Accelerating Dynamic Iteration Methods with Application to Semiconductor Device Simulation

In this paper, we apply a Galerkin method to solving the system of second-kind Volterra integral equations which characterize the classical dynamic iteration methods for the linear time-varying initial value problem. It is shown that the Galerkin approximations can be computed iteratively using conjugate-direction algorithms. The resulting iterative methods are combined with an operator Newton method and applied to solving the differential-algebraic system generated by spatial discretization of the time-dependent semiconductor device equations. Experimental results are included which demonstrate the conjugate-direction methods are significantly faster than classical dynamic iteration methods.

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