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Center for Nonlinear Studies |
Scientific and engineering disciplines depend on efficient numerical methods to model complex physical systems. Since the underlying dynamics frequently involve a range of temporal and spatial scales, specialized methods that can handle numerical challenges such as stiffness and high dimensionality are required. I will begin this talk by providing an overview of various time integration methodologies including classical implicit and explicit integration, and additive or component partitioning. I will then present a recently developed generalization known as nonlinear partitioning. Nonlinear partitioning encompasses additive and component partitioning while also introducing additional flexibility; for example, one can treat factors within nonlinearities with differing levels of implicitness. I will provide an overview of nonlinearly partitioned Runge-Kutta (NPRK) integrators, discuss their order conditions and linear stability, and show several numerical experiments that demonstrate the efficiency of these methods. I will close the talk by discussing multirate NPRK methods that treat each argument with a different timescale and make some comments on when such methods should be considered.
Bio: Tommaso Buvoli is an Assistant Professor in the Department of Mathematics at Tulane University. His research focuses on development, analysis, and applications of novel numerical methods for solving complex, high-dimensional differential equations.
Host: Ben Southworth (T-5) and Brian Tran (T-5/CNLS)