MC 5417 and Zoom (Please contact firstname.lastname@example.org for Zoom link)
Raymond Spiteri, Professor, Director of Centre for High-Performance Computing, Department of Computer Science, University of Saskatchewan
Fractional-Step Methods: Theory and Practice
Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. The basic premise is that the right-hand side of the differential equation is split into terms that are integrated separately, often by specialized methods. Fractional-step methods arise from the practical need to solve problems that are beyond the reach of monolithic methods in terms of computational requirements such as memory or runtime. Although fractional-step methods have been well studied, there is still a lot to learn about their various aspects, in particular, how should one choose the coefficients of the splitting method, the individual sub-integrators, and the order in which they are applied--- not to mention what makes for a good split of the right-hand side in the first place. In this presentation, we offer our experience with some observations in the literature about fractional-step methods in terms of these aspects.