Parallel One-Shot Lagrange--Newton--Krylov--Schwarz Algorithms for Shape Optimization of Steady Incompressible Flows

Rongliang Chen Xiao-Chuan Cai

Numerical Analysis and Scientific Computing mathscidoc:1910.43850

SIAM Journal on Scientific Computing, 34, (5), 584-605, 2012.9
We propose and study a new parallel one-shot Lagrange--Newton--Krylov--Schwarz (LNKSz) algorithm for shape optimization problems constrained by steady incompressible Navier--Stokes equations discretized by finite element methods on unstructured moving meshes. Most existing algorithms for shape optimization problems iteratively solve the three components of the optimality system: the state equations for the constraints, the adjoint equations for the Lagrange multipliers, and the design equations for the shape parameters. Such approaches are relatively easy to implement, but generally are not easy to converge as they are basically nonlinear Gauss--Seidel algorithms with three large blocks. In this paper, we introduce a fully coupled, or the so-called one-shot, approach which solves the three components simultaneously. First, we introduce a moving mesh finite element method for the shape optimization
No keywords uploaded!
[ Download ] [ 2019-10-20 22:23:08 uploaded by RongliangChen ] [ 739 downloads ] [ 0 comments ]
@inproceedings{rongliang2012parallel,
  title={Parallel One-Shot Lagrange--Newton--Krylov--Schwarz Algorithms for Shape Optimization of Steady Incompressible Flows},
  author={Rongliang Chen, and Xiao-Chuan Cai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020222308901238379},
  booktitle={SIAM Journal on Scientific Computing},
  volume={34},
  number={5},
  pages={584-605},
  year={2012},
}
Rongliang Chen, and Xiao-Chuan Cai. Parallel One-Shot Lagrange--Newton--Krylov--Schwarz Algorithms for Shape Optimization of Steady Incompressible Flows. 2012. Vol. 34. In SIAM Journal on Scientific Computing. pp.584-605. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020222308901238379.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved