Chang-Ock Lee

Abstract We solve elliptic interface problems using a discontinuous Galerkin (DG) method, for which discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. Standard ways to solve interface problems with finite element methods consist in enforcing the prescribed discontinuity of the solution in the finite element space. Here, we show that the DG method provides a natural framework to enforce both discontinuities weakly in the DG formulation,

We propose nonoverlapping domain decomposition methods for solving the total variation minimization problem. We decompose the domain of the dual problem into nonoverlapping rectangular subdomains, where local total variation problems are solved. We convert the local dual problems into the equivalent primal forms which reproduce the original problem at smaller dimensions. Sequential and parallel algorithms are presented. The convergence of both algorithms is analyzed and numerical results are pre

We consider nonoverlapping domain decomposition methods for the Rudin--Osher--Fatemi (ROF) model, which is one of the standard models in mathematical image processing. The image domain is partitioned into rectangular subdomains, and local problems in subdomains are solved in parallel. Local problems can adopt existing state-of-the-art solvers for the ROF model. We show that the nonoverlapping relaxed block Jacobi method for a dual formulation of the ROF model has the $O(1/n)$ convergence rate of

Abstract We propose a novel dual‐primal finite element tearing and interconnecting method for nonlinear variational inequalities. The proposed method is based on a particular Fenchel–Rockafellar dual formulation of the target problem, which yields linear local problems despite the nonlinearity of the target problem. Since local problems are linear, each iteration of the proposed method can be done very efficiently compared with usual nonlinear domain decomposition methods. We prove that the prop

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality visualizing static conductivity images of electrically conducting subjects. Recently, MREIT has rapidly progressed in its theory, algorithm, and experiment technique and now reached to the stage of in vivo animal experiments. In this paper, we present a software, named CoReHA 2.0 standing for the second version of conductivity reconstructor using harmonic algorithms, to facilitate in vivo MREIT reconstru

A dual iterative substructuring method with a penalty term was introduced in the previous works by the authors [1,2], which is a variant of the dual-primal finite element tearing and interconnecting method in terms of the way to deal with the continuity on the interface. In this talk, we will discuss a further study for the dual iterative substructuring method with a penalty term in terms of its convergence analysis and practical efficiency.