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A PARALLEL-IN-TIME ALGORITHM FOR HIGH-ORDER BDF METHODS FOR DIFFUSION AND SUBDIFFUSION EQUATIONS
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DOI：10.1137/20M1355690.png)
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摘要
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In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the k-step backward differentiation formula and then develop an iterative solver by using the waveform relaxation technique. Each resulting iteration rep-resents a periodic-like system, which could be further solved in parallel by using the diagonalization technique. The convergence of the waveform relaxation iteration is theoretically examined by using the generating function method. The argument could be further applied to the time-fractional sub -diffusion equation, whose discretization shares common properties of the standard BDF methods due to the nonlocality of the fractional differential operator. Illustrative numerical results are presented to complement the theoretical analysis.
Keyword:
parabolic equation
subdiffusion equation
backward differentiation formula
parallel-in-time algorithm
convergence analysis
convolution quadrature
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2.6
论文数:
5.1K
被引数:
1.8W
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