Stabilisation par filtrage de méthodes d'intégration explicites

Abstract : Mass spring systems have proved their efficiency for deformable behaviour simulation. Animation of such models highly depends on the numerical integration method used for solving ordinary differential equations. Two main formulations exist to solve these equations, namely explicit and implicit. Explicit methods exhibit poor stability properties (due to the Courant Frederick Levy condition, implying small time steps), contrary to implicit modelling which benefits from unconditional stability (larger time steps can be taken). Part of this stability is due to force filtering which is inherent to implicit formulation. Taking advantage of this, this paper presents an original post-processing velocity filtering algorithm for explicit schemes to enable larger time steps. Implementation of this method is straightforward for existing physically-based simulators. Results on all tested explicit methods show a computational time acceleration of about 20%. This directly comes from an increase of the time step in the same proportion, resulting from a decrease of eigenvalues (due to filtering). We also analyse frequencies and define a stability criterion for this post-processing filter. Applications to cloth and fish animations are presented.
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Alexandre Ahmad, Olivier Terraz, Samir Adly, Djamchid Ghazanfarpour. Stabilisation par filtrage de méthodes d'intégration explicites. Journées Association française de l'Informatique graphique, 2006, Bordeaux, France. pp.73-80. ⟨hal-00118849⟩

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