Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Xiaodi Zhang,Zhengzhou University
Inviter:	Doctor Donghang Zhang
Title:	A preconditioned Newton method for primal-dual finite element discretization of the ROF model
Language:	Chinese
Time & Venue:	2024.03.14 15:30-16:30 N224
Abstract:	In this talk, we propose a Newton-Krylov solver for primal-dual finite element discretization of the ROF model. We first discretize the primal-dual system by using mixed finite element methods, and then linearize the discrete system by Newton method. Exploiting the well-posedness of the linearized problem on appropriate Sobolev spaces equipped with proper norms, we propose block diagonal preconditioners for the corresponding system solved with the minimum residual method. The proposed preconditioners are further shown to be robust and optimal with respect to the mesh size, the penalization parameter, the regularization parameter, and the iterative step. Numerical results are given to confirm the theoretical results. This is joint work with Weiying Zheng, Xuecheng Tai and Ragnar Winther.