Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 417, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2020.109576
Keywords
Volterra partial integro-differential problems; Singular kernel; Parallel-in-time (PinT) algorithms; Diagonalization technique; Convolution quadratures; Convergence analysis
Funding
- NSFC [11801463, 11771313]
- Fundamental Research Funds for the Central Universities [JBK1902028]
- Applied Basic Research Project of Sichuan Province [2020YJ0007]
- NSF of Sichuan Province [2018JY0469]
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Volterra partial integro-differential problems with weakly singular kernel attract a lot of attentions in recent years, thanks to the numerous real world applications. Solving this kind of PDEs in a parallel-in-time (PinT) pattern is difficult, because of the nonlocal property of time evolution. In this paper, we consider a class of representative problems and propose a novel iterative algorithm for PinT computation. In each iteration, we can solve the PDEs for all the discrete time points simultaneously via the diagonalizationtechnique proposed recently. Convergence of the algorithm is analyzed by looking insight into the decreasing property of the convolution quadrature weights. We show that the convergence rate of the proposed algorithm is robust with respect to the discretization and problem parameters. Numerical results are reported to support our findings. (c) 2020 Elsevier Inc. All rights reserved.
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