Matlab application

The main goal of my project is to use Matlab's parallel toolbox
to parallelize an other Matlab toolbox, IRtoolbox ( an extention of pdetoolbox).

The reason of this parallelization is the nature of the problems that solved by IRtoolbox which uses a domain decomposition method, interface relaxation method


domain decomposition

The multi-domain/multi-physics problems consist of many different
componentsthat have distinct natures, shapes and capabilities.
In order to model these systems, we must use parallel computing
strategies that treat the systems’ components as independent
components, because the existing simulation software
is only used for simple geometrical shapes.
The computation of these systems is achieved by using several
methods that have been proposed. The first and the most common
computational approach is domain decomposition. Domain
decomposition refers to geometry discretization by using
grids and meshes. The decomposition creates small discrete
and inter-connected problems. Each discrete domain has its
own equation, but the basic idea is that neighboring components
communicate and exchange details and useful information.


interface relaxation method

The domain is decomposed into sub-domains. The sub-domains
have different mathematical models and as for the interface
between two neighboring components we can use interface
conditions that are derived from the physical phenomena
(e.g. continuity of mass temperature, conservation of momentum).
The models on each sub-domain are solved in the loop of the interface
relaxation iteration method to compute the global solution.