[{"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"keyword":["Optimal transport","Hamilton-Jacobi equation","convex optimization"],"article_number":"2312.12213","year":"2023","external_id":{"arxiv":["2312.12213"]},"arxiv":1,"month":"12","citation":{"chicago":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2312.12213\">https://doi.org/10.48550/arXiv.2312.12213</a>.","ista":"Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. arXiv, 2312.12213.","mla":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” <i>ArXiv</i>, 2312.12213, doi:<a href=\"https://doi.org/10.48550/arXiv.2312.12213\">10.48550/arXiv.2312.12213</a>.","apa":"Ishida, S., &#38; Lavenant, H. (n.d.). Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2312.12213\">https://doi.org/10.48550/arXiv.2312.12213</a>","ama":"Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2312.12213\">10.48550/arXiv.2312.12213</a>","short":"S. Ishida, H. Lavenant, ArXiv (n.d.).","ieee":"S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation,” <i>arXiv</i>. ."},"date_published":"2023-12-19T00:00:00Z","acknowledgement":"The authors would like to thank Chris Wojtan for his continuous support and several interesting discussions. Part of this research was performed during two visits: one of SI to the BIDSA research center at Bocconi University, and one of HL to the Institute of Science and Technology Austria. Both host institutions are warmly acknowledged for the hospital-\r\nity. HL is partially supported by the MUR-Prin 2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with Applications to Optimization and Machine Learning”, funded by the European Union - Next Generation EU. SI is supported in part by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"project":[{"grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"publication":"arXiv","status":"public","language":[{"iso":"eng"}],"date_updated":"2023-12-27T13:44:33Z","_id":"14703","type":"preprint","date_created":"2023-12-21T10:14:37Z","doi":"10.48550/arXiv.2312.12213","author":[{"last_name":"Ishida","full_name":"Ishida, Sadashige","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","first_name":"Sadashige"},{"full_name":"Lavenant, Hugo","last_name":"Lavenant","first_name":"Hugo"}],"day":"19","article_processing_charge":"No","title":"Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2312.12213"}],"publication_status":"submitted","abstract":[{"text":"We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation.","lang":"eng"}]},{"abstract":[{"text":"We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss-Bonnet theorem that requires measuring angles, the new formula mimics Green's theorem and is applicable to a wider range of degenerate spherical curves and polygons.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2303.14555"}],"publication_status":"submitted","day":"25","article_processing_charge":"No","author":[{"first_name":"Albert","full_name":"Chern, Albert","last_name":"Chern"},{"first_name":"Sadashige","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","full_name":"Ishida, Sadashige","last_name":"Ishida"}],"doi":"10.48550/arXiv.2303.14555","title":"Area formula for spherical polygons via prequantization","oa_version":"Preprint","_id":"12846","date_updated":"2023-04-25T06:51:21Z","date_created":"2023-04-18T19:16:06Z","type":"preprint","oa":1,"status":"public","language":[{"iso":"eng"}],"publication":"arXiv","project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena"}],"citation":{"ama":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2303.14555\">10.48550/arXiv.2303.14555</a>","ieee":"A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,” <i>arXiv</i>. .","short":"A. Chern, S. Ishida, ArXiv (n.d.).","chicago":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2303.14555\">https://doi.org/10.48550/arXiv.2303.14555</a>.","ista":"Chern A, Ishida S. Area formula for spherical polygons via prequantization. arXiv, 2303.14555.","apa":"Chern, A., &#38; Ishida, S. (n.d.). Area formula for spherical polygons via prequantization. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2303.14555\">https://doi.org/10.48550/arXiv.2303.14555</a>","mla":"Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via Prequantization.” <i>ArXiv</i>, 2303.14555, doi:<a href=\"https://doi.org/10.48550/arXiv.2303.14555\">10.48550/arXiv.2303.14555</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2023-03-25T00:00:00Z","acknowledgement":"The authors acknowledge Chris Wojtan for his continuous support to the present work through discussions and advice. The second author thanks Anna Sisak for a fruitful discussion on prequantum bundles. