Samet Kadioglu
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MATHEMATICS COLLOQUIUM
Speaker: Samet Kadioglu Abstract. We introduce a fully second order self-consistent Implicit/Explicit (IMEX) method for solving multi-physics and fluid problems that exhibit multiple time scales. The algorithm is a combination of an explicit block for the non-stiff and an implicit block for the stiff part of the problem. The explicit part is always solved inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-Free Newton Krylov (JFNK) method. In this way, there is a continuous interaction between the two algorithm blocks in that the improved solutions (in terms of time accuracy) at each nonlinear iteration are immediately felt by the explicit block and the improved explicit solutions are readily available to form the next set of nonlinear residuals. This continuous interaction results in an implicitly balanced algorithm in that all the nonlinearities due to coupling of different time terms are converged. In other words, we obtain a self-consistent IMEX method that eliminates the order reduction in time accuracy that a classical IMEX method would suffer from. We note that a classical IMEX method splits the operators such that the implicit and explicit blocks are executed independent of each other leading non-converged nonlinearities therefore time inaccuracies. We provide a mathematical analysis that examine/compare the time behavior of our self-consistent IMEX method versus the classic IMEX method. We also provide computational results coming from variety of applications. |