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We represent such forces using\n            <jats:italic>dissipation functions<\/jats:italic>\n            which may be nonlinear in both positions and velocities, enabling us to model a range of dissipative effects including Coulomb friction, Rayleigh damping, and power-law dissipation. We propose a general method for incorporating dissipative forces into optimization-based time integration schemes, which hitherto have been applied almost exclusively to systems with only conservative forces. To improve accuracy and minimize artificial damping, we provide an optimization-based version of the second-order accurate TR-BDF2 integrator. Finally, we present a method for modifying arbitrary dissipation functions to conserve linear and angular momentum, allowing us to eliminate the artificial angular momentum loss caused by Rayleigh damping.\n          <\/jats:p>","DOI":"10.1145\/3272127.3275011","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T19:16:10Z","timestamp":1543432570000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":33,"title":["Accurate dissipative forces in optimization integrators"],"prefix":"10.1145","volume":"37","author":[{"given":"George E.","family":"Brown","sequence":"first","affiliation":[{"name":"University of Minnesota"}]},{"given":"Matthew","family":"Overby","sequence":"additional","affiliation":[{"name":"University of Minnesota"}]},{"given":"Zahra","family":"Forootaninia","sequence":"additional","affiliation":[{"name":"University of Minnesota"}]},{"given":"Rahul","family":"Narain","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology"}]}],"member":"320","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.1985.1270142"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/122718.122722"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280821"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073300"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2006.09.004"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2005.08.001"},{"key":"e_1_2_2_7_1","volume-title":"Position-Based Simulation Methods in Computer Graphics. 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