Krylov Subspace Acceleration of Waveform Relaxation
نویسندگان
چکیده
منابع مشابه
Krylov Subspace Acceleration of Waveform Relaxation
In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving time dependent problems. A new class of accelerated waveform methods, convolution Krylov subspace methods, is presented. In particular, we give convolution variants of the conjugate gradient algorithm and two convolution variants of the GMRES algorithm and analyze...
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Dynamic iteration methods for treating linear systems of diierential equations are considered. It is shown that the discretized Picard-Lindell of (waveform relaxation) iteration can be accelerated by solving the defect equations with a larger timestep, or by using a recursive procedure based on a succession of increasing timesteps. A discussion of convergence is presented, including analysis of...
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In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a ‘preconditioner’ we use nonlinear multigrid schemes such as the Full Approximation Scheme (FAS) [1]. The benefits of nonlinear multigrid used in combination with the new accelerator are illustrated by difficult nonlinear elliptic scalar problems, such as the Bratu problem, and for systems of nonlinear equations, s...
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The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation method based on block Krylov subspaces. Second, we compare this new implementation against Krylov subspace methods combined with the shift and invert technique.
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The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation (WR) method based on block Krylov subspaces. Second, we compare this new WR–Krylov implementation against Krylov subspace methods combined with the shift and invert (SAI) technique. Some analysis and numerical experiments are presented. Since the WR–Krylov and SAI–Krylov m...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2003
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142996313142