analysis of an atomistic model for anti-plane fracture},
author = {M. Buze and T. Hudson and C. Ortner},
journal = {Math. Models Meth. Appl. Sc.},
volume = {29},
year = {2019},
url = {https://arxiv.org/abs/1810.05501},
pdf = {https://arxiv.org/pdf/1810.05501.pdf},
doi = {10.1142/S0218202519500520}
}
@article{2018-preconstring,
title = {A preconditioning scheme for minimum energy path finding methods},
author = {S. Makri and C. Ortner and J. R. Kermode},
journal = {J. Chem. Phys.},
volume = {150},
year = {2019},
url = {https://arxiv.org/abs/1810.02705},
pdf = {https://arxiv.org/pdf/1810.02705.pdf},
doi = {10.1063/1.5064465}
}
@article{2018-ffprecon,
title = {Preconditioners for the geometry optimisation and saddle point search of molecular systems},
author = {L. Mones and C. Ortner and G. Csanyi},
journal = {Scientific Reports},
volume = {8},
year = {2018},
pages = {13991},
url = {https://arxiv.org/abs/1804.01590},
pdf = {https://arxiv.org/pdf/1804.01590.pdf},
doi = {10.1038/s41598-018-32105-x}
}
@article{2017-bcscrew,
title = {The Effect of Crystal Symmetries on the Locality of Screw Dislocation Cores},
author = {J. Braun and M. Buze and C. Ortner},
journal = {SIAM J. Math. Anal.},
volume = {51},
year = {2019},
url = {http://arxiv.org/abs/1710.07708},
pdf = {http://arxiv.org/pdf/1710.07708.pdf},
doi = {10.1137/17M1157520}
}
@article{2017-bem,
title = {Coupling Atomistic, Elasticity and Boundary Element Models},
author = {A. S. Dedner and C. Ortner and H. Wu},
journal = {ArXiv e-prints},
volume = {1709.05977},
year = {2017},
url = {http://arxiv.org/abs/1709.05977},
pdf = {http://arxiv.org/pdf/1709.05977.pdf}
}
@article{2017-defects,
title = {Geometry Equilibration of Crystalline Defects in Quantum and Atomistic Descriptions},
author = {H. Chen and F. Q. Nazar and C. Ortner},
journal = {Math. Models Meth. Appl. Sc.},
volume = {29},
year = {2019},
url = {http://arxiv.org/abs/1709.02770},
pdf = {http://arxiv.org/pdf/1709.02770.pdf},
doi = {10.1142/S0218202519500131}
}
@article{2017-momentumspace,
title = {Incommensurate Heterostructures in Momentum Space},
author = {D. Massat and S. Carr and M. Luskin and C. Ortner},
journal = {SIAM Multiscale Model. Simul.},
volume = {16},
year = {2018},
url = {http://arxiv.org/abs/1708.02320},
pdf = {http://arxiv.org/pdf/1708.02320.pdf},
doi = {10.1137/17M1141035}
}
@article{2017-ljstacking,
title = {Polytypism in the ground state structure of the Lennard-Jonesium},
author = {L. B. P\'artay and C. Ortner and A. P. Bart\'ok and C. J.
Pickard and G. Cs\'anyi},
journal = {Phys. Chem. Chem. Phys.},
volume = {19},
year = {2017},
url = {http://arxiv.org/abs/1705.01751},
pdf = {http://arxiv.org/pdf/1705.01751.pdf},
doi = {10.1039/C7CP02923C}
}
@article{2016-pmd1,
title = {Some Remarks on Preconditioning Molecular Dynamics},
author = {H. Alrachid, L. Mones, C. Ortner},
journal = {SMAI J. Comp. Math.},
volume = {4},
year = {2018},
pages = {57--80},
url = {http://arxiv.org/abs/1612.05435},
pdf = {http://arxiv.org/pdf/1612.05435.pdf},
doi = {10.5802/smai-jcm.29}
}
@article{2016-multibqcf,
title = {Force-Based Atomistic/Continuum Blending for Multilattices},
author = {D. Olson and X. Li and C. Ortner and B. Van~Koten},
journal = {Numer. Math.},
volume = {140},
year = {2018},
doi = {10.1007/s00211-018-0979-x},
url = {http://arxiv.org/abs/1611.05935},
pdf = {http://arxiv.org/pdf/1611.05935v1.pdf}
}
@article{2016-multipt,
title = {Regularity and Locality of Point Defects in Multilattices},
author = {D. Olson and C. Ortner},
journal = {Appl. Math. Res. Express},
volume = {1-41},
year = {2017},
url = {http://arxiv.org/abs/1608.08930},
pdf = {http://arxiv.org/pdf/1608.08930v1.pdf},
doi = {10.1093/amrx/abw012}
}
@article{2016-realspace,
title = {Electronic Density of States for Incommensurate Layers},
