Adaptive time step selection for Spectral Deferred Correction

Autor:	Baumann, Thomas, Götschel, Sebastian, Lunet, Thibaut, Ruprecht, Daniel, Speck, Robert
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Computer Science - Distributed Parallel and Cluster Computing 65Y05 G.1.0
Druh dokumentu:	Working Paper
Popis:	Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM. Comment: 29 pages including references, 10 figures. Submitted to Springer Numerical Algorithms
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.13454 Zobrazit plný text záznamu View this record from Arxiv