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Initial condition strategies for multiple-time partial differential equations

Coffey, Todd S.

Many highly oscillatory circuits have a wide separation of time scales between the underlying oscillation and the behavior of interest. This is particularly true of communication circuits. Multiple-time Partial Differential Equation (MPDE) methods offer substantial speed-up for these circuits by introducing a periodic artificial time variable that represents the highly oscillatory behavior. This leaves just the slowly changing behavior of interest, which can be integrated with much larger steps. One problem of particular interest is the larger initial condition that must be specified for this periodic artificial time variable. One possible solution is to formulate an optimization problem in the hopes of increasing the step sizes taken in the slow time direction. This talk will discuss one possible unconstrained optimization problem for determining this initial condition. Numerical results and comparisons to several other initial condition strategies will be presented in addition to MPDE background research and implementation issues.

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TYPE Conference YEAR 2005
OSTI

Robust, stable time-domain methods for solving MPDEs of fast/slow systems

Coffey, Todd S.; Hutchinson, Scott A.

In this paper, we explore the stability properties of time-domain numerical methods for multitime partial differential equations (MPDEs) in detail. We demonstrate that simple techniques for numerical discretization can lead easily to instability. By investigating the underlying eigenstructure of several discretization techniques along different artificial time scales, we show that not all combinations of techniques are stable. We identify choices of discretization method and step size, along fast and slow time scales, that lead to robust, stable time-domain integration methods for the MPDE. One of our results is that applying overstable methods along one time-scale can compensate for unstable discretization along others. Our novel integration schemes bring robustness to time-domain MPDE solution methods, as we demonstrate with examples.

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TYPE Conference YEAR 2005
OSTI
Results 26–33 of 33
Results 26–33 of 33