author = {D. Massatt and M. Luskin and C. Ortner},
journal = {SIAM Multiscale Model. Simul.},
volume = {15},
year = {2017},
doi = {10.1137/16M1088363},
url = {http://arxiv.org/abs/1608.01968},
pdf = {http://arxiv.org/pdf/1608.01968v1.pdf}
}
@article{2016-dimercycling,
title = {Convergence and Cycling in Walker-type Saddle Search Algorithms},
author = {A. Levitt and C. Ortner},
journal = {SIAM J. Numer. Anal.},
volume = {55},
issue = {5},
year = {2017},
url = {http://arxiv.org/abs/1607.08875},
pdf = {http://arxiv.org/pdf/1607.08875v1.pdf},
doi = {10.1137/16M1087199}
}
@article{2016-tblimit,
title = {Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding},
author = {H. Chen and J. Lu and C. Ortner},
journal = {Arch. Ration. Mech. Anal.},
volume = {230},
year = {2018},
doi = {10.1007/s00205-018-1256-y},
url = {http://arxiv.org/abs/1607.06850},
pdf = {http://arxiv.org/pdf/1607.06850v1.pdf}
}
@article{2016-qcp2,
title = {Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements},
author = {A. Dedner and H. Wu and C. Ortner},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {51},
year = {2017},
doi = {https://doi.org/10.1051/m2an/2017013},
url = {http://arxiv.org/abs/1607.05936},
pdf = {http://arxiv.org/pdf/1607.05936v1.pdf}
}
@article{2016-scbpc,
title = {Analysis of a Predictor-Corrector Method for Computationally
Efficient Modeling of Surface Effects in 1D},
author = {A. J. Binder and M. Luskin and C. Ortner},
journal = {Multiscale Model. Simul.},
volume = {15},
number = {2},
year = {2017},
url = {http://arxiv.org/abs/1605.05750},
pdf = {http://arxiv.org/pdf/1605.05750v1.pdf},
doi = {10.1137/16M1065884}
}
@article{2016-defectFE1d,
title = {On assessing the accuracy of defect free energy computations},
author = {M. Dobson and M. H. Duong and C. Ortner},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {52},
year = {2018},
doi = {10.1051/m2an/2017052},
url = {http://arxiv.org/abs/1602.08643},
pdf = {http://arxiv.org/pdf/1602.08643v1.pdf}
}
@article{2016-precon1,
title = {A universal preconditioner for simulating condensed phase materials},
author = {D. Packwood and J. Kermode and L. Mones and N. Bernstein and
J. Woolley and N. I. M. Gould and C. Ortner and G. Csanyi},
journal = {J. Chem. Phys.},
year = {2016},
volume = {144},
numer = {16},
doi = {http://dx.doi.org/10.1063/1.4947024},
url = {http://arxiv.org/abs/1604.02570},
pdf = {http://arxiv.org/pdf/1604.02570v1.pdf}
}
@article{2015-tfw,
title = {Locality of the Thomas-Fermi-von Weizsäcker Equations},
author = {F. Q. Nazar and C. Ortner},
journal = {Arch. Ration. Mech. Anal.},
volume = {224},
number = {3},
year = {2017},
url = {http://arxiv.org/abs/1509.06753},
pdf = {http://arxiv.org/pdf/1509.06753.pdf},
doi = {http://www.springer.com/-/3/AVptXfqrBAK9zfPt6NeV}
}
@article{2015-qmtb2,
title = { {QM/MM} Methods for Crystalline Defects. {P}art 2: Consistent energy
and force-mixing},
author = {H. Chen and C. Ortner},
journal = {Multiscale Model. Simul.},
volume = {15(1)},
year = {2017},
doi = {http://dx.doi.org/10.1137/15M1041250},
url = {http://arxiv.org/abs/1509.06627},
pdf = {http://arxiv.org/pdf/1509.06627.pdf}
}
@article{2015-qmtb1,
title = { {QM/MM} Methods for Crystalline Defects. {P}art 1: Locality of the Tight
Binding Model},
author = {H. Chen and C. Ortner},
journal = {Multiscale Model. Simul.},
volume = {14(1)},
year = {2016},
doi = {http://dx.doi.org/10.1137/15M1022628},
url = {http://arxiv.org/abs/1505.05541},
pdf = {http://arxiv.org/pdf/1505.05541.pdf}
}
@article{2014-dimer,
title = {A dimer-type saddle search algorithm with preconditioning and linesearch},
author = {N. Gould and C. Ortner and D. Packwood},
journal = {Math. Comp.},
volume = {85},
year = {2016},
pages = {2939-2966},
url = {http://arxiv.org/abs/1407.2817},
pdf = {pdfs/2014-dimer.pdf}
}
