Konrad-zuse-zentrum Für Informationstechnik Berlin Dynamic Sparsing in Stii Extrapolation Methods Dynamic Sparsing in Stii Extrapolation Methods

Based on a simple stability analysis for the semi{implicit Euler discretization a new dynamic sparsing procedure is derived. This procedure automatically eliminates \small" elements of the Jacobian matrix. As a consequence, the amount of work needed to handle the linear algebra within a semi{implicit extrapolation integrator can be reduced drastically. Within the course of integration the sparsing criterion, which decides what \small" means, is dynamically adapted to ensure stability of the discretization scheme. Thus, stepsize restrictions due to instability can be avoided. Numerical experiments for quite diierent problems show robustness and eeciency of this dynamic sparsing technique. The techniques developed here in the context of stii extrapolation integrators can, in principle, be applied to W{methods, where exact Jacobians may be replaced by \suuciently good" approximations.