A hybrid parareal spectral deferred corrections method
نویسندگان
چکیده
منابع مشابه
A Hybrid Parareal Spectral Deferred Corrections Method
The parareal algorithm introduced in 2001 by Lions, Maday, and Turinici is an iterative method for the parallelization of the numerical solution of ODEs or discretized PDEs in the temporal direction. The temporal interval of interest is partitioned into successive domains which are assigned to separate processor units. Each iteration of the parareal algorithm consists of a high accuracy solutio...
متن کاملParareal and Spectral Deferred Corrections
A new class of iterative time parallel methods for initial value ordinary differential equations are developed. Methods based on a parallel variation of spectral deferred corrections (SDC) are compared and contrasted with the parareal method. It is shown that there is a strong similarity between the serial step in the parareal algorithm and the correction step in the SDC method. This observatio...
متن کاملSpectral Deferred Correction Method
φ(t) = F (t, φ(t)), t ∈ [a, b], φ(a) = φa. (1.1) where φa, φ(t) ∈ C n and F : R × C → C. Let {t}n=0 be equally spaced nodes in the interval [a, b] with t0 = a, tN = b. Let {t j n} M j=0 be the Legendre-Gauss-Lobatto nodes in the subinterval [tn, tn+1] with t 0 n = tn, t M n = tn+1. Denote ∆n = t j+1 n − t j n. 1.1 Forward Euler Scheme The Picard integral equation in each [tn, tn+1] associated w...
متن کاملA multi-level spectral deferred correction method
The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels...
متن کاملA Hybrid Algorithm Based on Optimal Quadratic Spline Collocation and Parareal Deferred Correction for Parabolic PDEs
This Article is brought to you for free and open access by the Computer Science at ODU Digital Commons. It has been accepted for inclusion in Computer Science Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Repository Citation Liu, Jun; Wang, Yan; and Li, Rongjian, "A Hybrid Algorithm Based on Optimal Quadr...
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ژورنال
عنوان ژورنال: Communications in Applied Mathematics and Computational Science
سال: 2010
ISSN: 2157-5452,1559-3940
DOI: 10.2140/camcos.2010.5.265