@article{2014-bgfc,
title = {Atomistic/Continuum Blending with Ghost Force Correction},
author = {C. Ortner and L. Zhang},
journal = {SIAM J. Sci. Comput.},
volume = {38},
year = {2016},
pdf = {https://arxiv.org/pdf/1407.0053},
url = {https://arxiv.org/abs/1407.0053},
doi = {10.1137/15M1020241}
}
@article{2014-bqce,
author = {X. H. Li and C. Ortner and A. Shapeev and B. Van~Koten},
title = {Analysis of blended atomistic/continuum hybrid methods},
journal = {Numer. Math.},
volume = {134},
year = {2016},
doi = {10.1007/s00211-015-0772-z},
url = {http://arxiv.org/abs/1404.4878},
pdf = {pdfs/2014-bqce.pdf}
}
@article{2014-dislift,
author = {T. Hudson and C. Ortner},
title = {Analysis of stable screw dislocation configurations in an anti-plane lattice model},
journal = {SIAM J. Math. Anal.},
year = {2015},
volume = {41},
pages = {291--320},
url = {http://arxiv.org/abs/1403.0518},
pdf = {pdfs/2014-dislift.pdf}
}
@article{2013-grac.bench,
author = {C. Ortner and L. Zhang},
title = {Energy-based atomisitic-to-continuum coupling without ghost forces},
journal = {Comput. Meth. Appl. Mech. Engrg.},
volume = {279},
year = {2014},
pages = {29-45},
url = {http://arxiv.org/abs/1312.6814},
pdf = {pdfs/2013-grac.bench.pdf}
}
@article{2013-stab.ac,
author = {C. Ortner and A. Shapeev and L. Zhang},
title = {(In-)Stability and Stabilisation of QNL-Type
Atomistic-to-Continuum Coupling Methods},
journal = {SIAM Multiscale Model. Simul.},
volume = 12,
issue = 3,
pages = {1258--1293},
year = 2014,
url = {http://arxiv.org/abs/1308.3894},
pdf = {pdfs/2013-stab.ac.pdf}
}
@article{2013-visc,
author = {A. Mielke and C. Ortner and Y. Sengul},
title = {An approach to nonlinear viscoleasticity via metric gradient flows},
journal = {SIAM J. Math. Anal.},
year = {2014},
volume = {46},
issue = {2},
pages = {1317--1347},
pdf = {pdfs/2013-visc.pdf}
}
@article{2013-defects,
author = {V. Ehrlacher and C. Ortner and A. V. Shapeev},
title = {Analysis of Boundary Conditions for Crystal Defect Atomistic
Simulations},
journal = {Arch. Ration. Mech. Anal.},
volume = {222},
year = {2016},
url = {https://arxiv.org/abs/1306.5334},
doi = {10.1007/s00205-016-1019-6},
pdf = {https://arxiv.org/pdf/1306.5334.pdf}
}
@article{2013-disl,
author = {T. Hudson and C. Ortner},
title = {Existence and stability of a screw dislocation under
anti-plane deformation},
journal = {Arch. Ration. Mech. Anal.},
year = {2014},
volume = {213},
number = {3},
pages = {887--929},
url = {http://arxiv.org/abs/1304.2500},
pdf = {pdfs/2013-ARMA-disl.pdf}
}
@article{2013-CMAME-bqcfcomp,
author = {X. Li and M. Luskin and C. Ortner and A. Shapeev},
title = {Theory-based Benchmarking of the Blended Force-Based
Quasicontinuum Method},
journal = {Comput. Methods Appl. Mech. Engrg.},
year = {2014},
volume = {268},
pages = {763--781},
url = {http://arxiv.org/abs/1304.1368},
pdf = {pdfs/2013-CMAME-bqcfcomp.pdf}
}
@article{2013-atc.acta,
author = {M. Luskin and C. Ortner},
title = {Atomistic-to-continuum-coupling},
journal = {Acta Numerica},
year = 2013,
url = {http://journals.cambridge.org/action/displayJournal?jid=anu},
pdf = {pdfs/2013-acta.pdf}
}
@misc{2012-partialvisc,
author = {P. Pathmanathan and C. Ortner and D. Kay},
title = {Existence of solutions of partially degenerate
visco-elastic problems, and applications to
modelling muscular contraction and cardiac
electro-mechanical activity},
pdf = {pdfs/2012-PartialVisc.pdf}
}
@article{2012-ac.aposteriori.1d,
author = {C. Ortner and H. Wang},
title = {A posteriori error control for a quasicontinuum approximation of a periodic chain},
journal = {ArXiV e-prints},
year = {2012},
volume = {1211.3346},
note = {to appear in IMA J. Numer. Anal.},
pdf = {pdfs/2012-IMAJNA-ac.aposteriori.1d.pdf}
}
@article{2012-lattint,
author = {C. Ortner and A. Shapeev},
