Extreme learning machine (ELM) is a methodology for solving partial differential equations
(PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias …

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 …

To enhance solution accuracy and training efficiency in neural network approximation to
partial differential equations, partitioned neural networks can be used as a solution …

This paper presents a novel backtracking strategy for additive Schwarz methods for general
convex optimization problems as an acceleration scheme. The proposed backtracking …

Abstract Domain decomposition algorithms are widely used as fast solutions of algebraic
equations arising from the discretization of partial differential equations. The original …

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 …

We propose a novel universal construction of two-level overlapping Schwarz
preconditioners for th-order elliptic boundary value problems, where is a positive integer …

Based on an observation that additive Schwarz methods for general convex optimization
can be interpreted as gradient methods, we propose an acceleration scheme for additive …