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High-order time integration for nonlinearly partitioned multiphysics

High-order time integration for nonlinearly partitioned multiphysics

Start: 
Friday, January 24, 2025 12:00 pm
End: 
Friday, January 24, 2025 12:50 pm
Location: 
STAG 111
Benjamin Southworth
LANL

In multiscale and multiphysics simulation, a predominant challenge is the accurate coupling of physics of different scales, stiffnesses, and dimensionalities. The underlying problems are usually time dependent, making the time integration scheme a fundamental component of the accuracy. Remarkably, most large-scale multiscale or multiphysics codes use a first-order operator split or (semi-)implicit integration scheme. Such approaches often yield poor accuracy, and can also have poor computational efficiency. There are technical reasons that more advanced and higher order time integration schemes have not been adopted however. One major challenge in realistic multiphysics is the nonlinear coupling of different scales or stiffnesses. Here I present a new class of nonlinearly partitioned Runge-Kutta (NPRK) methods that facilitate high-order integration of arbitrary nonlinear partitions of ODEs. Order conditions for an arbitrary number of partitions are derived via a novel edge-colored rooted-tree analysis. I then demonstrate NPRK methods on novel nonlinearly partitioned formulations of thermal radiative transfer and radiation hydrodynamics, demonstrating orders of magnitude improvement in wallclock time and accuracy compared with current standard (semi-)implicit and operator split approaches, respectively.

BIO:

Ben Southworth is a scientist at Los Alamos National Lab in the Applied Math and Plasma Physics group. He did his undergraduate degree in Mathematics at Dartmouth College and PhD in Applied Mathematics at CU Boulder, working with Professors Tom Manteuffel and Sascha Kempf. His work is broadly focused on numerical analysis and numerical methods targeting the efficient simulation of PDEs, particularly multiscale and multiphysics systems, including work on multilevel methods, preconditioners, and spatial and temporal discretizations.