title = {Interpolants of Lattice Functions for the Analysis of
Atomistic/Continuum Multiscale Methods},
journal = {ArXiv e-prints},
volume = {1204.3705},
year = {2012},
url = {http://arxiv.org/abs/1204.3705},
pdf = {pdfs/2012-lattint.pdf}
}
@article{2012-multi1,
author = {B. Van Koten and C. Ortner},
title = {Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model},
journal = {SIAM Multiscale Modelling and Simulation},
volume = {11},
year = {2013},
url = {http://arxiv.org/abs/1203.5854},
pdf = {pdfs/2012-MMS-multi1.pdf},
doi = {http://dx.doi.org/10.1137/120870220}
}
@article{2012-ARMA-cb,
author = {C. Ortner and F. Theil},
title = {Justification of the Cauchy--Born Approximation of Elastodynamics},
journal = {Arch. Ration. Mech. Anal.},
volume = 207,
year = 2013,
url = {http://arxiv.org/abs/1202.3858},
doi = {10.1007/s00205-012-0592-6},
pdf = {pdfs/2012-ARMA-cb.pdf}
}
@article{2012-ARXIV-ellRd,
author = {Ortner, C. and S\"{u}li, E.},
title = {A note on linear elliptic systems on $\mathbb{R}^d$},
journal = {ArXiv e-prints},
volume = {1202.3970},
year = {2012},
url = {http://arxiv.org/abs/1202.3970},
pdf = {pdfs/2012-ARXIV-ellRd.pdf}
}
@article{2012-encyclopedia,
author = {Luskin, M. and Ortner, C.},
title = {Atomistic-to-continuum coupling},
journal = {Springer Encyclopedia for Applied and Computational Mathematics},
year = {2013},
pdf = {pdfs/2012-encyclopedia.pdf},
url = {http://www.springer.com/mathematics/computational+science+engineering/book/978-3-540-70528-4}
}
@article{2012-MMS-bqcf.stab,
author = {Li, X. and Luskin, M. and Ortner, C.},
title = {Positive-Definiteness of the Blended Force-Based
Quasicontinuum Method},
journal = {Multiscale Model. Simul.},
volume = {10},
year = {2012},
url = {http://arxiv.org/abs/1112.2528},
doi = {http://dx.doi.org/10.1137/110859270},
pdf = {pdfs/2012-MMS-bqcf.stab.pdf}
}
@article{2012-CMAME-optbqce,
author = {Luskin, M. and Ortner, C. and Van Koten, B.},
title = {Formulation and optimization of the energy-based blended
quasicontinuum method},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {253},
year = {2013},
url = {http://arxiv.org/abs/1112.2377},
doi = {http://dx.doi.org/10.1016/j.cma.2012.09.007},
pdf = {pdfs/2013-CMAME-optbqce.pdf}
}
@article{2012-MMS-ac.dft.1d,
author = { {Langwallner}, B. and {Ortner}, C. and {S{\"u}li}, E.},
title = { {Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory}},
journal = {Multiscale Model. Simul.},
volume = {11},
year = 2013,
doi = {http://dx.doi.org/10.1137/110857787},
url = {http://arxiv.org/abs/1112.0746},
pdf = {pdfs/2012-MMS-ac.dft.1d.pdf}
}
@article{2013-ac.scb.1d,
author = { {Jayawardana}, K. and {Mordacq}, C. and {Ortner}, C. and {Park}, H.~S.},
title = { {An Analysis of the Boundary Layer in the 1D Surface Cauchy--Born Model}},
journal = {ESAIM: Math. Model. Numer. Anal.},
volume = {47},
year = 2013,
url = {http://dx.doi.org/10.1051/m2an/2012021},
pdf = {pdfs/2013-M2AN-ac.scb.1d.pdf}
}
@article{2012-SINUM-ac.2dcorners,
author = { {Ortner}, C. and {Zhang}, L.},
title = { {Construction and sharp consistency estimates for
atomistic/continuum coupling methods with general
interfaces: a 2D model problem}},
journal = {SIAM J. Numer. Anal.},
volume = {50},
year = 2012,
url = {http://arxiv.org/abs/1110.0168},
doi = {http://dx.doi.org/10.1137/110851791},
pdf = {pdfs/2012-SINUM-ac.2dcorners.pdf}
}
@article{2012-MATHCOMP-qce.pair,
author = { {Ortner}, C. and {Shapeev}, A.~V.},
title = { {Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice}},
journal = {Math. Comp.},
volume = {82},
year = {2013},
url = {http://arxiv.org/abs/1104.0311},
pdf = {pdfs/2012-MATHCOMP-qce.pair.pdf},
doi = {http://dx.doi.org/10.1090/S0025-5718-2013-02687-7}
}
@article{2012-M2AN-qc.patch.2d,
author = { {Ortner}, C.},
title = { {The role of the patch test in 2D atomistic-to-continuum coupling methods}},
