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About the structure of the discrete and continuous Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>, Article 108128652211080. <a href=\"https://doi.org/10.1177/10812865221108094\">https://doi.org/10.1177/10812865221108094</a>","mla":"Cresson, Jacky, and Khaled Hariz-Belgacem. “About the Structure of the Discrete and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics of Solids</i>, 108128652211080, SAGE Publications, 2022, doi:<a href=\"https://doi.org/10.1177/10812865221108094\">10.1177/10812865221108094</a>.","short":"J. Cresson, K. 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Hariz-Belgacem, “About the structure of the discrete and continuous Eringen’s nonlocal elastica,” <i>Mathematics and Mechanics of Solids</i>, Art. no. 108128652211080, 2022, doi: <a href=\"https://doi.org/10.1177/10812865221108094\">10.1177/10812865221108094</a>.","chicago":"Cresson, Jacky, and Khaled Hariz-Belgacem. “About the Structure of the Discrete and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics of Solids</i>, 2022. <a href=\"https://doi.org/10.1177/10812865221108094\">https://doi.org/10.1177/10812865221108094</a>.","ama":"Cresson J, Hariz-Belgacem K. About the structure of the discrete and continuous Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1177/10812865221108094\">10.1177/10812865221108094</a>"},"publication_status":"published","publication_identifier":{"issn":["1081-2865","1741-3028"]},"article_number":"108128652211080","article_type":"original","keyword":["Mechanics of Materials","General Materials Science","General Mathematics"],"language":[{"iso":"eng"}],"_id":"39412","user_id":"98857","abstract":[{"text":"<jats:p> The Eringen’s nonlocal elastica equation does not possess a Lagrangian formulation. In this article, we find a variational integrating factor which enables us to provide a Lagrangian and Hamiltonian structure associated to this equation. Explicit expressions of the solutions in terms of elliptic integrals of the first kind are then deduced. We then derive discrete version of the Eringen’s nonlocal elastica preserving the Lagrangian and Hamiltonian structure and compare it with Challamel’s and co-worker definition of a discrete Eringen’s nonlocal elastica. </jats:p>","lang":"eng"}],"status":"public","type":"journal_article","publication":"Mathematics and Mechanics of Solids"},{"author":[{"first_name":"Vikram","full_name":"Gavini, Vikram","last_name":"Gavini"},{"first_name":"Stefano","last_name":"Baroni","full_name":"Baroni, Stefano"},{"first_name":"Volker","last_name":"Blum","full_name":"Blum, Volker"},{"full_name":"Bowler, David R.","last_name":"Bowler","first_name":"David R."},{"last_name":"Buccheri","full_name":"Buccheri, Alexander","first_name":"Alexander"},{"first_name":"James R.","full_name":"Chelikowsky, James R.","last_name":"Chelikowsky"},{"full_name":"Das, Sambit","last_name":"Das","first_name":"Sambit"},{"first_name":"William","last_name":"Dawson","full_name":"Dawson, William"},{"first_name":"Pietro","last_name":"Delugas","full_name":"Delugas, Pietro"},{"full_name":"Dogan, Mehmet","last_name":"Dogan","first_name":"Mehmet"},{"last_name":"Draxl","full_name":"Draxl, Claudia","first_name":"Claudia"},{"first_name":"Giulia","last_name":"Galli","full_name":"Galli, Giulia"},{"first_name":"Luigi","full_name":"Genovese, Luigi","last_name":"Genovese"},{"full_name":"Giannozzi, Paolo","last_name":"Giannozzi","first_name":"Paolo"},{"first_name":"Matteo","last_name":"Giantomassi","full_name":"Giantomassi, Matteo"},{"full_name":"Gonze, Xavier","last_name":"Gonze","first_name":"Xavier"},{"first_name":"Marco","full_name":"Govoni, Marco","last_name":"Govoni"},{"first_name":"Andris","full_name":"Gulans, Andris","last_name":"Gulans"},{"first_name":"François","full_name":"Gygi, François","last_name":"Gygi"},{"first_name":"John M.","last_name":"Herbert","full_name":"Herbert, John M."},{"first_name":"Sebastian","full_name":"Kokott, Sebastian","last_name":"Kokott"},{"first_name":"Thomas","last_name":"Kühne","id":"49079","full_name":"Kühne, Thomas"},{"last_name":"Liou","full_name":"Liou, Kai-Hsin","first_name":"Kai-Hsin"},{"first_name":"Tsuyoshi","last_name":"Miyazaki","full_name":"Miyazaki, Tsuyoshi"},{"first_name":"Phani","last_name":"Motamarri","full_name":"Motamarri, Phani"},{"first_name":"Ayako","full_name":"Nakata, Ayako","last_name":"Nakata"},{"full_name":"Pask, John E.","last_name":"Pask","first_name":"John E."},{"first_name":"Christian","id":"16153","full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl"},{"first_name":"Laura E.","last_name":"Ratcliff","full_name":"Ratcliff, Laura E."},{"last_name":"Richard","full_name":"Richard, Ryan M.","first_name":"Ryan M."},{"full_name":"Rossi, Mariana","last_name":"Rossi","first_name":"Mariana"},{"full_name":"Schade, Robert","id":"75963","last_name":"Schade","orcid":"0000-0002-6268-539","first_name":"Robert"},{"first_name":"Matthias","last_name":"Scheffler","full_name":"Scheffler, Matthias"},{"first_name":"Ole","last_name":"Schütt","full_name":"Schütt, Ole"},{"full_name":"Suryanarayana, Phanish","last_name":"Suryanarayana","first_name":"Phanish"},{"first_name":"Marc","last_name":"Torrent","full_name":"Torrent, Marc"},{"first_name":"Lionel","last_name":"Truflandier","full_name":"Truflandier, Lionel"},{"full_name":"Windus, Theresa L.","last_name":"Windus","first_name":"Theresa L."},{"full_name":"Xu, Qimen","last_name":"Xu","first_name":"Qimen"},{"last_name":"Yu","full_name":"Yu, Victor W. -Z.","first_name":"Victor W. -Z."},{"full_name":"Perez, Danny","last_name":"Perez","first_name":"Danny"}],"date_created":"2022-09-28T05:25:10Z","date_updated":"2023-07-28T08:03:41Z","title":"Roadmap on Electronic Structure Codes in the Exascale Era","citation":{"ieee":"V. Gavini <i>et al.</i>, “Roadmap on Electronic Structure Codes in the Exascale Era,” <i>arXiv:2209.12747</i>. 