论文标题
灵活的简短复发Krylov子空间方法，用于在汉密尔顿港系统和ODES/DAE与耗散汉密尔顿的时间整合中产生的矩阵
A flexible short recurrence Krylov subspace method for matrices arising in the time integration of port Hamiltonian systems and ODEs/DAEs with a dissipative Hamiltonian
论文作者
论文摘要
对于产生线性系统的几类数学模型，将基质分解为其冬宫和偏斜部位自然与基础模型的属性有关。尤其是对于散发性哈密顿odes，DAE和汉密尔顿港系统的离散化，此外，Hermitian部分是积极的或半明确的。然后，可以开发短复发的最佳Krylov子空间方法，其中Hermitian部分被用作预处理器。在本文中，我们开发了这种方法的新的，正确的预处理变体，因为它们至关重要的新功能允许在每次迭代中大约求解具有遗传学部分的系统，同时保持短期复发。这种新的方法特别有效，因为它允许例如，在每种迭代中使用多式求解器或（预处理的）CG方法的几个步骤。我们通过大规模系统的几个数值实验来说明这一点。
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for discretizations of dissipative Hamiltonian ODEs, DAEs and port Hamiltonian systems where, in addition, the Hermitian part is positive definite or semi-definite. It is then possible to develop short recurrence optimal Krylov subspace methods in which the Hermitian part is used as a preconditioner. In this paper we develop new, right preconditioned variants of this approach which as their crucial new feature allow the systems with the Hermitian part to be solved only approximately in each iteration while keeping the short recurrences. This new class of methods is particularly efficient as it allows, for example, to use few steps of a multigrid solver or a (preconditioned) CG method for the Hermitian part in each iteration. We illustrate this with several numerical experiments for large scale systems.