journal = {ESAIM Math. Model. Numer. Anal.},
volume = {46},
year = {2012},
url = {http://dx.doi.org/10.1051/m2an/2012005},
pdf = {pdfs/2012-M2AN-qc.patch.2d.pdf}
}
@incollection{2012-SLN-DurhamSympProc,
author = {Van Koten, Brian and Li, Xingjie Helen and Luskin, Mitch and Ortner, Christoph},
title = {A computational and theoretical investigation of the
accuracy of quasicontinuum methods},
booktitle = {Numerical Analysis of Multiscale Problems},
publisher = {Springer Lecture Notes in Computational Science and Engineering 83},
year = {2012},
editor = {Ivan Graham and Tom Hou and Omar Lakkis and Rob Scheichl},
pdf = {pdfs/2012-DurhamSympProc.pdf}
}
@article{2012-MMS-qcf.spectrum,
author = { {Dobson}, M. and {Ortner}, C. and {Shapeev}, A.~V.},
title = { {The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain}},
journal = {Multiscale Model. Simul.},
volume = {10},
number = {3},
year = {2012},
url = {http://arxiv.org/abs/1004.3435},
pdf = {pdfs/2012-MMS-qcf.spectrum.pdf}
}
@article{2011-M3AS-qc.coarse,
author = {Ortner, C. and Wang, H.},
title = {A Priori Error Estimates for Energy-Based Quasicontinuum
Approximations of a Periodic Chain},
journal = {Math. Models Methods Appl. Sc.},
year = {2011},
volume = {21},
pages = {2491--2521},
doi = {10.1142/S0218202511005817},
url = {http://dx.doi.org/10.1142/S0218202511005817},
pdf = {pdfs/2011-M3AS-qc.coarse.pdf}
}
@article{2012-IJMCE-sac,
author = {Makridakis, C. and Ortner, C. and S\"{u}li, E.},
title = {Stress-based atomistic/continuum coupling: a new variant of the quasicontinuum approximation},
journal = {Int. J. Multiscale Comp. Engrg.},
volume = {10},
year = {2012},
pdf = {pdfs/2012-IJMCE-sac.pdf}
}
@incollection{2012-stat.qcf,
author = { {Luskin}, M. and {Ortner}, C.},
title = {Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation},
booktitle = {Numerical Analysis and Multiscale Computations},
publisher = {Springer Lect. Notes Comput. Sci. Eng. Springer 82},
year = {2011},
editor = {Bjorn Engquist and Olof Runborg and Richard Tsai},
url = {http://arxiv.org/abs/1104.1774},
pdf = {pdfs/2011-stat.qcf.pdf}
}
@article{2012-M3AS-genat,
author = {Burke, Siobhan and Ortner, Christoph and S{\"u}li, Endre},
title = {An adaptive finite element approximation of a
generalised Ambrosio--Tortorelli functional},
journal = {Math. Models Meth. Appl. Sc.},
volume = {23},
year = {2013},
url = {http://www2.maths.ox.ac.uk/oxmos/reports/},
doi = {10.1142/S021820251350019X},
pdf = {pdfs/2012-M3AS-genat.pdf}
}
@article{2012-M2AN-CBstab,
author = {Hudson, Thomas and Ortner, Christoph},
title = {On the stability of {B}ravais lattices and their
{C}auchy--{B}orn approximations},
journal = {M2AN Math. Model. Numer. Anal.},
fjournal = {M2AN. Mathematical Modelling and Numerical Analysis},
volume = {46},
year = {2012},
pages = {81--110},
pdf = {pdfs/2012-M2AN-CBstab.pdf}
}
@article{2011-NUMMATH-qcf1d,
author = {Makridakis, Charalambos and Ortner, Christoph and S\"{u}li, Endre},
title = {A priori error analysis of two force-based
atomistic/continuum models of a periodic chain},
journal = {Numer. Math.},
fjournal = {Numerische Mathematik},
volume = {119},
year = {2011},
number = {1},
pages = {83--121},
issn = {0029-599X},
coden = {NUMMA7},
mrclass = {65N12 (65N15 70C20)},
doi = {10.1007/s00211-011-0380-5},
url = {http://dx.doi.org/10.1007/s00211-011-0380-5},
pdf = {pdfs/2011-NUMMATH-qcf1d.pdf}
}
@article{2011-NUMMATH-GradConstr,
author = {Ortner, Christoph and Wollner, Winnifried},
title = {A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state},
journal = {Numerische Mathematik},
publisher = {Springer Berlin / Heidelberg},
issn = {0029-599X},
keyword = {Mathematics and Statistics},
pages = {587-600},
volume = {118},
issue = {3},
url = {http://dx.doi.org/10.1007/s00211-011-0360-9},
