We investigate additive Schwarz methods for semilinear elliptic problems with convex
energy functionals, which have wide scientific applications. A key observation is that the …

We consider additive Schwarz methods for boundary value problems involving the-
Laplacian. While existing theoretical estimates suggest a sublinear convergence rate for …

Fourth-order variational inequalities are encountered in various scientific and engineering
disciplines, including elliptic optimal control problems and plate obstacle problems. In this …

This paper presents the domain decomposition methods (DDMs) for achieving fast parallel
computing on multi-core computers when dealing with the multi-phase labeling problem. To …

We present new convergence analyses for subspace correction methods for semicoercive
and nearly semicoercive convex optimization problems, generalizing the theory of singular …

We consider additive Schwarz methods for boundary value problems involving the $ p $-
Laplacian. Although the existing theoretical estimates indicate a sublinear convergence rate …

We consider a convex constrained optimization problem composed in part of finding fixed
points of nonexpansive mappings and in part of solving a minimization problem. Two …

In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace
Correction Method (NPSC) for the finite neuron method that approximates numerical …

In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace
Correction Method (NPSC) for training ReLU neural networks for numerical solution of …