research-article

Mixed Variational Finite Elements for Implicit Simulation of Deformables

Authors:

David I.W. LevinAuthors Info & Claims

SA '22: SIGGRAPH Asia 2022 Conference Papers

Article No.: 40, Pages 1 - 8

https://doi.org/10.1145/3550469.3555418

Published: 30 November 2022 Publication History

Abstract

We propose and explore a new method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn, its finite element discretization leads to an efficient and accurate sequential quadratic programming solver with a superset of the desirable properties of many previous integration strategies. This framework fits a range of elastic constitutive models and remains stable across a wide span of time step sizes and material parameters (including problems that are approximately rigid). Our method exhibits convergence on par with full Newton type solvers and also generates visually plausible results in just a few iterations comparable to recent fast simulation methods that do not converge. These properties make it suitable for both offline accurate simulation and performant applications with expressive physics. We demonstrate the efficacy of our approach on a number of simulated examples.

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Cited By

Trusty TBenchekroun OGrinspun EKaufman DLevin D(2023)Subspace Mixed Finite Elements for Real-Time Heterogeneous ElastodynamicsSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618220(1-10)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.1145/3610548.3618220
Löschner FFernández-Fernández JJeske SLongva ABender J(2023)Micropolar Elasticity in Physically-Based AnimationProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36069226:3(1-24)Online publication date: 24-Aug-2023
https://dl.acm.org/doi/10.1145/3606922

Index Terms

Mixed Variational Finite Elements for Implicit Simulation of Deformables
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation

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cover image ACM Conferences

SA '22: SIGGRAPH Asia 2022 Conference Papers

November 2022

482 pages

ISBN:9781450394703

DOI:10.1145/3550469

Editors:
Soon Ki Jung
Kyungpook National University, South Korea
,
Jehee Lee
Seoul National University, South Korea
,
Adam Bargteil
University of Maryland Baltimore County, USA

Copyright © 2022 ACM.

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Published: 30 November 2022

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Supplemental Video https://dl.acm.org/doi/10.1145/3550469.3555418#mfem_video.mp4

Funding Sources

CFI-JELF Fund
Connaught Fund
Canada Research Chairs Program
Accelerator
Ontario Early Researchers Award
NSERC Discovery

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SA '22

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SIGGRAPH

SA '22: SIGGRAPH Asia 2022

December 6 - 9, 2022

Daegu, Republic of Korea

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Cited By

Trusty TBenchekroun OGrinspun EKaufman DLevin D(2023)Subspace Mixed Finite Elements for Real-Time Heterogeneous ElastodynamicsSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618220(1-10)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.1145/3610548.3618220
Löschner FFernández-Fernández JJeske SLongva ABender J(2023)Micropolar Elasticity in Physically-Based AnimationProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36069226:3(1-24)Online publication date: 24-Aug-2023
https://dl.acm.org/doi/10.1145/3606922

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