Variational integrators for electric circuits

JOURNAL OF COMPUTATIONAL PHYSICS

卷:242

Article

Ober-Bloebaum, Sina¹  Tao, Molei²  Cheng, Mulin³  Owhadi, Houman³  Marsden, Jerrold E.³ 

[1] Univ Paderborn, Paderborn, Germany

[2] NYU, Courant Inst Math Sci, New York, NY 10003 USA

[3] CALTECH, Pasadena, CA 91125 USA

关键词: Structure-preserving integration;    Variational integrators;    Degenerate systems;    Electric circuits;    Noisy systems;    Multiscale integration;   

DOI  :  10.1016/j.jcp.2013.02.006

来源: Elsevier

【 摘 要 】

In this contribution, we develop a variational integrator for the simulation of (stochastic and multiscale) electric circuits. When considering the dynamics of an electric circuit, one is faced with three special situations: 1. The system involves external (control) forcing through external (controlled) voltage sources and resistors. 2. The system is constrained via the Kirchhoff current (KCL) and voltage laws (KVL). 3. The Lagrangian is degenerate. Based on a geometric setting, an appropriate variational formulation is presented to model the circuit from which the equations of motion are derived. A time-discrete variational formulation provides an iteration scheme for the simulation of the electric circuit. Dependent on the discretization, the intrinsic degeneracy of the system can be canceled for the discrete variational scheme. In this way, a variational integrator is constructed that gains several advantages compared to standard integration tools for circuits; in particular, a comparison to BDF methods (which are usually the method of choice for the simulation of electric circuits) shows that even for simple LCR circuits, a better energy behavior and frequency spectrum preservation can be observed using the developed variational integrator. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free