Long-Time-Step Methods for Oscillatory Differential Equations
SIAM Journal on Scientific Computing
Interconnection of port-Hamiltonian systems and composition of Dirac structures
Automatica (Journal of IFAC)
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
Journal of Computational Physics
Mollified Impulse Methods for Highly Oscillatory Differential Equations
SIAM Journal on Numerical Analysis
Multilevel Monte Carlo Path Simulation
Operations Research
Long-Run Accuracy of Variational Integrators in the Stochastic Context
SIAM Journal on Numerical Analysis
A Multiscale Method for Highly Oscillatory Dynamical Systems Using a Poincaré Map Type Technique
Journal of Scientific Computing
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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.