Newton-Krylov solvers for time-steppers
Newton-Krylov solvers for time-steppers
复制标题
时间步进器的牛顿-克雷洛夫求解器
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
L. Qiao
中科院分区：
文献类型：
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作者：
C. Kelley;I. Kevrekidis;L. Qiao
摘要：我们研究如何牛顿GMRES迭代可以使动态模拟器（时间步进器）执行固定点和路径跟踪计算。对于一类耗散问题，其动力学的特点是一个缓慢的流形，雅可比矩阵在这样的计算是紧凑的扰动的身份。我们研究的GMRES迭代次数为每个非线性迭代所需的慢子空间和时间步进报告地平线的尺寸的函数。在路径跟踪计算中，只需要少量（一个或两个）额外的GMRES迭代。
Abstract : We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations. For a class of dissipative problems, whose dynamics are characterized by a slow manifold, the Jacobian matrices in such computations are compact perturbations of the identity. We examine the number of GMRES iterations required for each nonlinear iteration as a function of the dimension of the slow subspace and the time-stepper reporting horizon. In a path-following computation, only a small number (one or two) of additional GMRES iterations is required.