Rigid Body Contact Problems using Proximal Operators

Kenny Erleben

Iterative methods are popular for solving contact force problems in rigid body dynamics. They are loved for their robustness and surrounded by mystery as to whether they converge or not. We provide a mathematical foundation for iterative (PROX) schemes based on proximal operators. This is a class of iterative Jacobi and blocked Gauss–Seidel variants that theoretically proven always converge and provides a flexible plug and play framework for exploring different friction laws. We provide a portfolio of experience for choosing r-Factor strategies for such schemes and we analyze the distribution of convergence behaviors. Our results indicate the Gauss-Seidel variant is superior in terms of delivering predictable convergence behaviour and hence should be preferred over Jacobi variants. Our results also suggest that Global r -Factor strategies are better for structured stacking scenarios and can achieve absolute convergence in more cases.

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A numerical strategy for finite element modeling of frictionless asymmetric vocal fold collision

Alba Granados, Marek Krzysztof Misztal, Jonas Brunskog, Vincent Visseq and Kenny Erleben

Analysis of voice pathologies may require vocal fold models that include relevant features such as vocal fold asymmetric collision. The present study numerically addresses the problem of frictionless asymmetric collision in a self-sustained three-dimensional continuum model of the vocal folds. Theoretical background and numerical analysis of the finite-element position-based contact model are presented, along with validation. A novel contact detection mechanism capable to detect collision in asymmetric oscillations is developed. The effect of inexact contact constraint enforcement on vocal fold dynamics is examined by different variational methods for inequality constrained minimization problems, namely the Lagrange multiplier method and the penalty method. In contrast to the penalty solution, which is related to classical spring-like contact forces, numerical examples show that the parameter-independent Lagrange multiplier solution is more robust and accurate in the estimation of dynamical and mechanical features at vocal fold contact. Furthermore, special attention is paid to the temporal integration schemes in relation to the contact problem, the results suggesting an advantage of highly diffusive schemes. Finally, vocal fold contact enforcement is shown to affect asymmetric oscillations. The present model may be adapted to existing vocal fold models, which may contribute to a better understanding of the effect of the non-linear contact phenomenon on phonation.

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Teaching Inverse Kinematics

Screen casts and slides by Kenny Erleben for Teaching in Inverse Kinematics

This material was used to give students in Numerical Optimization classes a case-study to apply their own implemented methods on.

Special Issue on Physics based Animation in IEEE Computer Graphics & Animations

Guest Editors: Jan Bender, Barbara Solenthaler, and Kenny Erleben.

This special issue of IEEE Computer Graphics and Applications will provide an opportunity for researchers and practitioners in the field of physically based animation to publish their latest work.

Have a look at the call for papers.

Teaser on new boundary conditions

This took 1/2 year to get from left image to right image. Nice we final got our boundary conditions on our moving mesh to work as we mathematically wanted them to work…

Numerical Methods for Linear Complementarity Problems in Physics-Based Animation

Sarah Niebe and Kenny Erleben

Our new book is out from January 2015. Have a look at it here. Get the supplementary code and have fun (Old google code project ).

Finite element modeling of the vocal folds with deformable interface tracking

Alba Granados, Jonas Brunskog, Marek Krzysztof Misztal, Vincent Visseq, and Kenny Erleben

Continuous and prolonged use of the speaking voice may lead to functional speech disorders that are not apparent for voice clinicians from high-speed imaging of the vocal folds’ vibration. However, it is hypothesized that time dependent tissue properties provide some insight into the injury process. To infer material parameters via an inverse optimization problem from recorded deformation, a self sustained theoretical model of the vocal folds is needed. With this purpose, a transversely isotropic three-dimensional nite element model is proposed and investigated. Special attention is paid to the collision and time integration schemes. Accuracy in the deformation process is introduced by means of a topology-adaptive method for deformable interface tracking, called the Deformable Simplicial Complex, which has been previously applied to immiscible uids. For computational reasons, aerodynamic driving forces are derived from Bernoulli’s principle.

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