KIOPS: A fast adaptive Krylov subspace solver for exponential integrators
KIOPS: A fast adaptive Krylov subspace solver for exponential integrators
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DOI：
10.1016/j.jcp.2018.06.026
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
S. Gaudreault;Greg Rainwater;M. Tokman
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文献类型：
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作者：
S. Gaudreault;Greg Rainwater;M. Tokman
本文提出了一种计算指数积分器中φ函数线性组合的新算法KIOPS。该算法适用于计算物理中的大规模问题，其中关于雅可比矩阵的谱或范数的信息很少或根本不知道。我们首先表明，这样的问题可以有效地解决通过计算一个单一的指数的修改矩阵。然后，我们的方法是计算一个适当的基的Krylov子空间使用不完全正交化过程和项目的矩阵指数在这个子空间。我们还提出了一种新的自适应过程，显着降低了计算复杂性的指数积分。我们的数值实验表明，KIOPS优于当前国家的最先进的自适应Krylov算法。
This paper presents a new algorithm KIOPS for computing linear combinations ofφ-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 knowna 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 algorithmphipm.