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","year":"2023","month":"03","arxiv":1,"external_id":{"arxiv":["2303.14555"]},"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"article_number":"2303.14555"},{"quality_controlled":"1","ddc":["000"],"_id":"12431","date_updated":"2023-08-04T09:37:23Z","type":"journal_article","article_processing_charge":"No","doi":"10.1145/3550454.3555459","publisher":"Association for Computing Machinery","date_published":"2022-12-01T00:00:00Z","acknowledgement":"We thank the visual computing group at IST Austria for their valuable discussions and feedback. Houdini Education licenses were provided by SideFX software. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).","publication":"ACM Transactions on Graphics","status":"public","project":[{"name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"isi":1,"year":"2022","external_id":{"isi":["000891651900061"]},"file_date_updated":"2023-01-30T07:15:48Z","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"publication_status":"published","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"text":"This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent curves implicitly with a new co-dimensional 2 level set description. Our implicit representation admits several redundant mathematical degrees of freedom in both the configuration and the dynamics of the curves, which can be tailored specifically to improve numerical robustness, in contrast to naive approaches for implicit curve dynamics that suffer from overwhelming numerical stability problems. Furthermore, we note how these hidden degrees of freedom perfectly map to a Clebsch representation in fluid dynamics. Motivated by these observations, we introduce untwisted level set functions and non-swirling dynamics which successfully regularize sources of numerical instability, particularly in the twisting modes around curve filaments. A consequence is a novel simulation method which produces stable dynamics for large numbers of interacting vortex filaments and effortlessly handles topological changes and re-connection events.","lang":"eng"}],"intvolume":"        41","volume":41,"date_created":"2023-01-29T23:00:59Z","article_type":"original","scopus_import":"1","day":"01","author":[{"full_name":"Ishida, Sadashige","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","last_name":"Ishida","first_name":"Sadashige"},{"first_name":"Christopher J","orcid":"0000-0001-6646-5546","last_name":"Wojtan","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Chern","full_name":"Chern, Albert","first_name":"Albert"}],"oa_version":"Published Version","title":"Hidden degrees of freedom in implicit vortex filaments","citation":{"chicago":"Ishida, Sadashige, Chris Wojtan, and Albert Chern. “Hidden Degrees of Freedom in Implicit Vortex Filaments.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3550454.3555459\">https://doi.org/10.1145/3550454.3555459</a>.","ista":"Ishida S, Wojtan C, Chern A. 2022. Hidden degrees of freedom in implicit vortex filaments. ACM Transactions on Graphics. 41(6), 241.","apa":"Ishida, S., Wojtan, C., &#38; Chern, A. (2022). Hidden degrees of freedom in implicit vortex filaments. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3550454.3555459\">https://doi.org/10.1145/3550454.3555459</a>","mla":"Ishida, Sadashige, et al. “Hidden Degrees of Freedom in Implicit Vortex Filaments.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 6, 241, Association for Computing Machinery, 2022, doi:<a href=\"https://doi.org/10.1145/3550454.3555459\">10.1145/3550454.3555459</a>.","ama":"Ishida S, Wojtan C, Chern A. Hidden degrees of freedom in implicit vortex filaments. <i>ACM Transactions on Graphics</i>. 2022;41(6). doi:<a href=\"https://doi.org/10.1145/3550454.3555459\">10.1145/3550454.3555459</a>","ieee":"S. Ishida, C. Wojtan, and A. Chern, “Hidden degrees of freedom in implicit vortex filaments,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 6. Association for Computing Machinery, 2022.","short":"S. Ishida, C. Wojtan, A. Chern, ACM Transactions on Graphics 41 (2022)."},"issue":"6","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"ChWo"}],"file":[{"success":1,"file_name":"2022_ACM_Ishida.pdf","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"a2fba257fdefe0e747182be6c0f7c70c","file_size":15551202,"date_created":"2023-01-30T07:15:48Z","creator":"dernst","date_updated":"2023-01-30T07:15:48Z","file_id":"12433"}],"article_number":"241","month":"12"},{"publication":"ACM Transactions on Graphics","status":"public","project":[{"_id":"2533E772-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Efficient Simulation of Natural Phenomena at Extremely Large Scales","grant_number":"638176"}],"date_published":"2020-07-08T00:00:00Z","acknowledgement":"We wish to thank the anonymous reviewers and the members of the Visual Computing Group at IST Austria for their valuable feedback, especially Camille Schreck for her help in rendering. This research was supported by the Scientific Service Units (SSU) of IST Austria through resources provided by Scientific Computing. We would like to thank the authors of [Belcour and Barla 2017] for providing their implementation, the