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Dynamic Sparsing in Stiff Extrapolation Methods.

Please always quote using this URN: urn:nbn:de:0297-zib-911
  • 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. {\bf Keywords:} Large scale integration, extrapolation methods, stiff ODEs, W--methods, sparse matrix techniques.

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Metadaten
Author:Ulrich Nowak
Document Type:ZIB-Report
Tag:W-methods; extrapolation methods; large scale integration; sparse matrix techniques; stiff ODEs
Date of first Publication:1992/10/09
Series (Serial Number):ZIB-Report (SC-92-21)
ZIB-Reportnumber:SC-92-21
Published in:Appeared in: Impact of Comput. in Science and Engrg., 5 (1993), pp. 53-74
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