Abstract: We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.
Abstract: In this paper developed and realized absolutely new
algorithm for solving three-dimensional Poisson equation. This
equation used in research of turbulent mixing, computational fluid
dynamics, atmospheric front, and ocean flows and so on. Moreover in
the view of rising productivity of difficult calculation there was
applied the most up-to-date and the most effective parallel
programming technology - MPI in combination with OpenMP
direction, that allows to realize problems with very large data
content. Resulted products can be used in solving of important
applications and fundamental problems in mathematics and physics.
Abstract: In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.