2022.","chicago":"Gavini, Vikram, Stefano Baroni, Volker Blum, David R. Bowler, Alexander Buccheri, James R. Chelikowsky, Sambit Das, et al. “Roadmap on Electronic Structure Codes in the Exascale Era.” <i>ArXiv:2209.12747</i>, 2022.","ama":"Gavini V, Baroni S, Blum V, et al. Roadmap on Electronic Structure Codes in the Exascale Era. <i>arXiv:220912747</i>. Published online 2022.","mla":"Gavini, Vikram, et al. “Roadmap on Electronic Structure Codes in the Exascale Era.” <i>ArXiv:2209.12747</i>, 2022.","short":"V. Gavini, S. Baroni, V. Blum, D.R. Bowler, A. Buccheri, J.R. Chelikowsky, S. Das, W. Dawson, P. Delugas, M. Dogan, C. Draxl, G. Galli, L. Genovese, P. Giannozzi, M. Giantomassi, X. Gonze, M. Govoni, A. Gulans, F. Gygi, J.M. Herbert, S. Kokott, T. Kühne, K.-H. Liou, T. Miyazaki, P. Motamarri, A. Nakata, J.E. Pask, C. Plessl, L.E. Ratcliff, R.M. Richard, M. Rossi, R. Schade, M. Scheffler, O. Schütt, P. Suryanarayana, M. Torrent, L. Truflandier, T.L. Windus, Q. Xu, V.W.-Z. Yu, D. Perez, ArXiv:2209.12747 (2022).","bibtex":"@article{Gavini_Baroni_Blum_Bowler_Buccheri_Chelikowsky_Das_Dawson_Delugas_Dogan_et al._2022, title={Roadmap on Electronic Structure Codes in the Exascale Era}, journal={arXiv:2209.12747}, author={Gavini, Vikram and Baroni, Stefano and Blum, Volker and Bowler, David R. and Buccheri, Alexander and Chelikowsky, James R. and Das, Sambit and Dawson, William and Delugas, Pietro and Dogan, Mehmet and et al.}, year={2022} }","apa":"Gavini, V., Baroni, S., Blum, V., Bowler, D. R., Buccheri, A., Chelikowsky, J. R., Das, S., Dawson, W., Delugas, P., Dogan, M., Draxl, C., Galli, G., Genovese, L., Giannozzi, P., Giantomassi, M., Gonze, X., Govoni, M., Gulans, A., Gygi, F., … Perez, D. (2022). Roadmap on Electronic Structure Codes in the Exascale Era. In <i>arXiv:2209.12747</i>."},"year":"2022","user_id":"24135","department":[{"_id":"27"},{"_id":"518"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"external_id":{"arxiv":["2209.12747"]},"_id":"33493","language":[{"iso":"eng"}],"type":"preprint","publication":"arXiv:2209.12747","status":"public","abstract":[{"lang":"eng","text":"Electronic structure calculations have been instrumental in providing many\r\nimportant insights into a range of physical and chemical properties of various\r\nmolecular and solid-state systems. Their importance to various fields,\r\nincluding materials science, chemical sciences, computational chemistry and\r\ndevice physics, is underscored by the large fraction of available public\r\nsupercomputing resources devoted to these calculations. As we enter the\r\nexascale era, exciting new opportunities to increase simulation numbers, sizes,\r\nand accuracies present themselves. In order to realize these promises, the\r\ncommunity of electronic structure software developers will however first have\r\nto tackle a number of challenges pertaining to the efficient use of new\r\narchitectures that will rely heavily on massive parallelism and hardware\r\naccelerators. This roadmap provides a broad overview of the state-of-the-art in\r\nelectronic structure calculations and of the various new directions being\r\npursued by the community. It covers 14 electronic structure codes, presenting\r\ntheir current status, their development priorities over the next five years,\r\nand their plans towards tackling the challenges and leveraging the\r\nopportunities presented by the advent of exascale computing."}]},{"main_file_link":[{"open_access":"1","url":"https://dl.acm.org/doi/pdf/10.1145/3492805.3492808"}],"doi":"10.1145/3492805.3492808","title":"A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays: Design, Evaluation, and Future Challenges","author":[{"last_name":"Karp","full_name":"Karp, Martin","first_name":"Martin"},{"first_name":"Artur","last_name":"Podobas","full_name":"Podobas, Artur"},{"last_name":"Kenter","id":"3145","full_name":"Kenter, Tobias","first_name":"Tobias"},{"first_name":"Niclas","last_name":"Jansson","full_name":"Jansson, Niclas"},{"first_name":"Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","id":"16153","full_name":"Plessl, Christian"},{"full_name":"Schlatter, Philipp","last_name":"Schlatter","first_name":"Philipp"},{"full_name":"Markidis, Stefano","last_name":"Markidis","first_name":"Stefano"}],"date_created":"2023-07-28T11:51:55Z","publisher":"ACM","oa":"1","date_updated":"2023-07-28T11:53:15Z","citation":{"chicago":"Karp, Martin, Artur Podobas, Tobias Kenter, Niclas Jansson, Christian Plessl, Philipp Schlatter, and Stefano Markidis. “A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays: Design, Evaluation, and Future Challenges.” In <i>International Conference on High Performance Computing in Asia-Pacific Region</i>. ACM, 2022. <a href=\"https://doi.org/10.1145/3492805.3492808\">https://doi.org/10.1145/3492805.3492808</a>.","ieee":"M. Karp <i>et al.</i>, “A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays: Design, Evaluation, and Future Challenges,” 2022, doi: <a href=\"https://doi.org/10.1145/3492805.3492808\">10.1145/3492805.3492808</a>.","ama":"Karp M, Podobas A, Kenter T, et al. A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays: Design, Evaluation, and Future Challenges. In: <i>International Conference on High Performance Computing in Asia-Pacific Region</i>. ACM; 2022. doi:<a href=\"https://doi.org/10.1145/3492805.3492808\">10.1145/3492805.3492808</a>","bibtex":"@inproceedings{Karp_Podobas_Kenter_Jansson_Plessl_Schlatter_Markidis_2022, title={A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays: Design, Evaluation, and Future Challenges}, DOI={<a href=\"https://doi.org/10.1145/3492805.3492808\">10.1145/3492805.3492808</a>}, booktitle={International Conference on High Performance Computing in Asia-Pacific Region}, publisher={ACM}, author={Karp, Martin and Podobas, Artur and Kenter, Tobias and Jansson, Niclas and Plessl, Christian and Schlatter, Philipp and Markidis, Stefano}, year={2022} }","mla":"Karp, Martin, et al. “A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays: Design, Evaluation, and Future Challenges.” <i>International Conference on High Performance Computing in Asia-Pacific Region</i>, ACM, 2022, doi:<a href=\"https://doi.org/10.1145/3492805.3492808\">10.1145/3492805.3492808</a>.","short":"M. Karp, A. Podobas, T. Kenter, N. Jansson, C. Plessl, P. Schlatter, S. Markidis, in: International Conference on High Performance Computing in Asia-Pacific Region, ACM, 2022.","apa":"Karp, M., Podobas, A., Kenter, T., Jansson, N., Plessl, C., Schlatter, P., &#38; Markidis, S. (2022). A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays: Design, Evaluation, and Future Challenges. <i>International Conference on High Performance Computing in Asia-Pacific Region</i>. <a href=\"https://doi.org/10.1145/3492805.3492808\">https://doi.org/10.1145/3492805.3492808</a>"},"year":"2022","publication_status":"published","quality_controlled":"1","language":[{"iso":"eng"}],"user_id":"3145","department":[{"_id":"27"},{"_id":"518"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"46193","status":"public","type":"conference","publication":"International Conference on High Performance Computing in Asia-Pacific Region"},{"title":"Hermeneutik zwischen Logik und Ethik","doi":"10.30965/9783657793785_004","date_updated":"2023-07-28T14:42:01Z","publisher":"Brill | Schöningh","author":[{"last_name":"Ficara","full_name":"Ficara, Elena","first_name":"Elena"}],"date_created":"2023-07-28T14:29:09Z","year":"2022","citation":{"ieee":"E. Ficara, “Hermeneutik zwischen Logik und Ethik,” in <i>Ethik in der Hermeneutik – Hermeneutik in der Ethik</i>, Brill | Schöningh, 2022.","chicago":"Ficara, Elena. “Hermeneutik Zwischen Logik Und Ethik.” In <i>Ethik in Der Hermeneutik – Hermeneutik in Der Ethik</i>. Brill | Schöningh, 2022. <a href=\"https://doi.org/10.30965/9783657793785_004\">https://doi.org/10.30965/9783657793785_004</a>.","ama":"Ficara E. Hermeneutik zwischen Logik und Ethik. In: <i>Ethik in Der Hermeneutik – Hermeneutik in Der Ethik</i>. Brill | Schöningh; 2022. doi:<a href=\"https://doi.org/10.30965/9783657793785_004\">10.30965/9783657793785_004</a>","mla":"Ficara, Elena. “Hermeneutik Zwischen Logik Und Ethik.” <i>Ethik in Der Hermeneutik – Hermeneutik in Der Ethik</i>, Brill | Schöningh, 2022, doi:<a href=\"https://doi.org/10.30965/9783657793785_004\">10.30965/9783657793785_004</a>.","short":"E. Ficara, in: Ethik in Der Hermeneutik – Hermeneutik in Der Ethik, Brill | Schöningh, 2022.","bibtex":"@inbook{Ficara_2022, title={Hermeneutik zwischen Logik und Ethik}, DOI={<a href=\"https://doi.org/10.30965/9783657793785_004\">10.30965/9783657793785_004</a>}, booktitle={Ethik in der Hermeneutik – Hermeneutik in der Ethik}, publisher={Brill | Schöningh}, author={Ficara, Elena}, year={2022} }","apa":"Ficara, E. (2022). Hermeneutik zwischen Logik und Ethik. In <i>Ethik in der Hermeneutik – Hermeneutik in der Ethik</i>. Brill | Schöningh. <a href=\"https://doi.org/10.30965/9783657793785_004\">https://doi.org/10.30965/9783657793785_004</a>"},"publication_status":"published","publication_identifier":{"isbn":["9783657793785","9783506793782"]},"_id":"46200","user_id":"35768","status":"public","type":"book_chapter","publication":"Ethik in der Hermeneutik – Hermeneutik in der Ethik"},{"title":"About the structure of the discrete and continuous Eringen’s nonlocal elastica","doi":"10.1177/10812865221108094","publisher":"SAGE Publications","date_updated":"2023-08-01T11:52:17Z","date_created":"2023-01-24T10:18:34Z","author":[{"last_name":"Cresson","full_name":"Cresson, Jacky","first_name":"Jacky"},{"first_name":"Khaled","id":"98857","full_name":"Hariz Belgacem, Khaled","last_name":"Hariz Belgacem"}],"year":"2022","citation":{"short":"J. Cresson, K. Hariz Belgacem, Mathematics and Mechanics of Solids (2022).","bibtex":"@article{Cresson_Hariz Belgacem_2022, title={About the structure of the discrete and continuous Eringen’s nonlocal elastica}, DOI={<a href=\"https://doi.org/10.1177/10812865221108094\">10.1177/10812865221108094</a>}, number={108128652211080}, journal={Mathematics and Mechanics of Solids}, publisher={SAGE Publications}, author={Cresson, Jacky and Hariz Belgacem, Khaled}, year={2022} }","mla":"Cresson, Jacky, and Khaled Hariz Belgacem. “About the Structure of the Discrete and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics of Solids</i>, 108128652211080, SAGE Publications, 2022, doi:<a href=\"https://doi.org/10.1177/10812865221108094\">10.1177/10812865221108094</a>.","apa":"Cresson, J., &#38; Hariz Belgacem, K. (2022). About the structure of the discrete and continuous Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>, Article 108128652211080. <a href=\"https://doi.org/10.1177/10812865221108094\">https://doi.org/10.1177/10812865221108094</a>","chicago":"Cresson, Jacky, and Khaled Hariz Belgacem. “About the Structure of the Discrete and Continuous Eringen’s Nonlocal Elastica.” <i>Mathematics and Mechanics of Solids</i>, 2022. <a href=\"https://doi.org/10.1177/10812865221108094\">https://doi.org/10.1177/10812865221108094</a>.","ieee":"J. Cresson and K. Hariz Belgacem, “About the structure of the discrete and continuous Eringen’s nonlocal elastica,” <i>Mathematics and Mechanics of Solids</i>, Art. no. 108128652211080, 2022, doi: <a href=\"https://doi.org/10.1177/10812865221108094\">10.1177/10812865221108094</a>.","ama":"Cresson J, Hariz Belgacem K. About the structure of the discrete and continuous Eringen’s nonlocal elastica. <i>Mathematics and Mechanics of Solids</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1177/10812865221108094\">10.1177/10812865221108094</a>"},"publication_identifier":{"issn":["1081-2865","1741-3028"]},"publication_status":"published","keyword":["Mechanics of Materials","General Materials Science","General Mathematics"],"article_number":"108128652211080","language":[{"iso":"eng"}],"_id":"39400","user_id":"98857","abstract":[{"lang":"eng","text":"<jats:p> The Eringen’s nonlocal elastica equation does not possess a Lagrangian formulation. In this article, we find a variational integrating factor which enables us to provide a Lagrangian and Hamiltonian structure associated to this equation. Explicit expressions of the solutions in terms of elliptic integrals of the first kind are then deduced. We then derive discrete version of the Eringen’s nonlocal elastica preserving the Lagrangian and Hamiltonian structure and compare it with Challamel’s and co-worker definition of a discrete Eringen’s nonlocal elastica. </jats:p>"}],"status":"public","publication":"Mathematics and Mechanics of Solids","type":"journal_article"},{"status":"public","abstract":[{"text":"The CP2K program package, which can be considered as the swiss army knife of\r\natomistic