A new approach to constructing efficient stiffly accurate EPIRK methods
A new approach to constructing efficient stiffly accurate EPIRK methods
复制标题
构建高效、严格精确的 EPIRK 方法的新方法
DOI：
10.1016/j.jcp.2016.07.026
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Tokman
中科院分区：
文献类型：
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作者：
Greg Rainwater;M. Tokman
龙格-库塔型（EPIRK）的指数传播迭代方法的结构灵活性，使特别有效的指数时间积分器的建设。虽然EPIRK方法已被证明在刚性问题上表现良好，但到目前为止提出的所有方案都是使用经典阶条件导出的。本文将指数Rosenbrock方法的刚性阶条件和收敛性理论推广到EPIRK积分器。我们推导出刚性顺序条件的EPIRK方法，并开发算法来解决这些问题，以获得具体的计划。此外，我们提出了一种新的方法来构建特别有效的EPIRK积分器，优化工作的自适应Krylov算法。我们使用一组数值例子来说明新构造的EPIRK方法提供的计算优势相比，以前提出的指数积分。
The structural flexibility of the exponential propagation iterative methods of Runge–Kutta type (EPIRK) enables construction of particularly efficient exponential time integrators. While the EPIRK methods have been shown to perform well on stiff problems, all of the schemes proposed up to now have been derived using classical order conditions. In this paper we extend the stiff order conditions and the convergence theory developed for the exponential Rosenbrock methods to the EPIRK integrators. We derive stiff order conditions for the EPIRK methods and develop algorithms to solve them to obtain specific schemes. Moreover, we propose a new approach to constructing particularly efficient EPIRK integrators that are optimized to work with an adaptive Krylov algorithm. We use a set of numerical examples to illustrate the computational advantages that the newly constructed EPIRK methods offer compared to previously proposed exponential integrators.