A circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems
The authors consider an iterative solution of the algebraic system which arises from discretization of a second-order elliptic Neumann problem on a bounded region \(\Omega \subset \mathbb{R}^ 2\) via a finite discretization method. The region \(\Omega\) is decomposed into two subregions. They develop a preconditioned conjugate gradient decomposition method by using a symmetric-cyclic matrix. The ideas of the method are given in the paper of \textit{B. Kiss} and \textit{G. Molnárka} [ibid. 24, No. 3, 151-165 (1992; Zbl 0762.65068)]. The full algorithm, involving the method of calculation of the matrix entries is considered. A numerical example for the Dirichlet problem is presented. The calculation was made using MATLAB for Sun Workstations.
preconditioned conjugate gradient decomposition method
scientific article; zbMATH DE number 736856
scientific article