An implicit multistep numerical method for real-time simulation of stiff systems

Abstract

Simulating a physical system in real-time is widely used in equipment design, test, and validation. Though an implicit multistep numerical method excels at solving physical models that are usually composed of stiff ordinary differential equations, it is not suitable for real-time simulation because of state discontinuity and massive iterations for root finding. Thus, a method based on the backward differential formula is presented. It divides the main fixed step of real-time simulation into limited minor steps according to computing cost and accuracy demand. By analyzing and testing its capability, this method shows advantage and efficiency in real-time simulation, especially when the system contains stiff equations. A simulation application will have more flexibility while using this method.

Finite-element simulation of semi-solid metal processing of tool steel encased in carbon steel

“…In this sense, Eidel and Kuhn 22 suggest an algorithmic framework that overcomes order reduction making use of diagonally implicit Runge–Kutta methods, improving the quality of the finite-element results in finite inelasticity, with applications to viscoelasticity by Eidel et al 23 and Stumpf. 24 More recently, Lei et al 25 propose an implicit numerical method also applied to stiff problems (such as in the case of Elasticity) for real-time simulations.…”