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These changes we introduce allow simulating complex contact scenarios involving rigid bodies with stacking and friction, articulated bodies connected with hard constraints, including joints with limited degrees of freedom, and stiff systems interacting with soft bodies. We present evaluations using a parallel GPU implementation that can deliver real-time performance and stable simulations with low iteration counts for millions of objects interacting via collisions, various joint\/attachment constraints, and springs of various stiffness. Our results show superior performance, convergence, and stability compared to the state-of-the-art alternatives.<\/jats:p>","DOI":"10.1145\/3731195","type":"journal-article","created":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T04:02:41Z","timestamp":1753588961000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Augmented Vertex Block Descent"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1502-3487","authenticated-orcid":false,"given":"Chris","family":"Giles","sequence":"first","affiliation":[{"name":"Roblox, San Mateo, California, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-9493-1684","authenticated-orcid":false,"given":"Elie","family":"Diaz","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, Utah, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0122-4159","authenticated-orcid":false,"given":"Cem","family":"Yuksel","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, Utah, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13122"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13122"},{"key":"e_1_2_2_3_1","unstructured":"David Baraff. 1997. An Introduction to Physically Based Modeling: Rigid Body Simulation I\u2014Unconstrained Rigid Body Dynamics. Technical Report CMU-RI-TR-97-13. Robotics Institute Carnegie Mellon University. Available at https:\/\/www.cs.cmu.edu\/~baraff\/sigcourse\/notesd1.pdf."},{"key":"e_1_2_2_4_1","doi-asserted-by":"crossref","unstructured":"David Baraff and Andrew Witkin. 1998. Large Steps in Cloth Simulation. (1998).","DOI":"10.1145\/280814.280821"},{"key":"e_1_2_2_5_1","volume-title":"Practical augmented Lagrangian methods for constrained optimization","author":"Birgin E G","unstructured":"E G Birgin and J M Mart\u00ednez. 2014. Practical augmented Lagrangian methods for constrained optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA."},{"key":"e_1_2_2_6_1","volume-title":"Proceedings of the Game Developers Conference.","author":"Catto Erin","year":"2006","unstructured":"Erin Catto. 2006. Fast and Simple Physics using Sequential Impulses. 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