simulations, is presented with a special emphasis on ab-initio\r\nmolecular dynamics using the second-generation Car-Parrinello method. After\r\noutlining current and near-term development efforts with regards to massively\r\nparallel low-scaling post-Hartree-Fock and eigenvalue solvers, novel approaches\r\non how we plan to take full advantage of future low-precision hardware\r\narchitectures are introduced. Our focus here is on combining our submatrix\r\nmethod with the approximate computing paradigm to address the immanent exascale\r\nera.","lang":"eng"}],"publication":"arXiv:2205.14741","type":"preprint","language":[{"iso":"eng"}],"department":[{"_id":"27"},{"_id":"518"},{"_id":"304"}],"user_id":"75963","_id":"32404","external_id":{"arxiv":["2205.14741"]},"project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"citation":{"chicago":"Kühne, Thomas, Christian Plessl, Robert Schade, and Ole Schütt. “CP2K on the Road to Exascale.” <i>ArXiv:2205.14741</i>, 2022.","ieee":"T. Kühne, C. Plessl, R. Schade, and O. Schütt, “CP2K on the road to exascale,” <i>arXiv:2205.14741</i>. 2022.","ama":"Kühne T, Plessl C, Schade R, Schütt O. CP2K on the road to exascale. <i>arXiv:220514741</i>. Published online 2022.","mla":"Kühne, Thomas, et al. “CP2K on the Road to Exascale.” <i>ArXiv:2205.14741</i>, 2022.","short":"T. Kühne, C. Plessl, R. Schade, O. Schütt, ArXiv:2205.14741 (2022).","bibtex":"@article{Kühne_Plessl_Schade_Schütt_2022, title={CP2K on the road to exascale}, journal={arXiv:2205.14741}, author={Kühne, Thomas and Plessl, Christian and Schade, Robert and Schütt, Ole}, year={2022} }","apa":"Kühne, T., Plessl, C., Schade, R., &#38; Schütt, O. (2022). CP2K on the road to exascale. In <i>arXiv:2205.14741</i>."},"year":"2022","main_file_link":[{"url":"https://arxiv.org/abs/2205.14741"}],"title":"CP2K on the road to exascale","author":[{"first_name":"Thomas","last_name":"Kühne","id":"49079","full_name":"Kühne, Thomas"},{"first_name":"Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","full_name":"Plessl, Christian","id":"16153"},{"full_name":"Schade, Robert","id":"75963","orcid":"0000-0002-6268-539","last_name":"Schade","first_name":"Robert"},{"last_name":"Schütt","full_name":"Schütt, Ole","first_name":"Ole"}],"date_created":"2022-07-22T08:14:08Z","date_updated":"2023-08-02T14:55:35Z"},{"year":"2022","quality_controlled":"1","title":"Parallel quantum chemistry on noisy intermediate-scale quantum computers","date_created":"2022-08-29T14:07:01Z","publisher":"American Physical Society","abstract":[{"lang":"eng","text":"A parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory (RDMFT) formulation of the electronic structure problem. For that purpose, the density-matrix functional of the full system is decomposed into an indirectly coupled sum of density-matrix functionals for all its subsystems using the adaptive cluster approximation to RDMFT. The approximations involved in the decomposition and the adaptive cluster approximation itself can be systematically converged to the exact result. The solutions for the density-matrix functionals of the effective subsystems involves a constrained minimization over many-particle states that are approximated by parametrized trial states on the quantum computer similarly to the variational quantum eigensolver. The independence of the density-matrix functionals of the effective subsystems introduces a new level of parallelization and allows for the computational treatment of much larger molecules on a quantum computer with a given qubit count. In addition, for the proposed algorithm techniques are presented to reduce the qubit count, the number of quantum programs, as well as its depth. The evaluation of a density-matrix functional as the essential part of our approach is demonstrated for Hubbard-like systems on IBM quantum computers based on superconducting transmon qubits."}],"publication":"Phys. Rev. Research","language":[{"iso":"eng"}],"citation":{"ama":"Schade R, Bauer C, Tamoev K, Mazur L, Plessl C, Kühne T. Parallel quantum chemistry on noisy intermediate-scale quantum computers. <i>Phys Rev Research</i>. 2022;4:033160. doi:<a href=\"https://doi.org/10.1103/PhysRevResearch.4.033160\">10.1103/PhysRevResearch.4.033160</a>","apa":"Schade, R., Bauer, C., Tamoev, K., Mazur, L., Plessl, C., &#38; Kühne, T. (2022). Parallel quantum chemistry on noisy intermediate-scale quantum computers. <i>Phys. Rev. Research</i>, <i>4</i>, 033160. <a href=\"https://doi.org/10.1103/PhysRevResearch.4.033160\">https://doi.org/10.1103/PhysRevResearch.4.033160</a>","bibtex":"@article{Schade_Bauer_Tamoev_Mazur_Plessl_Kühne_2022, title={Parallel quantum chemistry on noisy intermediate-scale quantum computers}, volume={4}, DOI={<a href=\"https://doi.org/10.1103/PhysRevResearch.4.033160\">10.1103/PhysRevResearch.4.033160</a>}, journal={Phys. Rev. Research}, publisher={American Physical Society}, author={Schade, Robert and Bauer, Carsten and Tamoev, Konstantin and Mazur, Lukas and Plessl, Christian and Kühne, Thomas}, year={2022}, pages={033160} }","short":"R. Schade, C. Bauer, K. Tamoev, L. Mazur, C. Plessl, T. Kühne, Phys. Rev. Research 4 (2022) 033160.","mla":"Schade, Robert, et al. “Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers.” <i>Phys. Rev. Research</i>, vol. 4, American Physical Society, 2022, p. 033160, doi:<a href=\"https://doi.org/10.1103/PhysRevResearch.4.033160\">10.1103/PhysRevResearch.4.033160</a>.","ieee":"R. Schade, C. Bauer, K. Tamoev, L. Mazur, C. Plessl, and T. Kühne, “Parallel quantum chemistry on noisy intermediate-scale quantum computers,” <i>Phys. Rev. Research</i>, vol. 4, p. 033160, 2022, doi: <a href=\"https://doi.org/10.1103/PhysRevResearch.4.033160\">10.1103/PhysRevResearch.4.033160</a>.","chicago":"Schade, Robert, Carsten Bauer, Konstantin Tamoev, Lukas Mazur, Christian Plessl, and Thomas Kühne. “Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers.” <i>Phys. Rev. Research</i> 4 (2022): 033160. <a href=\"https://doi.org/10.1103/PhysRevResearch.4.033160\">https://doi.org/10.1103/PhysRevResearch.4.033160</a>."