Využití teorie grafů pro optimalizaci BEM

Abstract

The topic of this thesis includes two mathematical areas. The first topic is graph theory and the second topic is numerical analysis. In this thesis, we focuse on the problem with collision in parallel matrix update, while solving the Laplace equation by boundary element method. The goal of this thesis is to use graph theory tools to design an effective algorithm. This algorithm has to divide pairs of elements into disjoint sets. For each pair of elements from the disjoint set the matrix update must not collide with other pair from same set. Thanks to this distribution of pairs of elements, we can compute tasks in parralell over pairs of elements from the samedisjoint set.