期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 372, 期 -, 页码 236-255出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.06.026
关键词
Adaptive Krylov subspace methods; Incomplete orthogonalization; Time integration; Exponential integrators; phi-functions; Matrix exponential
资金
- National Science Foundation, Computational Mathematics Program [1115978]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1115978] Funding Source: National Science Foundation
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.
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