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Graph."],"published-print":{"date-parts":[[2013,7,21]]},"abstract":"<jats:p>\n            We present a new subspace integration method that is capable of efficiently adding and subtracting dynamics from an existing high-resolution fluid simulation. We show how to analyze the results of an existing high-resolution simulation, discover an efficient reduced approximation, and use it to quickly \"re-simulate\" novel variations of the original dynamics. Prior subspace methods have had difficulty re-simulating the original input dynamics because they lack efficient means of handling semi-Lagrangian advection methods. We show that multi-dimensional\n            <jats:italic>cubature<\/jats:italic>\n            schemes can be applied to this and other advection methods, such as MacCormack advection. The remaining pressure and diffusion stages can be written as a single matrix-vector multiply, so as with previous subspace methods, no matrix inversion is needed at runtime. We additionally propose a novel importance sampling-based fitting algorithm that asymptotically accelerates the precomputation stage, and show that the Iterated Orthogonal Projection method can be used to elegantly incorporate moving internal boundaries into a subspace simulation. In addition to efficiently producing variations of the original input, our method can produce novel, abstract fluid motions that we have not seen from any other solver.\n          <\/jats:p>","DOI":"10.1145\/2461912.2461987","type":"journal-article","created":{"date-parts":[[2013,7,16]],"date-time":"2013-07-16T18:06:45Z","timestamp":1373998005000},"page":"1-9","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":55,"title":["Subspace fluid re-simulation"],"prefix":"10.1145","volume":"32","author":[{"given":"Theodore","family":"Kim","sequence":"first","affiliation":[{"name":"University of California, Santa Barbara"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Delaney","sequence":"additional","affiliation":[{"name":"University of California, Santa Barbara"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,7,21]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4274"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1409060.1409118"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(03)90005-7"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/133994.134084"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073300"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.2033624"},{"key":"e_1_2_2_7_1","doi-asserted-by":"crossref","unstructured":"Berkooz G. 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