Abstract: Simulating deformable objects based on physical laws has become the most popular technique for modeling textiles, skin, or volumetric soft objects like human tissue. The physical model leads to an ordinary differential equation. Recently, several approaches to fast algorithms have been proposed.

In this work, more profound numerical background about numerical stiffness is provided. Stiff equations impose stability restrictions on a numerical integrator. Some one-step and multistep methods with adequate stability properties are presented. For an efficient implementation, the inexact Newton method is discussed. Applications to 2D and 3D elasticity problems show that the discussed methods are faster and give higher-quality solutions than the commonly used linearized Euler method.