[{"project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819","call_identifier":"H2020"}],"volume":22,"oa_version":"Preprint","date_created":"2024-08-25T22:01:08Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.06798"}],"corr_author":"1","abstract":[{"text":"We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale l in an infinite heterogeneous correlated random medium, in a situation where the medium is only known in a box of diameter L >>l around the support of the charge. We show that the algorithm in [J. Lu, F. Otto, and L. Wang, Optimal Artificial Boundary Conditions Based on Second-Order Correctors for Three Dimensional Random Ellilptic Media, preprint, arXiv:2109.01616, 2021], suggesting optimal Dirichlet boundary conditions motivated by the multipole expansion [P. Bella, A. Giunti, and F. Otto, Comm. Partial Differential Equations, 45 (2020), pp. 561–640], still performs well in correlated media. With overwhelming probability, we obtain a convergence rate in terms of l, L, and the size of the correlations for which optimality is supported with numerical simulations. These estimates are provided for ensembles which satisfy a multiscale logarithmic Sobolev inequality, where our main tool is an extension of the semigroup estimates in [N. Clozeau, Stoch. Partial Differ. Equ. Anal. Comput., 11 (2023), pp. 1254–1378]. As part of our strategy, we construct sublinear second-order correctors in this correlated setting, which is of independent interest.","lang":"eng"}],"publication":"Multiscale Modeling and Simulation","date_published":"2024-09-01T00:00:00Z","article_processing_charge":"No","doi":"10.1137/23M1603819","acknowledgement":"We would like to thank our affiliations, Institute of Science and Technology Austria and Max Planck Institute for Mathematics in the Sciences, for supporting the authors’ visits to each other, which greatly facilitated this work. We would like to thank Marc Josien and Quinn Winters for assistance in numerical implementation.","intvolume":"        22","year":"2024","arxiv":1,"OA_place":"repository","oa":1,"publication_identifier":{"issn":["1540-3459"],"eissn":["1540-3467"]},"day":"01","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","external_id":{"isi":["001285416500001"],"arxiv":["2309.06798"]},"author":[{"id":"fea1b376-906f-11eb-847d-b2c0cf46455b","full_name":"Clozeau, Nicolas","first_name":"Nicolas","last_name":"Clozeau"},{"last_name":"Wang","full_name":"Wang, Lihan","first_name":"Lihan"}],"publication_status":"published","OA_type":"green","isi":1,"_id":"17462","title":"Artificial boundary conditions for random elliptic systems with correlated coefficient field","status":"public","month":"09","type":"journal_article","publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","department":[{"_id":"JuFi"}],"issue":"3","article_type":"original","ec_funded":1,"page":"973-1029","date_updated":"2025-09-08T09:01:00Z","citation":{"ista":"Clozeau N, Wang L. 2024. Artificial boundary conditions for random elliptic systems with correlated coefficient field. Multiscale Modeling and Simulation. 22(3), 973–1029.","short":"N. Clozeau, L. Wang, Multiscale Modeling and Simulation 22 (2024) 973–1029.","ieee":"N. Clozeau and L. Wang, “Artificial boundary conditions for random elliptic systems with correlated coefficient field,” <i>Multiscale Modeling and Simulation</i>, vol. 22, no. 3. Society for Industrial and Applied Mathematics, pp. 973–1029, 2024.","apa":"Clozeau, N., &#38; Wang, L. (2024). Artificial boundary conditions for random elliptic systems with correlated coefficient field. <i>Multiscale Modeling and Simulation</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/23M1603819\">https://doi.org/10.1137/23M1603819</a>","mla":"Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random Elliptic Systems with Correlated Coefficient Field.” <i>Multiscale Modeling and Simulation</i>, vol. 22, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 973–1029, doi:<a href=\"https://doi.org/10.1137/23M1603819\">10.1137/23M1603819</a>.","ama":"Clozeau N, Wang L. Artificial boundary conditions for random elliptic systems with correlated coefficient field. <i>Multiscale Modeling and Simulation</i>. 2024;22(3):973-1029. doi:<a href=\"https://doi.org/10.1137/23M1603819\">10.1137/23M1603819</a>","chicago":"Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random Elliptic Systems with Correlated Coefficient Field.” <i>Multiscale Modeling and Simulation</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/23M1603819\">https://doi.org/10.1137/23M1603819</a>."}},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1540-3459"],"eissn":["1540-3467"]},"oa":1,"language":[{"iso":"eng"}],"day":"16","publication_status":"published","scopus_import":"1","external_id":{"arxiv":["1808.04200"],"isi":["000487931800002"]},"author":[{"last_name":"Friesecke","first_name":"Gero","full_name":"Friesecke, Gero"},{"id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5645-4333","last_name":"Kniely","first_name":"Michael","full_name":"Kniely, Michael"}],"main_file_link":[{"url":"https://arxiv.org/abs/1808.04200","open_access":"1"}],"date_created":"2019-08-04T21:59:21Z","oa_version":"Preprint","volume":17,"intvolume":"        17","arxiv":1,"year":"2019","article_processing_charge":"No","date_published":"2019-07-16T00:00:00Z","publication":"Multiscale Modeling and Simulation","doi":"10.1137/18M1207272","abstract":[{"text":"We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level\r\nof theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the doping profiles < system size.","lang":"eng"}],"issue":"3","citation":{"chicago":"Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” <i>Multiscale Modeling and Simulation</i>. SIAM, 2019. <a href=\"https://doi.org/10.1137/18M1207272\">https://doi.org/10.1137/18M1207272</a>.","mla":"Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density Functional Theory Motivated by Photovoltaics.” <i>Multiscale Modeling and Simulation</i>, vol. 17, no. 3, SIAM, 2019, pp. 926–47, doi:<a href=\"https://doi.org/10.1137/18M1207272\">10.1137/18M1207272</a>.","ama":"Friesecke G, Kniely M. New optimal control problems in density functional theory motivated by photovoltaics. <i>Multiscale Modeling and Simulation</i>. 2019;17(3):926-947. doi:<a href=\"https://doi.org/10.1137/18M1207272\">10.1137/18M1207272</a>","apa":"Friesecke, G., &#38; Kniely, M. (2019). New optimal control problems in density functional theory motivated by photovoltaics. <i>Multiscale Modeling and Simulation</i>. SIAM. <a href=\"https://doi.org/10.1137/18M1207272\">https://doi.org/10.1137/18M1207272</a>","ieee":"G. Friesecke and M. Kniely, “New optimal control problems in density functional theory motivated by photovoltaics,” <i>Multiscale Modeling and Simulation</i>, vol. 17, no. 3. SIAM, pp. 926–947, 2019.","short":"G. Friesecke, M. Kniely, Multiscale Modeling and Simulation 17 (2019) 926–947.","ista":"Friesecke G, Kniely M. 2019. New optimal control problems in density functional theory motivated by photovoltaics. Multiscale Modeling and Simulation. 17(3), 926–947."},"date_updated":"2025-07-10T11:53:49Z","page":"926-947","publisher":"SIAM","title":"New optimal control problems in density functional theory motivated by photovoltaics","status":"public","type":"journal_article","month":"07","isi":1,"_id":"6762","quality_controlled":"1","department":[{"_id":"JuFi"}]}]