On the Integration of Stiff Nonlinear Problems
14:30 - 15:00
We discuss a new integration algorithm for the accurate and efficient solution of stiff non-linear problems governed by the second-order ordinary differential equations, like the simulation of deformable bodies, textiles, and fibers. Traditional methods have the shortcoming that their performances are highly dependent on the numerical stiffness.
Advanced state-of-the-art methods in visual computing (like Gautschi-type exponential integrators) are most efficient, if the nonlinearity is moderately stiff. To overcome these limitations, we discuss a new integration method which is based on an exponential treatment of the full nonlinear forcing operator as opposed to more standard Gautschi-type exponential integrators, and the utilization of the concept of stiff accuracy. This results in significant increases of accuracy and efficiency, and allows for more complex and realistic models to be explored without compromising efficiency.