This paper reviews the theory and application of decomposition techniques in the context of spatial inequality. It establishes some new theoretical results with potentially wide applicability, and examines empirical evidence drawn from a large number of countries.

The Neumann-Neumann algorithm is known to be an e cient domain decomposition preconditioner with unstructured subdomains for iterative solution of nite element discretizations of di cult problems with strongly discontinuous coe cients [6]. However, this algorithm su ers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorate...

In this paper we propose a semi-blind watermarking scheme using Discrete Wavelet Transform, Discrete Cosine Transform and Singular Value Decomposition for copyright protection. We used a gray scale image as a watermark to hide in another gray scale image as a cover image. The cover image is modified (Zig-Zag) and divided to number of blocks of size n x n. We find the spatial frequency of each b...

Overlapping domain decomposition methods are efficient and flexible. It is also important that such methods are inherently suitable for parallel computing. In this chapter, we will first explain the mathematical formulation and algorithmic composition of the overlapping domain decomposition methods. Afterwards, we will focus on a generic implementation framework and its applications within Diff...

The domain decomposition method embodies large potentials for a parallelization of FEM methods. In this data-parallel approach, the domain of interest is partitioned into smaller subdomains, either before the mesh generation or afterwards (mesh partitioning). The subdomains are assigned to processors that calculate the corresponding part of the approximation. The mesh decomposition and assignme...

Moving object extraction is a critical stage in a measurable 2D and 3D photogrammetric surveillance systems. In order to keep the frame rate of the live video, the chosen automatic method should be fast enough. Moreover, it is important to extract the moving objects precisely to be able to increase the accuracy of the measurements. Prior to the boundary extraction stage, the moving objects must...

In this talk we discuss the use of domain decomposition parallel iterative solvers for highly heterogeneous problems of flow in porous media, in both the deterministic and (Monte-Carlo simulated) stochastic cases. We are particularly interested in the case of highly unstructured coefficient variation where standard periodic or stochastic homogenisation theory is not applicable, and where there ...

Domain Decomposition (DD) techniques are not only the basic tools for data partitioning but also methods for constructing new parallel pde solvers. Domain Decomposition, mesh adaption and load balance seem to be in contradiction to the eecient use of massively parallel computers with serveral hundered, or even several thousand powerful, distributed memory processors. In the case of plane bounda...