Variational Settings and Domain Decomposition Based Solution Schemes for a Coupled Deformation‐Diffusion Problem

A Benders\' Decomposition Based Solution Method for Solving User Equilibrium Problem: Deterministic and Stochastic Cases

The traffic assignment problem is one of the most important problems for analyzing and optimizing the transportation network to find optimal flows. This study presented a new formulation based on a generalized Benders' decomposition approach to solve its important part, i.e. user equilibrium problems, in deterministic and stochastic cases. The new approach decomposed the problem into a master p...

Variational domain decomposition for parallel image processing

Domain Decomposition Methods for Variational Inequalities

Variational inequalities have found many applications in applied science. A partial list includes obstacles problems, fluid flow in porous media, management science, traffic network, and financial equilibrium problems. However, solving variational inequalities remain a challenging task as they are often subject to some set of complex constraints, for example the obstacle problem. Domain decompo...

Domain decomposition schemes for the Stokes equation

Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value problems for the Stokes system of equations in the primitive variables pressure-velocity. Unconditionally stable schemes of domain decomposition are based on the ...

Domain Decomposition Methods for a Complementarity Problem∗

We introduce a family of parallel Newton-Krylov-Schwarz methods for solving complementarity problems. The methods are based on a smoothed grid sequencing method, a semismooth inexact Newton method, and a twogrid restricted overlapping Schwarz preconditioner. We show numerically that such an approach is highly scalable in the sense that the number of Newton iterations and the number of linear it...