In this paper using the eigenvalues and eigenvectors symmetric block diagonal matrices with infinite dimension and numerical method of finite difference a closed form solution for exact solving of Laplace equation is presented. Moreover, the method of this paper has applications in different states of boundary conditions like Newman, Dirichlet and other mixed boundary conditions. Moreover, with the method of this paper, a mathematical model for the exact solution of the Poisson equation is derived. Since these equations have many applications in engineering problems, in each part examples like water seepage problem through the soil and torsion of prismatic bars are presented. Finally the method is provided for torsion problem of prismatic bars with non-circular and non-rectangular cross sections by using of conformal mapping.

This study proposes an efficient method for allocating the blood centers to hospitals based on the concept of graph partitioning (p-median methodology) and meta- heuristic optimization algorithms. For this purpose a weighted graph is first constructed for the network denoted by G0. A coarsening process is then performed to match the edges in n stages. Following the coarsening phase, the enhanced colliding bodies (ECBO) algorithm is applied to decompose the graph into a number of sub domains by use of p-median methodology. In our problem p is the number of blood centers which hospitals are intended to allocate. The results indicate that the proposed algorithm performs quite satisfactory from computational time and optimum points of view.