doi = {10.1007/s00211-011-0360-9},
year = {2011},
pdf = {pdfs/2011-NUMMATH-GradConstr.pdf}
}
@article{2011-CMAME-qcf.iter,
author = {Dobson, Matthew and Luskin, Mitch and Ortner, Christoph},
title = {Iterative methods for the force-based quasicontinuum
approximation: Analysis of a 1D model problem},
journal = {Comput. Methods Appl. Mech. Engrg.},
fjournal = {Computer Methods in Applied Mechanics and Engineering},
volume = {200},
year = {2011},
pages = {2697-2709},
doi = {doi:10.1016/j.cma.2010.07.008},
url = {http://dx.doi.org/10.1016/j.cma.2010.07.008},
pdf = {pdfs/2011-CMAME-qcf.iter.pdf}
}
@article{2011-IMAJNA-lavrentiev_nc,
author = {Ortner, Christoph},
title = {Nonconforming finite-element discretization of convex
variational problems},
journal = {IMA J. Numer. Anal.},
fjournal = {IMA Journal of Numerical Analysis},
volume = {31},
year = {2011},
pages = {847--864},
pdf = {pdfs/2011-IMAJNA-lavrentiev_nc.pdf}
}
@article{2011-MCOM-qnl1d,
author = {Ortner, Christoph},
title = {A priori and a posteriori analysis of the quasinonlocal
quasicontinuum method in 1{D}},
journal = {Math. Comp.},
fjournal = {Mathematics of Computation},
volume = {80},
year = {2011},
number = {275},
pages = {1265--1285},
issn = {0025-5718},
coden = {MCMPAF},
mrclass = {82Cxx (65N12 65N15 74A25 74G15)},
mrnumber = {2785458},
doi = {10.1090/S0025-5718-2010-02453-6},
url = {http://dx.doi.org/10.1090/S0025-5718-2010-02453-6},
pdf = {pdfs/2011-MCOM-qnl1d.pdf}
}
@article{2011-SINUM_ANCFEM,
author = {Ortner, Christoph and Praetorius, Dirk},
title = {On the convergence of adaptive nonconforming finite element
methods for a class of convex variational problems},
journal = {SIAM J. Numer. Anal.},
fjournal = {SIAM Journal on Numerical Analysis},
volume = {49},
year = {2011},
number = {1},
pages = {346--367},
issn = {0036-1429},
mrclass = {49M25 (49J45 65N12 65N30)},
mrnumber = {2783229},
doi = {10.1137/090781073},
url = {http://dx.doi.org/10.1137/090781073},
pdf = {pdfs/2011-SINUM_ANCFEM.pdf}
}
@article{2011-SINUM-allencahn,
author = {Bartels, S{\"o}ren and M{\"u}ller, R{\"u}diger and Ortner,
Christoph},
title = {Robust a priori and a posteriori error analysis for the
approximation of {A}llen-{C}ahn and {G}inzburg-{L}andau
equations past topological changes},
journal = {SIAM J. Numer. Anal.},
fjournal = {SIAM Journal on Numerical Analysis},
volume = {49},
year = {2011},
number = {1},
pages = {110--134},
issn = {0036-1429},
mrclass = {65M60 (65M15)},
mrnumber = {2764423},
doi = {10.1137/090751530},
url = {http://dx.doi.org/10.1137/090751530},
pdf = {pdfs/2011-SINUM-allencahn.pdf}
}
@incollection{2011-Ch-frac,
author = {Burke, Siobhan and Ortner, Christoph and S{\"u}li, Endre},
title = {Adaptive finite element approximation of the
{F}rancfort-{M}arigo model of brittle fracture},
booktitle = {Approximation and computation},
series = {Springer Optim. Appl.},
volume = {42},
pages = {297--310},
publisher = {Springer},
address = {New York},
year = {2011},
mrclass = {74R10 (65M60 74S05)},
mrnumber = {2759092},
pdf = {pdfs/2011-Ch-frac.pdf}
}
@article{2010-CMAM-PenaltyMethod,
author = {Carstensen, C. and Ortner, C.},
title = {Analysis of a class of penalty methods for computing singular
minimizers},
journal = {Comput. Methods Appl. Math.},
fjournal = {Computational Methods in Applied Mathematics},
volume = {10},
year = {2010},
number = {2},
pages = {137--163},
issn = {1609-4840},
mrclass = {65N30 (49M25 65N12 65N50)},
mrnumber = {2770287},
pdf = {pdfs/2010-CMAM-PenaltyMethod.pdf}
}
@article{2010-M3AS-tfwd,
author = {Langwallner, Bernhard and Ortner, Christoph and S{\"u}li,
Endre},
title = {Existence and convergence results for the {G}alerkin
approximation of an electronic density functional},
journal = {Math. Models Methods Appl. Sci.},
