JOURNAL OF COMPUTATIONAL PHYSICS | 卷:372 |
KIOPS: A fast adaptive Krylov subspace solver for exponential integrators | |
Article | |
Gaudreault, Stephane1  Rainwater, Greg2  Tokman, Mayya2  | |
[1] Environm & Changement Climat Canada, Rech Previs Numer Atmospher, 2121 Route Transcanadienne, Dorval, PQ H9P 1J3, Canada | |
[2] Univ Calif, Sch Nat Sci, 5200 N Lake Rd, Merced, CA 95343 USA | |
关键词: Adaptive Krylov subspace methods; Incomplete orthogonalization; Time integration; Exponential integrators; phi-functions; Matrix exponential; | |
DOI : 10.1016/j.jcp.2018.06.026 | |
来源: Elsevier | |
【 摘 要 】
This paper presents a new algorithm KIOPS for computing linear combinations of phi-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no information about the spectrum or norm of the Jacobian matrix is known a priori. We first show that such problems can be solved efficiently by computing a single exponential of a modified matrix. Then our approach is to compute an appropriate basis for the Krylov subspace using the incomplete orthogonalization procedure and project the matrix exponential on this subspace. We also present a novel adaptive procedure that significantly reduces the computational complexity of exponential integrators. Our numerical experiments demonstrate that KIOPS outperforms the current state-of-the-art adaptive Krylov algorithm phipm. Crown Copyright (C) 2018 Published by Elsevier Inc.
【 授权许可】
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【 预 览 】
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