Dynamic Sparsing in Stiff Extrapolation Methods.
Appeared in: Impact of Comput. in Science and Engrg., 5 (1993), pp. 53-74
| SC 92-21 | Ulrich Nowak
Dynamic Sparsing in Stiff Extrapolation Methods. Appeared in: Impact of Comput. in Science and Engrg., 5 (1993), pp. 53-74 | |
Abstract: 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
different problems show robustness and efficiency of this
dynamic sparsing technique. The techniques developed here in
the context of stiff extrapolation integrators can, in
principle, be applied to W-methods, where exact Jacobians
may be replaced by ``sufficiently good approximations.
Keywords: Large scale integration, extrapolation
methods, stiff ODEs, W-methods, sparse matrix techniques.
Keywords: large scale integration,
extrapolation methods,
stiff ODEs,
W-methods,
sparse matrix techniques