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Graph."],"published-print":{"date-parts":[[2018,2,28]]},"abstract":"<jats:p>We present a new time integration method featuring excellent stability and energy conservation properties, making it particularly suitable for real-time physics. The commonly used backward Euler method is stable but introduces artificial damping. Methods such as implicit midpoint do not suffer from artificial damping but are unstable in many common simulation scenarios. We propose an algorithm that blends between the implicit midpoint and forward\/backward Euler integrators such that the resulting simulation is stable while introducing only minimal artificial damping. We achieve this by tracking the total energy of the simulated system, taking into account energy-changing events: damping and forcing. To facilitate real-time simulations, we propose a local\/global solver, similar to Projective Dynamics, as an alternative to Newton\u2019s method. Compared to the original Projective Dynamics, which is derived from backward Euler, our final method introduces much less numerical damping at the cost of minimal computing overhead. Stability guarantees of our method are derived from the stability of backward Euler, whose stability is a widely accepted empirical fact. However, to our knowledge, theoretical guarantees have so far only been proven for linear ODEs. We provide preliminary theoretical results proving the stability of backward Euler also for certain cases of nonlinear potential functions.<\/jats:p>","DOI":"10.1145\/3153420","type":"journal-article","created":{"date-parts":[[2018,1,10]],"date-time":"2018-01-10T16:51:38Z","timestamp":1515603098000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":25,"title":["Stabilizing Integrators for Real-Time Physics"],"prefix":"10.1145","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1703-3178","authenticated-orcid":false,"given":"Dimitar","family":"Dinev","sequence":"first","affiliation":[{"name":"University of Utah, Salt Lake City, UT"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiantian","family":"Liu","sequence":"additional","affiliation":[{"name":"University of Pennsylvania, PA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ladislav","family":"Kavan","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, UT"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,1,10]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366170"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971392"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597316059"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280821"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2014.07.004"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12346"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566623"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778775"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566624"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.2900803"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19870670128"},{"volume-title":"Geometric Methods for Discrete Dynamical Systems","author":"Easton Robert W.","key":"e_1_2_2_14_1"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.12.009"},{"volume-title":"Proceedings of the Eurographics\/ACM SIGGRAPH Symposium on Computer Animation.","author":"Theodore","key":"e_1_2_2_16_1"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2459687"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(96)01009-2"},{"volume-title":"Long-Time Energy Conservation of Numerical Integrators","author":"Hairer Ernst","key":"e_1_2_2_19_1"},{"volume-title":"Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations","author":"Hairer Ernst","key":"e_1_2_2_20_1"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531393"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.3424303"},{"volume-title":"A First Course in the Numerical Analysis of Differential Equations","author":"Iserles Arieh","key":"e_1_2_2_23_1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511995569"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.532892"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.5555\/1218064.1218071"},{"volume-title":"Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation. 305--310","year":"2012","author":"Kim Tae-Yong","key":"e_1_2_2_27_1"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19990620)45:5%3C569::AID-NME595%3E3.0.CO;2-A"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396331"},{"volume-title":"Numerical Methods for Ordinary Differential Systems: The Initial Value Problem","author":"Lambert J. 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