authors of [Atkins and Elliott 2010] and [Seychelles et al. 2008] for allowing us to use their results, and Rok Grah for helpful discussions. Finally, we thank Ryoichi Ando for many discussions from the beginning of the project that resulted in important contents of the paper including our formulation, numerical scheme, and initial implementation. This project has received funding from the\r\nEuropean Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 638176.","ec_funded":1,"external_id":{"isi":["000583700300004"]},"isi":1,"year":"2020","ddc":["000"],"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.1145/3386569.3392405","open_access":"1"}],"publisher":"Association for Computing Machinery","article_processing_charge":"No","doi":"10.1145/3386569.3392405","type":"journal_article","_id":"8384","date_updated":"2024-02-28T12:57:31Z","language":[{"iso":"eng"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"S. Ishida, P. Synak, F. Narita, T. Hachisuka, C. Wojtan, ACM Transactions on Graphics 39 (2020).","ieee":"S. Ishida, P. Synak, F. Narita, T. Hachisuka, and C. Wojtan, “A model for soap film dynamics with evolving thickness,” <i>ACM Transactions on Graphics</i>, vol. 39, no. 4. Association for Computing Machinery, 2020.","ama":"Ishida S, Synak P, Narita F, Hachisuka T, Wojtan C. A model for soap film dynamics with evolving thickness. <i>ACM Transactions on Graphics</i>. 2020;39(4). doi:<a href=\"https://doi.org/10.1145/3386569.3392405\">10.1145/3386569.3392405</a>","mla":"Ishida, Sadashige, et al. “A Model for Soap Film Dynamics with Evolving Thickness.” <i>ACM Transactions on Graphics</i>, vol. 39, no. 4, 31, Association for Computing Machinery, 2020, doi:<a href=\"https://doi.org/10.1145/3386569.3392405\">10.1145/3386569.3392405</a>.","apa":"Ishida, S., Synak, P., Narita, F., Hachisuka, T., &#38; Wojtan, C. (2020). A model for soap film dynamics with evolving thickness. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3386569.3392405\">https://doi.org/10.1145/3386569.3392405</a>","ista":"Ishida S, Synak P, Narita F, Hachisuka T, Wojtan C. 2020. A model for soap film dynamics with evolving thickness. ACM Transactions on Graphics. 39(4), 31.","chicago":"Ishida, Sadashige, Peter Synak, Fumiya Narita, Toshiya Hachisuka, and Chris Wojtan. “A Model for Soap Film Dynamics with Evolving Thickness.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2020. <a href=\"https://doi.org/10.1145/3386569.3392405\">https://doi.org/10.1145/3386569.3392405</a>."},"issue":"4","month":"07","file":[{"file_name":"2020_soapfilm_submitted.pdf","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"813831ca91319d794d9748c276b24578","file_size":14935529,"date_created":"2020-11-23T09:03:19Z","creator":"dernst","date_updated":"2020-11-23T09:03:19Z","file_id":"8795"}],"article_number":"31","department":[{"_id":"ChWo"}],"acknowledged_ssus":[{"_id":"ScienComp"}],"abstract":[{"lang":"eng","text":"Previous research on animations of soap bubbles, films, and foams largely focuses on the motion and geometric shape of the bubble surface. These works neglect the evolution of the bubble’s thickness, which is normally responsible for visual phenomena like surface vortices, Newton’s interference patterns, capillary waves, and deformation-dependent rupturing of films in a foam. In this paper, we model these natural phenomena by introducing the film thickness as a reduced degree of freedom in the Navier-Stokes equations and deriving their equations of motion. We discretize the equations on a nonmanifold triangle mesh surface and couple it to an existing bubble solver. In doing so, we also introduce an incompressible fluid solver for 2.5D films and a novel advection algorithm for convecting fields across non-manifold surface junctions. Our simulations enhance state-of-the-art bubble solvers with additional effects caused by convection, rippling, draining, and evaporation of the thin film."}],"intvolume":"        39","has_accepted_license":"1","file_date_updated":"2020-11-23T09:03:19Z","publication_identifier":{"eissn":["15577368"],"issn":["07300301"]},"publication_status":"published","title":"A model for soap film dynamics with evolving thickness","oa_version":"Submitted Version","scopus_import":"1","day":"08","author":[{"last_name":"Ishida","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","full_name":"Ishida, Sadashige","first_name":"Sadashige"},{"id":"331776E2-F248-11E8-B48F-1D18A9856A87","full_name":"Synak, Peter","last_name":"Synak","first_name":"Peter"},{"last_name":"Narita","full_name":"Narita, Fumiya","first_name":"Fumiya"},{"last_name":"Hachisuka","full_name":"Hachisuka, Toshiya","first_name":"Toshiya"},{"id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","full_name":"Wojtan, Christopher J","last_name":"Wojtan","first_name":"Christopher J","orcid":"0000-0001-6646-5546"}],"date_created":"2020-09-13T22:01:18Z","article_type":"original","volume":39}]