Improved convergence of the Arrow–Hurwicz iteration for the Navier–Stokes equation via grad–div stabilization and Anderson acceleration
Improved convergence of the Arrow–Hurwicz iteration for the Navier–Stokes equation via grad–div stabilization and Anderson acceleration
复制标题
通过梯度稳定和安德森加速改进了纳维斯托克斯方程的 Arrow–Hurwicz 迭代的收敛性
DOI：
10.1016/j.cam.2022.114920
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发表时间：
2023
影响因子：
2.4
通讯作者：
Zytoon, Ahmed
中科院分区：
文献类型：
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作者：
Geredeli, Pelin G.;Rebholz, Leo G.;Vargun, Duygu;Zytoon, Ahmed
为了加速算法，我们考虑了求解不可压定常N-S方程的Arrow-Hurwicz(AH)迭代法的两种修正：梯度-div稳定化和Anderson加速。AH是一般鞍点线性方程组的经典迭代法，后来在S等人的70年代推广到N-S迭代法，最近又被重新研究。我们将最近发展的梯度-div稳定化和无散度有限元方法的思想以及不动点迭代的Anderson加速应用到AH中，以改善其收敛。分析和数值结果表明，这些方法都改善了AH收敛，但它们的结合产生了一种与更常用的求解器相竞争的高效方法。
We consider two modifications of the Arrow–Hurwicz (AH) iteration for solving the incompressible steady Navier–Stokes equations for the purpose of accelerating the algorithm: grad–div stabilization, and Anderson acceleration. AH is a classical iteration for general saddle point linear systems and it was later extended to Navier–Stokes iterations in the 1970’s which has recently come under study again. We apply recently developed ideas for grad–div stabilization and divergence-free finite element methods along with Anderson acceleration of fixed point iterations to AH in order to improve its convergence. Analytical and numerical results show that each of these methods improves AH convergence, but the combination of them yields an efficient and effective method that is competitive with more commonly used solvers.