},"intvolume":"         4","page":"033160","publication_status":"published","main_file_link":[{"url":"https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.033160","open_access":"1"}],"doi":"10.1103/PhysRevResearch.4.033160","author":[{"first_name":"Robert","orcid":"0000-0002-6268-539","last_name":"Schade","full_name":"Schade, Robert","id":"75963"},{"first_name":"Carsten","full_name":"Bauer, Carsten","id":"90082","last_name":"Bauer"},{"first_name":"Konstantin","last_name":"Tamoev","id":"50177","full_name":"Tamoev, Konstantin"},{"first_name":"Lukas","id":"90492","full_name":"Mazur, Lukas","last_name":"Mazur","orcid":" 0000-0001-6304-7082"},{"first_name":"Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","id":"16153","full_name":"Plessl, Christian"},{"first_name":"Thomas","id":"49079","full_name":"Kühne, Thomas","last_name":"Kühne"}],"volume":4,"oa":"1","date_updated":"2023-08-02T15:04:22Z","status":"public","type":"journal_article","article_type":"original","user_id":"75963","department":[{"_id":"27"},{"_id":"518"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"33226"},{"status":"public","abstract":[{"lang":"eng","text":"Electronic structure calculations have been instrumental in providing many\r\nimportant insights into a range of physical and chemical properties of various\r\nmolecular and solid-state systems. Their importance to various fields,\r\nincluding materials science, chemical sciences, computational chemistry and\r\ndevice physics, is underscored by the large fraction of available public\r\nsupercomputing resources devoted to these calculations. As we enter the\r\nexascale era, exciting new opportunities to increase simulation numbers, sizes,\r\nand accuracies present themselves. In order to realize these promises, the\r\ncommunity of electronic structure software developers will however first have\r\nto tackle a number of challenges pertaining to the efficient use of new\r\narchitectures that will rely heavily on massive parallelism and hardware\r\naccelerators. This roadmap provides a broad overview of the state-of-the-art in\r\nelectronic structure calculations and of the various new directions being\r\npursued by the community. It covers 14 electronic structure codes, presenting\r\ntheir current status, their development priorities over the next five years,\r\nand their plans towards tackling the challenges and leveraging the\r\nopportunities presented by the advent of exascale computing."}],"type":"preprint","publication":"arXiv:2209.12747","language":[{"iso":"eng"}],"user_id":"75963","department":[{"_id":"27"}],"project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"external_id":{"arxiv":["2209.12747"]},"_id":"46275","citation":{"apa":"Gavini, V., Baroni, S., Blum, V., Bowler, D. R., Buccheri, A., Chelikowsky, J. R., Das, S., Dawson, W., Delugas, P., Dogan, M., Draxl, C., Galli, G., Genovese, L., Giannozzi, P., Giantomassi, M., Gonze, X., Govoni, M., Gulans, A., Gygi, F., … Perez, D. (2022). Roadmap on Electronic Structure Codes in the Exascale Era. In <i>arXiv:2209.12747</i>.","short":"V. Gavini, S. Baroni, V. Blum, D.R. Bowler, A. Buccheri, J.R. Chelikowsky, S. Das, W. Dawson, P. Delugas, M. Dogan, C. Draxl, G. Galli, L. Genovese, P. Giannozzi, M. Giantomassi, X. Gonze, M. Govoni, A. Gulans, F. Gygi, J.M. Herbert, S. Kokott, T. Kühne, K.-H. Liou, T. Miyazaki, P. Motamarri, A. Nakata, J.E. Pask, C. Plessl, L.E. Ratcliff, R.M. Richard, M. Rossi, R. Schade, M. Scheffler, O. Schütt, P. Suryanarayana, M. Torrent, L. Truflandier, T.L. Windus, Q. Xu, V.W.-Z. Yu, D. Perez, ArXiv:2209.12747 (2022).","bibtex":"@article{Gavini_Baroni_Blum_Bowler_Buccheri_Chelikowsky_Das_Dawson_Delugas_Dogan_et al._2022, title={Roadmap on Electronic Structure Codes in the Exascale Era}, journal={arXiv:2209.12747}, author={Gavini, Vikram and Baroni, Stefano and Blum, Volker and Bowler, David R. and Buccheri, Alexander and Chelikowsky, James R. and Das, Sambit and Dawson, William and Delugas, Pietro and Dogan, Mehmet and et al.}, year={2022} }","mla":"Gavini, Vikram, et al. “Roadmap on Electronic Structure Codes in the Exascale Era.” <i>ArXiv:2209.12747</i>, 2022.","chicago":"Gavini, Vikram, Stefano Baroni, Volker Blum, David R. Bowler, Alexander Buccheri, James R. Chelikowsky, Sambit Das, et al. “Roadmap on Electronic Structure Codes in the Exascale Era.” <i>ArXiv:2209.12747</i>, 2022.","ieee":"V. Gavini <i>et al.</i>, “Roadmap on Electronic Structure Codes in the Exascale Era,” <i>arXiv:2209.12747</i>. 2022.","ama":"Gavini V, Baroni S, Blum V, et al. Roadmap on Electronic Structure Codes in the Exascale Era. <i>arXiv:220912747</i>. Published online 2022."},"year":"2022","title":"Roadmap on Electronic Structure Codes in the Exascale Era","date_created":"2023-08-02T14:59:18Z","author":[{"first_name":"Vikram","full_name":"Gavini, Vikram","last_name":"Gavini"},{"last_name":"Baroni","full_name":"Baroni, Stefano","first_name":"Stefano"},{"last_name":"Blum","full_name":"Blum, Volker","first_name":"Volker"},{"full_name":"Bowler, David R.","last_name":"Bowler","first_name":"David R."},{"last_name":"Buccheri","full_name":"Buccheri, Alexander","first_name":"Alexander"},{"first_name":"James R.","last_name":"Chelikowsky","full_name":"Chelikowsky, James R."},{"full_name":"Das, Sambit","last_name":"Das","first_name":"Sambit"},{"full_name":"Dawson, William","last_name":"Dawson","first_name":"William"},{"first_name":"Pietro","last_name":"Delugas","full_name":"Delugas, Pietro"},{"first_name":"Mehmet","full_name":"Dogan, Mehmet","last_name":"Dogan"},{"first_name":"Claudia","last_name":"Draxl","full_name":"Draxl, Claudia"},{"last_name":"Galli","full_name":"Galli, Giulia","first_name":"Giulia"},{"last_name":"Genovese","full_name":"Genovese, Luigi","first_name":"Luigi"},{"full_name":"Giannozzi, Paolo","last_name":"Giannozzi","first_name":"Paolo"},{"last_name":"Giantomassi","full_name":"Giantomassi, Matteo","first_name":"Matteo"},{"full_name":"Gonze, Xavier","last_name":"Gonze","first_name":"Xavier"},{"first_name":"Marco","full_name":"Govoni, Marco","last_name":"Govoni"},{"full_name":"Gulans, Andris","last_name":"Gulans","first_name":"Andris"},{"full_name":"Gygi, François","last_name":"Gygi","first_name":"François"},{"first_name":"John M.","full_name":"Herbert, John M.","last_name":"Herbert"},{"last_name":"Kokott","full_name":"Kokott, Sebastian","first_name":"Sebastian"},{"full_name":"Kühne, Thomas","id":"49079","last_name":"Kühne","first_name":"Thomas"},{"first_name":"Kai-Hsin","last_name":"Liou","full_name":"Liou, Kai-Hsin"},{"first_name":"Tsuyoshi","full_name":"Miyazaki, Tsuyoshi","last_name":"Miyazaki"},{"first_name":"Phani","full_name":"Motamarri, Phani","last_name":"Motamarri"},{"full_name":"Nakata, Ayako","last_name":"Nakata","first_name":"Ayako"},{"full_name":"Pask, John E.","last_name":"Pask","first_name":"John E."