Relaxation techniques for the simulation of VLSI circuits
Relaxation techniques for the simulation of VLSI circuits
Simulation of dynamic systems using multirate integration techniques
Transactions of the Society for Computer Simulation International
Stability properties of backward differentiation multirate formulas
Applied Numerical Mathematics - Recent Theoretical Results in Numerical Ordinary Differential Equations
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
PLATO: a new piecewise linear simulation tool
EURO-DAC '90 Proceedings of the conference on European design automation
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Multirate integration is a technique in which a set of differential equations is solved with different timesteps assigned to subsets of equations [4][10]. In circuit simulation this is commonly used in the waveform relaxation method, where different subcircuits are analyzed independently from the others. An important and obvious advantage is the simulation efficiency: subcircuits which are temporarily changing relatively slowly, can be analyzed with large stepsizes, independent of the activity in other subcircuits. In this paper an approach is presented to fit multirate integration in a direct simulation scheme, thus bringing comparable advantages without the relaxation process and its related problems. An event driven scheme is proposed for the circuit simulation problem, with individual timesteps for every component in the circuit.Only with the new combination of a highly efficient update scheme for the L/U decomposition, and some event clustering method, leads the multirate scheme to the expected speedup of the simulation process.