Partitioned time discretization for parallel solution of coupled ODE systems

Abstract

One decoupling method for multiphysics, multiscale, multidomain applications involves partitioning the problem via explicit time discretizations in the coupling terms. Specialized, problem-specific techniques are needed for the resulting partitioned methods to avoid time step restrictions which make long time calculations costly. This report studies unconditionally stable, uncoupled time stepping methods for a model problem sharing mathematical structure akin to the coupled atmosphereocean system. Three decoupled time stepping algorithms are introduced and their stability and consistency are rigorously examined. Numerical experiments are performed that study their stability and convergence properties.

Multiphysics simulations: challenges and opportunities.

“…Spatial discretization of multiphysics problems (2a-2b) may result in problems in which the tendency f puq has components with widely different dynamics, often classified as stiff and nonstiff (Ascher et al, 1997;Verwer and Sommeijer, 2004;Shampine et al, 2006;Hundsdorfer and Ruuth, 2007;Constantinescu and Sandu, 2010b;Connors and Miloua, 2011). This case, called additive splitting, generally corresponds to problems in which the physics components act in the same spatial domain, such as reactive transport or radiation-hydrodynamics (Giraldo et al, 2003;Estep et al, 2008a;Giraldo and Restelli, 2009;Durran and Blossey, 2012;Giraldo et al, 2010;Ruuth, 1995).…”

Recent developments in IMEX methods with time filters for systems of evolution equations

“…There is a well-known gap for IMEX methods (e.g., [10], [11], [12], [13], [14]) between necessary conditions from root condition analysis and sufficient stability conditions for systems. Root condition analysis of CNLF for the scalar test problem (2) leads to the necessary timestep condition, essentially from [4].…”

Analysis of partitioned methods for the Biot System

“…Often, after a partitioned method is formulated, the intermediate variable can be eliminated and the method stated in an equivalent form in the variables . Among the methods, we explore are ones adapted from the Stokes–Darcy coupled system to the Biot system, and include backward Euler‐forward Euler (BEFE) , see also for other applications, Backward Euler—Leap Frog (BELF) , Crank–Nicolson Leap‐Frog (CNLF) , and ω ‐method .…”