},{"first_name":"Christian","id":"16153","full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl"},{"last_name":"Ratcliff","full_name":"Ratcliff, Laura E.","first_name":"Laura E."},{"last_name":"Richard","full_name":"Richard, Ryan M.","first_name":"Ryan M."},{"full_name":"Rossi, Mariana","last_name":"Rossi","first_name":"Mariana"},{"first_name":"Robert","last_name":"Schade","orcid":"0000-0002-6268-539","full_name":"Schade, Robert","id":"75963"},{"first_name":"Matthias","full_name":"Scheffler, Matthias","last_name":"Scheffler"},{"full_name":"Schütt, Ole","last_name":"Schütt","first_name":"Ole"},{"last_name":"Suryanarayana","full_name":"Suryanarayana, Phanish","first_name":"Phanish"},{"full_name":"Torrent, Marc","last_name":"Torrent","first_name":"Marc"},{"full_name":"Truflandier, Lionel","last_name":"Truflandier","first_name":"Lionel"},{"first_name":"Theresa L.","last_name":"Windus","full_name":"Windus, Theresa L."},{"last_name":"Xu","full_name":"Xu, Qimen","first_name":"Qimen"},{"first_name":"Victor W. -Z.","full_name":"Yu, Victor W. -Z.","last_name":"Yu"},{"full_name":"Perez, Danny","last_name":"Perez","first_name":"Danny"}],"date_updated":"2023-08-02T15:00:47Z"},{"article_number":"102920","department":[{"_id":"613"},{"_id":"27"},{"_id":"518"}],"user_id":"75963","_id":"33684","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"status":"public","type":"journal_article","doi":"10.1016/j.parco.2022.102920","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0167819122000242","open_access":"1"}],"volume":111,"author":[{"first_name":"Robert","id":"75963","full_name":"Schade, 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Christian"}],"date_updated":"2023-08-02T15:03:55Z","oa":"1","intvolume":"       111","citation":{"mla":"Schade, Robert, et al. “Towards Electronic Structure-Based Ab-Initio Molecular Dynamics Simulations with Hundreds of Millions of Atoms.” <i>Parallel Computing</i>, vol. 111, 102920, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.parco.2022.102920\">10.1016/j.parco.2022.102920</a>.","bibtex":"@article{Schade_Kenter_Elgabarty_Lass_Schütt_Lazzaro_Pabst_Mohr_Hutter_Kühne_et al._2022, title={Towards electronic structure-based ab-initio molecular dynamics simulations with hundreds of millions of atoms}, volume={111}, DOI={<a href=\"https://doi.org/10.1016/j.parco.2022.102920\">10.1016/j.parco.2022.102920</a>}, number={102920}, journal={Parallel Computing}, publisher={Elsevier BV}, author={Schade, Robert and Kenter, Tobias and Elgabarty, Hossam and Lass, Michael and Schütt, Ole and Lazzaro, Alfio and Pabst, Hans and Mohr, Stephan and Hutter, Jürg and Kühne, Thomas and et al.}, year={2022} }","short":"R. Schade, T. Kenter, H. Elgabarty, M. Lass, O. Schütt, A. Lazzaro, H. Pabst, S. Mohr, J. Hutter, T. Kühne, C. Plessl, Parallel Computing 111 (2022).","apa":"Schade, R., Kenter, T., Elgabarty, H., Lass, M., Schütt, O., Lazzaro, A., Pabst, H., Mohr, S., Hutter, J., Kühne, T., &#38; Plessl, C. (2022). Towards electronic structure-based ab-initio molecular dynamics simulations with hundreds of millions of atoms. <i>Parallel Computing</i>, <i>111</i>, Article 102920. <a href=\"https://doi.org/10.1016/j.parco.2022.102920\">https://doi.org/10.1016/j.parco.2022.102920</a>","chicago":"Schade, Robert, Tobias Kenter, Hossam Elgabarty, Michael Lass, Ole Schütt, Alfio Lazzaro, Hans Pabst, et al. “Towards Electronic Structure-Based Ab-Initio Molecular Dynamics Simulations with Hundreds of Millions of Atoms.” <i>Parallel Computing</i> 111 (2022). <a href=\"https://doi.org/10.1016/j.parco.2022.102920\">https://doi.org/10.1016/j.parco.2022.102920</a>.","ieee":"R. Schade <i>et al.</i>, “Towards electronic structure-based ab-initio molecular dynamics simulations with hundreds of millions of atoms,” <i>Parallel Computing</i>, vol. 111, Art. no. 102920, 2022, doi: <a href=\"https://doi.org/10.1016/j.parco.2022.102920\">10.1016/j.parco.2022.102920</a>.","ama":"Schade R, Kenter T, Elgabarty H, et al. 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Stahl (Eds.), <i>TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists </i>. Pabst Science Publishers. <a href=\"https://doi.org/10.23668/psycharchives.5677\">https://doi.org/10.23668/psycharchives.5677</a>","bibtex":"@inproceedings{Banh_Scharlau_2022, title={Effects of verbal negation on TVA’s capacity and weight parameters}, DOI={<a href=\"https://doi.org/10.23668/psycharchives.5677\">10.23668/psycharchives.5677</a>}, booktitle={TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists }, publisher={Pabst Science Publishers}, author={Banh, Ngoc Chi and Scharlau, Ingrid}, editor={Malejka, Simone and Barth, Marius and Haider, Hilde and Stahl, Christoph}, year={2022} }","mla":"Banh, Ngoc Chi, and Ingrid Scharlau. “Effects of Verbal Negation on TVA’s Capacity and Weight Parameters.” <i>TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists </i>, edited by Simone Malejka et al., Pabst Science Publishers, 2022, doi:<a href=\"https://doi.org/10.23668/psycharchives.5677\">10.23668/psycharchives.5677</a>.","short":"N.C. Banh, I. Scharlau, in: S. Malejka, M. Barth, H. Haider, C. Stahl (Eds.), TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists , Pabst Science Publishers, 2022.","ama":"Banh NC, Scharlau I. Effects of verbal negation on TVA’s capacity and weight parameters. In: Malejka S, Barth M, Haider H, Stahl C, eds. <i>TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists </i>. Pabst Science Publishers; 2022. doi:<a href=\"https://doi.org/10.23668/psycharchives.5677\">10.23668/psycharchives.5677</a>","chicago":"Banh, Ngoc Chi, and Ingrid Scharlau. “Effects of Verbal Negation on TVA’s Capacity and Weight Parameters.” In <i>TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists </i>, edited by Simone Malejka, Marius Barth, Hilde Haider, and Christoph Stahl. Pabst Science Publishers, 2022. <a href=\"https://doi.org/10.23668/psycharchives.5677\">https://doi.org/10.23668/psycharchives.5677</a>.","ieee":"N. C. Banh and I. Scharlau, “Effects of verbal negation on TVA’s capacity and weight parameters,” in <i>TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists </i>, Cologne, Germany, 2022, doi: <a href=\"https://doi.org/10.23668/psycharchives.5677\">10.23668/psycharchives.5677</a>."