Newton-Schwarz Optimised Waveform Relaxation Krylov Accelerators for Nonlinear Reactive Transport
Newton-Schwarz Optimised Waveform Relaxation Krylov Accelerators for Nonlinear Reactive Transport
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用于非线性无功传输的牛顿-施瓦茨优化波形弛豫 Krylov 加速器
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Michel
中科院分区：
文献类型：
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作者：
Florian Haeberlein;L. Halpern;A. Michel
Krylov型方法是为了加速Schwarz型方法在线性情况下的收敛而广泛使用的。作者在文[2]中证明了在不同类型的传输条件下，他们在没有开销的情况下加速了Schwarz方法的收敛速度。在非线性背景下，著名的牛顿-克雷洛夫-施瓦茨方法(参看。[5])对于稳态问题或时变问题，采用如下策略：首先对时间相关问题进行时间上的均匀离散，然后像稳态问题那样继续进行，即用牛顿方法求解非线性问题，其中每次迭代用Krylov型方法求解线性系统，该方法由代数Schwarz方法预条件。NKS方法的主要局限性是不允许在子域中进行不同的时间离散化，因为问题从一开始就在时间上均匀离散化。
Krylov-type methods are widely used in order to accelerate the convergence of Schwarz-type methods in the linear case. Authors in [2] have shown that they accelerate without overhead cost the convergence speed of Schwarz methods for different types of transmission conditions. In the nonlinear context, the well-known class of Newton-Krylov-Schwarz methods (cf. [5]) for steady-state problems or timedependent problems uses the following strategy: time-dependent problems are discretised uniformly in time first and then one proceeds as for steady-state problems, i.e. the nonlinear problem is solved by a Newton method where the linear system at each iteration is solved by a Krylov-type method preconditioned by an algebraic Schwarz method. The major limitation is that NKS methods do not allow different time discretisations in the subdomains since the problem is discretised in time uniformly up from the beginning.