5 papers
A Novel Preconditioning Framework for Solving Nonlinear PDEs based on Fenchel-Rockafellar Duality and Transformed Primal-Dual Techniques
Long Chen, Ruchi Guo, Jingrong Wei +1
A DualTPD method is proposed for solving nonlinear partial differential equations. The method is characterized by three main features. First, decoupling via Fenchel--Rockafellar du…
Variable-preconditioned transformed primal-dual method for generalized Wasserstein Gradient Flows
Jin Zeng, Dawei Zhan, Ruchi Guo +1
We propose a Variable-Preconditioned Transformed Primal-Dual (VPTPD) method for solving generalized Wasserstein gradient flows based on the structure-preserving JKO scheme. This is…
Inexact projected preconditioned gradient methods with variable metrics: a Lyapunov convergence theory (extended version)
Ruchi Guo, Jun Zou
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents p…
Virtual element methods based on boundary triangulation:fitted and unfitted meshes
Ruchi Guo
One remarkable feature of virtual element methods (VEMs) is their great flexibility and robustness when used on almost arbitrary polytopal meshes. This very feature makes it widely…
Transformed Primal-Dual Methods with Variable-Preconditioners
Long Chen, Ruchi Guo, Jingrong Wei
This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems c…