},"year":"2022","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://pada.psycharchives.org/bitstream/55709d4f-a663-4038-9514-7f8cdee55089"}],"doi":"10.23668/psycharchives.5677","conference":{"location":"Cologne, Germany","end_date":"2022-03-23","start_date":"2022-03-20","name":"Tagung experimentell arbeitender Psycholog:innen (TeaP)"},"title":"Effects of verbal negation on TVA’s capacity and weight parameters","author":[{"orcid":"0000-0002-5946-4542","last_name":"Banh","full_name":"Banh, Ngoc Chi","id":"38219","first_name":"Ngoc Chi"},{"first_name":"Ingrid","full_name":"Scharlau, Ingrid","id":"451","orcid":"0000-0003-2364-9489","last_name":"Scharlau"}],"date_created":"2023-08-03T13:09:31Z","oa":"1","publisher":"Pabst Science Publishers","date_updated":"2023-08-03T14:08:31Z","status":"public","editor":[{"full_name":"Malejka, Simone","last_name":"Malejka","first_name":"Simone"},{"last_name":"Barth","full_name":"Barth, Marius","first_name":"Marius"},{"last_name":"Haider","full_name":"Haider, Hilde","first_name":"Hilde"},{"first_name":"Christoph","full_name":"Stahl, Christoph","last_name":"Stahl"}],"type":"conference_abstract","publication":"TeaP 2022 - Abstracts of the 64th Conference of Experimental Psychologists ","language":[{"iso":"eng"}],"user_id":"38219","department":[{"_id":"424"}],"project":[{"name":"TRR 318 - A05: TRR 318 - Echtzeitmessung der Aufmerksamkeit im Mensch-Roboter-Erklärdialog (Teilprojekt A05)","_id":"115","grant_number":"438445824"}],"_id":"46282"},{"year":"2022","citation":{"chicago":"Banh, Ngoc Chi, Ingrid Scharlau, and Katharina J. Rohlfing. “Folgen Wiederholter Negation Auf Die Aufmerksamkeit.” In <i>52. Kongress Der Deutschen Gesellschaft Für Psychologie</i>, edited by Christina  Bermeitinger and Werner  Greve. Pabst Science Publishers, 2022.","ieee":"N. C. Banh, I. Scharlau, and K. J. Rohlfing, “Folgen wiederholter Negation auf die Aufmerksamkeit,” in <i>52. Kongress der Deutschen Gesellschaft für Psychologie</i>, Hildesheim, Germany, 2022.","bibtex":"@inproceedings{Banh_Scharlau_Rohlfing_2022, series={Pabst Science Publishers}, title={Folgen wiederholter Negation auf die Aufmerksamkeit}, booktitle={52. Kongress der Deutschen Gesellschaft für Psychologie}, author={Banh, Ngoc Chi and Scharlau, Ingrid and Rohlfing, Katharina J.}, editor={Bermeitinger, Christina  and Greve, Werner }, year={2022}, collection={Pabst Science Publishers} }","short":"N.C. Banh, I. Scharlau, K.J. Rohlfing, in: C. Bermeitinger, W. Greve (Eds.), 52. 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Kongress der Deutschen Gesellschaft für Psychologie","language":[{"iso":"eng"}],"project":[{"_id":"115","name":"TRR 318 - A05: TRR 318 - Echtzeitmessung der Aufmerksamkeit im Mensch-Roboter-Erklärdialog (Teilprojekt A05)","grant_number":"438445824"}],"_id":"46289","series_title":"Pabst Science Publishers","user_id":"38219","department":[{"_id":"424"},{"_id":"660"}]},{"_id":"46293","department":[{"_id":"462"}],"user_id":"71124","language":[{"iso":"eng"}],"publication":"MedienPädagogik ","type":"journal_article","status":"public","date_updated":"2023-08-03T18:25:00Z","volume":49,"author":[{"last_name":"Drossel","full_name":"Drossel, Kerstin","id":"48921","first_name":"Kerstin"},{"first_name":"M","full_name":"Heldt, M","last_name":"Heldt"}],"date_created":"2023-08-03T18:22:58Z","title":"Unterrichtsbezogene Lehrpersonenkooperationen im Zeitalter der digitalen Transformation – Alles digital oder alles wie bisher? ","doi":" https://doi.org/10.21240/mpaed/49/2022.06.23.X","publication_status":"published","year":"2022","intvolume":"        49","page":"68-93","citation":{"apa":"Drossel, K., &#38; Heldt, M. (2022). Unterrichtsbezogene Lehrpersonenkooperationen im Zeitalter der digitalen Transformation – Alles digital oder alles wie bisher? . <i>MedienPädagogik </i>, <i>49</i>, 68–93. <a href=\"https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X\">https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X</a>","ama":"Drossel K, Heldt M. Unterrichtsbezogene Lehrpersonenkooperationen im Zeitalter der digitalen Transformation – Alles digital oder alles wie bisher? . <i>MedienPädagogik </i>. 2022;49:68-93. doi:<a href=\"https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X\"> https://doi.org/10.21240/mpaed/49/2022.06.23.X</a>","mla":"Drossel, Kerstin, and M. Heldt. “Unterrichtsbezogene Lehrpersonenkooperationen Im Zeitalter Der Digitalen Transformation – Alles Digital Oder Alles Wie Bisher? .” <i>MedienPädagogik </i>, vol. 49, 2022, pp. 68–93, doi:<a href=\"https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X\"> https://doi.org/10.21240/mpaed/49/2022.06.23.X</a>.","short":"K. Drossel, M. Heldt, MedienPädagogik  49 (2022) 68–93.","bibtex":"@article{Drossel_Heldt_2022, title={Unterrichtsbezogene Lehrpersonenkooperationen im Zeitalter der digitalen Transformation – Alles digital oder alles wie bisher? }, volume={49}, DOI={<a href=\"https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X\"> https://doi.org/10.21240/mpaed/49/2022.06.23.X</a>}, journal={MedienPädagogik }, author={Drossel, Kerstin and Heldt, M}, year={2022}, pages={68–93} }","ieee":"K. Drossel and M. Heldt, “Unterrichtsbezogene Lehrpersonenkooperationen im Zeitalter der digitalen Transformation – Alles digital oder alles wie bisher? ,” <i>MedienPädagogik </i>, vol. 49, pp. 68–93, 2022, doi: <a href=\"https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X\"> https://doi.org/10.21240/mpaed/49/2022.06.23.X</a>.","chicago":"Drossel, Kerstin, and M Heldt. “Unterrichtsbezogene Lehrpersonenkooperationen Im Zeitalter Der Digitalen Transformation – Alles Digital Oder Alles Wie Bisher? .” <i>MedienPädagogik </i> 49 (2022): 68–93. <a href=\"https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X\">https://doi.org/ https://doi.org/10.21240/mpaed/49/2022.06.23.X</a>."