fjournal = {Mathematical Models \& Methods in Applied Sciences},
volume = {20},
year = {2010},
number = {12},
pages = {2237--2265},
issn = {0218-2025},
mrclass = {65K10 (65Z05 78A30)},
mrnumber = {2755499},
mrreviewer = {Fritz Keinert},
doi = {10.1142/S021820251000491X},
url = {http://dx.doi.org/10.1142/S021820251000491X},
pdf = {pdfs/2010-M3AS-tfwd.pdf}
}
@article{2010-JMPS-qce.stab,
author = {Dobson, M. and Luskin, M. and Ortner, C.},
title = {Accuracy of quasicontinuum approximations near instabilities},
journal = {J. Mech. Phys. Solids},
fjournal = {Journal of the Mechanics and Physics of Solids},
volume = {58},
year = {2010},
number = {10},
pages = {1741--1757},
issn = {0022-5096},
coden = {JMPSA8},
mrclass = {74G10 (74G70 74R10)},
mrnumber = {2742030},
mrreviewer = {Stefano Lenci},
doi = {10.1016/j.jmps.2010.06.011},
url = {http://dx.doi.org/10.1016/j.jmps.2010.06.011},
pdf = {pdfs/2010-JMPS-qce.stab.pdf}
}
@article{2010-NUMMATH-ABEM,
author = {Ferraz-Leite, S. and Ortner, C. and Praetorius, D.},
title = {Convergence of simple adaptive {G}alerkin schemes based on
{$h-h/2$} error estimators},
journal = {Numer. Math.},
fjournal = {Numerische Mathematik},
volume = {116},
year = {2010},
number = {2},
pages = {291--316},
issn = {0029-599X},
coden = {NUMMA7},
mrclass = {65N30 (65N15 65N38)},
mrnumber = {2672266 (2011f:65257)},
mrreviewer = {R{\'e}mi Vaillancourt},
doi = {10.1007/s00211-010-0292-9},
url = {http://dx.doi.org/10.1007/s00211-010-0292-9},
pdf = {pdfs/2010-NUMMATH-ABEM.pdf}
}
@article{2010-SINUM-afemat,
author = {Burke, Siobhan and Ortner, Christoph and S{\"u}li, Endre},
title = {An adaptive finite element approximation of a variational
model of brittle fracture},
journal = {SIAM J. Numer. Anal.},
fjournal = {SIAM Journal on Numerical Analysis},
volume = {48},
year = {2010},
number = {3},
pages = {980--1012},
issn = {0036-1429},
mrclass = {65N30 (65N50 74R10)},
mrnumber = {2669398 (2011j:65265)},
mrreviewer = {Luca Formaggia},
doi = {10.1137/080741033},
url = {http://dx.doi.org/10.1137/080741033},
pdf = {pdfs/2010-SINUM-afemat.pdf}
}
@article{2010-M3AS-dynafracat,
author = {Larsen, Christopher J. and Ortner, Christoph and S{\"u}li,
Endre},
title = {Existence of solutions to a regularized model of dynamic
fracture},
journal = {Math. Models Methods Appl. Sci.},
fjournal = {Mathematical Models \& Methods in Applied Sciences},
volume = {20},
year = {2010},
number = {7},
pages = {1021--1048},
issn = {0218-2025},
mrclass = {74R10 (74H20 74R15)},
mrnumber = {2673410 (2011g:74146)},
doi = {10.1142/S0218202510004520},
url = {http://dx.doi.org/10.1142/S0218202510004520},
pdf = {pdfs/2010-M3AS-dynafracat.pdf}
}
@article{2010-ARMA-QCF,
author = {Dobson, Matthew and Luskin, Mitchell and Ortner, Christoph},
title = {Stability, instability, and error of the force-based
quasicontinuum approximation},
journal = {Arch. Ration. Mech. Anal.},
fjournal = {Archive for Rational Mechanics and Analysis},
volume = {197},
year = {2010},
number = {1},
pages = {179--202},
issn = {0003-9527},
mrclass = {74A25 (35Q74 74S05)},
mrnumber = {2646818 (2011h:74009)},
mrreviewer = {Carsten Hartmann},
doi = {10.1007/s00205-009-0276-z},
url = {http://dx.doi.org/10.1007/s00205-009-0276-z},
pdf = {pdfs/2010-ARMA-QCF.pdf}
}
@article{2010-MMS-SharpStabQCF,
author = {Dobson, M. and Luskin, M. and Ortner, C.},
title = {Sharp stability estimates for the force-based quasicontinuum
approximation of homogeneous tensile deformation},
journal = {Multiscale Model. Simul.},
fjournal = {Multiscale Modeling \& Simulation. A SIAM Interdisciplinary
Journal},
volume = {8},
year = {2010},
number = {3},
pages = {782--802},
issn = {1540-3459},
mrclass = {74H55 (74A25 74B05)},
mrnumber = {2609639 (2011b:74055)},
doi = {10.1137/090767005},
url = {http://dx.doi.org/10.1137/090767005},
pdf = {pdfs/2010-MMS-SharpStabQCF.pdf}
}
@article{2009-IMAJNA-DGFEM,
author = {Buffa, Annalisa and Ortner, Christoph},
title = {Compact embeddings of broken {S}obolev spaces and
applications},
journal = {IMA J. Numer. Anal.},
fjournal = {IMA Journal of Numerical Analysis},
volume = {29},
year = {2009},
number = {4},
pages = {827--855},
issn = {0272-4979},
coden = {IJNADN},
mrclass = {65J05 (65N30)},
mrnumber = {2557047 (2010k:65097)},
doi = {10.1093/imanum/drn038},
url = {http://dx.doi.org/10.1093/imanum/drn038},
pdf = {pdfs/2009-IMAJNA-DGFEM.pdf}
}
@article{2009-SINUM-QCCluster,
author = {Luskin, Mitchell and Ortner, Christoph},
title = {An analysis of node-based cluster summation rules in the
quasicontinuum method},
journal = {SIAM J. Numer. Anal.},
fjournal = {SIAM Journal on Numerical Analysis},
volume = {47},
year = {2009},
number = {4},
pages = {3070--3086},
issn = {0036-1429},
mrclass = {65N30 (70C20 74A25)},
mrnumber = {2551158 (2010k:65263)},
doi = {10.1137/080743391},
url = {http://dx.doi.org/10.1137/080743391},
pdf = {pdfs/2009-SINUM-QCCluster.pdf}
}
@article{2009-SINUM-ApostEx,
author = {Ortner, C.},
title = {A posteriori existence in numerical computations},
journal = {SIAM J. Numer. Anal.},
fjournal = {SIAM Journal on Numerical Analysis},
volume = {47},
year = {2009},
number = {4},
pages = {2550--2577},
issn = {0036-1429},
mrclass = {65N15},
mrnumber = {2525611 (2010g:65189)},
doi = {10.1137/060668183},
url = {http://dx.doi.org/10.1137/060668183},
pdf = {pdfs/2009-SINUM-ApostEx.pdf}
}
@article{2008-M3AS-Griffith,
author = {Negri, Matteo and Ortner, Christoph},
title = {Quasi-static crack propagation by {G}riffith's criterion},
journal = {Math. Models Methods Appl. Sci.},
fjournal = {Mathematical Models \& Methods in Applied Sciences},
volume = {18},
year = {2008},
number = {11},
pages = {1895--1925},
issn = {0218-2025},
mrclass = {74R10 (74G15)},
mrnumber = {2472402 (2010a:74057)},
mrreviewer = {Kohji Ohtsuka},
doi = {10.1142/S0218202508003236},
url = {http://dx.doi.org/10.1142/S0218202508003236},
pdf = {pdfs/2008-M3AS-Griffith.pdf}
}
@article{2008-M2AN-QC1D,
author = {Ortner, Christoph and S{\"u}li, Endre},
title = {Analysis of a quasicontinuum method in one dimension},
journal = {M2AN Math. Model. Numer. Anal.},
fjournal = {M2AN. Mathematical Modelling and Numerical Analysis},
volume = {42},
year = {2008},
number = {1},
pages = {57--91},
issn = {0764-583X},
mrclass = {74A05 (65N99 70-08 70C20 70F45)},
mrnumber = {2387422 (2009e:74006)},
mrreviewer = {Paul Steinmann},
doi = {10.1051/m2an:2007057},
url = {http://dx.doi.org/10.1051/m2an:2007057},
pdf = {pdfs/2008-M2AN-QC1D.pdf}
}
@article{2007-SINUM-DGFEM,
author = {Ortner, Christoph and S{\"u}li, Endre},
title = {Discontinuous {G}alerkin finite element approximation of
nonlinear second-order elliptic and hyperbolic systems},
journal = {SIAM J. Numer. Anal.},
fjournal = {SIAM Journal on Numerical Analysis},
volume = {45},
year = {2007},
number = {4},
pages = {1370--1397},
issn = {0036-1429},
mrclass = {74S05 (65M60 74H15)},
mrnumber = {2338392 (2008g:74092)},
mrreviewer = {Jos{\'e} R. Fern{\'a}ndez},
doi = {10.1137/06067119X},
url = {http://dx.doi.org/10.1137/06067119X},
pdf = {pdfs/2007-SINUM-DGFEM.pdf}
}
@article{2006-SIMA-GFlow,
author = {Ortner, Christoph},
title = {Gradient flows as a selection procedure for equilibria of
nonconvex energies},
journal = {SIAM J. Math. Anal.},
fjournal = {SIAM Journal on Mathematical Analysis},
volume = {38},
year = {2006},
number = {4},
pages = {1214--1234},
issn = {0036-1410},
mrclass = {74G65 (26B25 35A15 35B38)},
mrnumber = {2274480 (2008h:74044)},
doi = {10.1137/050643982},
url = {http://dx.doi.org/10.1137/050643982},
pdf = {pdfs/2006-SIMA-GFlow.pdf}
}
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