Multiscale Domain decomposition: Algorithms and Analysis.

A research project funded by the Research Council of Norway, University of Bergen and Bergen University College.

Project Period: June 2010 to July 2014.

Project Objectives: The primary objective of this project is to investigate new Multiscale algorithms based on the framework of domain decomposition.

1. Multiscale in the framework of Domain Decomposition: Understand Multiscale methods in the framework of Domain Decomposition methods, derive and analyze effective methods exploiting the features of Multiscale methods and involving the computational power of the Domain Decomposition iteration.

2. Multiscale Domain Decomposition with less regular subdomains: In the first part, we assume that the coarse cells, consequently the subdomains, are typically the union of few coarse triangle or rectangles in the 2D, which is not realistic. In this part of the project, we will consider subdomains which are less regular.

The proposed project aims at understanding the existing Multiscale methods, developing new algorithms and their theoretical analysis based on the theory of Domain Decomposition methods.