Year: 2013
Type: preprint
Abstract: This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods (Sandu and Guenther, 2013). Multirate schemes use different step sizes for different components and for different partitions of the right-hand side based on the local activity levels. We show that the new multirate GARK family includes many well-known multirate schemes as special cases. The order conditions theory follows directly from the GARK accuracy theory. Nonlinear stability and monotonicity investigations show that these properties are inherited from the base schemes provided that additional coupling conditions hold.
Source: arXiv (Cornell University)
Authors: Guenther, Michael, Sandu, Adrian
Institutions: University of Wuppertal, Virginia Tech
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1523888516, Optimal Design of Constrained Multibody Dynamical Systems, CIF:Small: General Linear Time-stepping Methods for Large-Scale Simulations, G4503139999, G5350959906, G559745938, G6071252945, G6354276058, A Fully Discrete Framework for the Adaptive Solution of Inverse Problems, G7830320759, Collaborative Research: A Computational Framework for Assessing the Observation Impact in Air Quality Forecasting, G8072043338, G8390931773
OpenAlex ID: W2952955073