Performance assessment of mixed methods for time integration using an assembly-type queueing model

Abstract

Many mathematical models of dynamical systems use some form of time integration method for solving the representative set of differential equations. For problems comprised of several different, interacting systems it is often more advantageous to use a mixture of integration methods for the solution process rather than a single method. Using a single integration method is often inefficient because maintaining numerical stability in the overall solution requires performing more integration steps than are necessary on some parts of the problem. However, using a mixture of integration methods alleviates this difficulty by assigning more efficient integration methods to each system or group of systems contained in the problem. The coupled solution is achieved by having these methods exchange common boundary condition data during the transient being modelled. The computation time for a problem employing a mixed-time integration method can be affected by the allocation of the different methods to available processors and the selection of time-step sizes. Finding the combination of processor allocation and time-step mix that minimizes the computation time requires quantifying these effects. This thesis proposes that data transfer among the methods in a mixed-time integration problem be viewed in the same way as product movement in an assembly system. With this analogy established, the above effects can be quantified using an assembly-type queueing model. The complex assembly process associated with these data transfers requires the development of a new model and one is proposed that employs Markov Arrival Processes and Phase-Type distributions. The capabilities of this new model are demonstrated on a sample set of exercises.