Variational integrators for electric circuits

Journal Article · Sat Jun 01 00:00:00 EDT 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.02.006· OSTI ID:22233579

Ober-Blöbaum, Sina ^[1]; Tao, Molei ^[2]; Cheng, Mulin ^[3]; Owhadi, Houman; Marsden, Jerrold E. ^[4]

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1. Computational Dynamics and Optimal Control, University of Paderborn (Germany)
2. Courant Institute of Mathematical Sciences, New York University (United States)
3. Applied and Computational Mathematics, California Institute of Technology (United States)
4. Control and Dynamical Systems, California Institute of Technology (United States)

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.

• OSTI ID: 22233579
• Journal Information: Journal of Computational Physics, Vol. 242; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
COMPARATIVE EVALUATIONS
CONTROL
ELECTRIC POTENTIAL
EQUATIONS OF MOTION
GAIN
LAGRANGIAN FUNCTION
RESISTORS
SIMULATION
STOCHASTIC PROCESSES
VARIATIONAL METHODS