Construction of Direct and Iterative Decomposition Methods

In order to solve the boundary value problems by the method of decomposing the computation region $G$ into subregions without overlapping and with the Dirichlet–Dirichlet type conditions, the Poincaré–Steklov operator equation on the junction boundary $\gamma$ of the subregions, which involves the difference of the normal derivatives of the solutions on the opposite sides of $\gamma$, is approximated by using the discrete Green's functions. Basing on this, we construct some direct and iterative decomposition methods which are parallel in nature. Sample computations show the precision and convergence of the proposed algorithms.