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Graph."],"published-print":{"date-parts":[[2025,8,1]]},"abstract":"<jats:p>\n                    We propose the Epsilon Difference Gradient Evolution (EDGE) method for accurate flow-map calculation on grids via Hermite interpolation without using velocity buffers. Our key idea is to integrate Gradient Evolution for accurate first-order derivatives and a tetrahedron-based Epsilon Difference scheme to compute higher-order derivatives with reduced memory consumption. EDGE achieves\n                    <jats:italic toggle=\"yes\">O<\/jats:italic>\n                    (1) memory usage, independent of flow map length, while maintaining vorticity preservation comparable to buffer-based methods. We validate our methods across diverse vortical flow scenarios, demonstrating up to 90% backward map memory reduction and significant computational efficiency, broadening the applicability of flow-map methods to large-scale and complex fluid simulations.\n                  <\/jats:p>","DOI":"10.1145\/3731193","type":"journal-article","created":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T04:02:41Z","timestamp":1753588961000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["EDGE: Epsilon-Difference Gradient Evolution for Buffer-Free Flow Maps"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6892-8097","authenticated-orcid":false,"given":"Zhiqi","family":"Li","sequence":"first","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6119-1544","authenticated-orcid":false,"given":"Ruicheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-4372-0085","authenticated-orcid":false,"given":"Junlin","family":"Li","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6833-6312","authenticated-orcid":false,"given":"Duowen","family":"Chen","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-9322-2351","authenticated-orcid":false,"given":"Sinan","family":"Wang","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1392-0928","authenticated-orcid":false,"given":"Bo","family":"Zhu","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology, Atlanta, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766935"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073606"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073380"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/2422356.2422371"},{"key":"e_1_2_2_5_1","doi-asserted-by":"crossref","unstructured":"Tomas F Buttke. 1992. 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