Numerical Analysis of a Parallel Domain Decomposition Method for Linear Acoustic Problems on a Caveman Network

In this work, transport on a network and the advantages of using a parallel architecture for computations for three distinct network configurations are explored. The aim is to exploit mathematical methods coupled with modern computing techniques to arrive at an efficient and effective solution. Results obtained on serial and parallel architectures are presented and compared on the configurations. The three dimensional transport problem is modeled as a two dimensional network problem to reduce dimensionality, a common practice when dealing with complicated systems. This system is represented on a given domain as a graph. The domain decomposition method is implemented for the linear acoustic problem on three network configurations. The convergence of this method is examined in order to determine an a priori estimate for the total number of iterations to convergence. The numerical solution of the multidimensional problem is justified by algebraic conditions that model the multi-dimensional effects at the network junctions. The results demonstrate an approximate bound on the number of iterations for a given network and provide insight into the advantages of parallel processing on networks of a certain size.