A multirate ROW-scheme for index-1 network equations

Authors:
Michael Striebel;Andreas Bartel;Michael Günther
Affiliations:
Technische Universität Chemnitz, Fakultät für Mathematik, Professur Mathematik in Industrie und Technik, D-09126 Chemnitz, Germany;Bergische Universität Wuppertal, Department of Mathematics, Chair of Applied Mathematics/Numerical Analysis, D-42097 Wuppertal, Germany;Bergische Universität Wuppertal, Department of Mathematics, Chair of Applied Mathematics/Numerical Analysis, D-42097 Wuppertal, Germany
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

Multirate methods exploit latency in electrical circuits to simulate the transient behaviour more efficiently. To this end, different step-sizes are used for various subsystems. The size of these time steps reflect the different levels of activity. Following the idea of mixed multirate for ordinary differential equations, a Rosenbrock-Wanner based multirate method is developed for index-1 differential-algebraic equations (DAEs) arising in circuit simulation. To obtain order conditions for a method with two activity levels, P-series (and DA-series) are generalised and combined for an application to partitioned DAE systems. A working scheme and results for a benchmarking circuit are presented.