}},{"doi":"10.3934/jgm.2022014","author":[{"last_name":"McLachlan","full_name":"McLachlan, Robert I","first_name":"Robert I"},{"first_name":"Christian","id":"85279","full_name":"Offen, Christian","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen"}],"volume":14,"date_updated":"2023-08-10T08:44:55Z","oa":"1","citation":{"chicago":"McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i> 14, no. 3 (2022): 447–71. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>.","ieee":"R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations of partial  differential equations,” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, pp. 447–471, 2022, doi: <a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","ama":"McLachlan RI, Offen C. Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>. 2022;14(3):447-471. doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>","apa":"McLachlan, R. I., &#38; Offen, C. (2022). Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>, <i>14</i>(3), 447–471. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>","mla":"McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","bibtex":"@article{McLachlan_Offen_2022, title={Backward error analysis for variational discretisations of partial  differential equations}, volume={14}, DOI={<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>}, number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan, Robert I and Offen, Christian}, year={2022}, pages={447–471} }","short":"R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471."},"page":"447 - 471","intvolume":"        14","related_material":{"link":[{"url":"https://github.com/Christian-Offen/multisymplectic","relation":"software"}]},"publication_status":"published","has_accepted_license":"1","file_date_updated":"2022-06-13T09:11:38Z","article_type":"original","user_id":"85279","department":[{"_id":"636"}],"_id":"19941","status":"public","type":"journal_article","title":"Backward error analysis for variational discretisations of partial  differential equations","date_created":"2020-10-06T16:33:19Z","publisher":"AIMS","year":"2022","issue":"3","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["2006.14172"]},"file":[{"content_type":"application/pdf","relation":"main_file","date_updated":"2022-06-13T09:11:38Z","date_created":"2022-06-13T09:11:38Z","creator":"coffen","file_size":1507248,"description":"In backward error analysis, an approximate solution to an equa-\ntion is compared to the exact solution to a nearby ‘modified’ equation. In\nnumerical ordinary differential equations, the two agree up to any power of\nthe step size. If the differential equation has a geometric property then the\nmodified equation may share it. In this way, known properties of differential\nequations can be applied to the approximation. But for partial differential\nequations, the known modified equations are of higher order, limiting appli-\ncability of the theory. Therefore, we study symmetric solutions of discretized\npartial differential equations that arise from a discrete variational principle.\nThese symmetric solutions obey infinite-dimensional functional equations. We\nshow that these equations admit second-order modified equations which are\nHamiltonian and also possess first-order Lagrangians in modified coordinates.\nThe modified equation and its associated structures are computed explicitly\nfor the case of rotating travelling waves in the nonlinear wave equation.","title":"Backward error analysis for variational discretisations of PDEs","file_name":"2_BlendedBEASymmPDE.pdf","access_level":"open_access","file_id":"31859"}],"abstract":[{"text":"In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized\r\npartial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation.","lang":"eng"}],"publication":"Journal of Geometric Mechanics"},{"main_file_link":[{"url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913","open_access":"1"}],"doi":"10.1063/5.0065913","author":[{"full_name":"Offen, Christian","id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"}],"volume":"32(1)","oa":"1","date_updated":"2023-08-10T08:48:14Z","citation":{"chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i> 32(1) (2022). <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian systems,” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), 2022, doi: <a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","ama":"Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. 2022;32(1). doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), AIP, 2022, doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","bibtex":"@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned Hamiltonian systems}, volume={32(1)}, DOI={<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }","short":"C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2022). Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, <i>32(1)</i>. <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>"},"related_material":{"link":[{"url":"https://github.com/Christian-Offen/symplectic-shadow-integration","description":"GitHub","relation":"software"}]},"publication_status":"published","has_accepted_license":"1","file_date_updated":"2021-12-13T14:56:15Z","article_type":"original","user_id":"85279","department":[{"_id":"636"}],"_id":"23382","status":"public","type":"journal_article","title":"Symplectic integration of learned Hamiltonian systems","date_created":"2021-08-11T08:24:02Z","publisher":"AIP","year":"2022","quality_controlled":"1","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["2108.02492"]},"file":[{"file_size":2285059,"access_level":"open_access","file_name":"SymplecticShadowIntegration_AIP.pdf","file_id":"28734","date_updated":"2021-12-13T14:56:15Z","date_created":"2021-12-13T14:56:15Z","creator":"coffen","relation":"main_file","content_type":"application/pdf"}],"abstract":[{"lang":"eng","text":"Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes."}],"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science"}]