Stability Analysis of Filtered Mass-Spring Systems

Abstract

Mass-spring systems simulations rely on the numerical integration method used for solving the resulting ordinary differential equations. Implicit schemes, which solve such equations, are unconditionally stable and are thus widely used. Part of this stability is due to force filtering which is inherent to the implicit formulation and is referred to artificial damping. We extract this artificial damping and we analyse frequencies. This analysis enables us to define a non arbitrary damping value and a stability criterion in accordance to filtering. This directly comes from a decrease of velocity vectors eigenvalues resulting in an increase of the time step in the same proportion. Moreover we applied a simple filtering model reproducing artificial damping to explicit schemes and results reveal an increase of the time step. Implementation of this method is straightforward for existing physically based simulators. Applications to cloth and fish animations are presented.