Prof. Dr. Jochen Schütz from the Hasselt University, Department of Mathematics and Statistics, will give a SFB 1313 seminar:
Title: "A parallel-in-time IMEX multiderivative method”
Date: Thursday, May 7, 2020
Time: 4 pm
Place: public online seminar >>> https://unistuttgart.webex.com/unistuttgart-en/j.php?MTID=m0d29c752f649f223a33c8fdd1acc889b
In this talk, we present a novel IMEX (partly IMplicit, partly EXplicit) method of predictor-corrector type for the stable and high-order approximation of singularly perturbed ODEs. Due to the predictor-corrector approach it is relatively straightforward to parallelize the method in time. Contrary to more established approaches, high order is not (only) reached by introducing additional stages or steps, but by adding more derivatives of the unknown solution which leads to very storage-efficient schemes.
Given a suitable splitting, it is shown that the method is well-defined even if the small parameter epsilon tends to zero. We also comment on asymptotic consistency properties. In particular, it is shown that the concept of well-prepared initial data has to be extended to also cope with higher-order derivatives of the limiting solution.
Finally, we conclude by showing how the method can be extended to singularly perturbed partial differential equations, e.g., the low-Mach Euler equations. We do also point to open questions concerning the development of the method. (This is joint work with David Seal, US Naval Academy, Annapolis MD, USA. See also http://www.uhasselt.be/Documents/CMAT/Preprints/2019/UP1909.pdf for a recent preprint.)