Circuit Simulation — an Application for Parallel ODE Solvers?

Abstract

Parallel ODE solvers were mentioned long before parallel computers were available. But now the interest partly seems to decrease. One reason is that we cannot expect much progress from the theory. This is shown for arbitrary explicit one-step methods and implicit Runge-Kutta methods, i.e.: full implicit Runge-Kutta (IRK) methods, diagonal implicit Runge-Kutta (DIRK) methods, singly diagonal implicit Runge-Kutta (SDIRK) methods, semi-implicit Runge-Kutta (SIRK) methods and Rosenbrock-Wanner (ROW) methods.But due to communication overhead parallelism is not always economical. The construction of special parallel methods turns out to be useful only for very special applications. Circuit Simulation is one of the most interesting candidates.