2008 Volume 2 Issue 1 Pages 150-161
The balancing domain decomposition (BDD) method is a well-known preconditioner due to its excellent convergence rate. The BDD method includes the Neumann-Neumann preconditioner and a coarse grid correction. Several studies have considered applications of the BDD method to various phenomena and improvement of its convergence rate. However, in applying the BDD method to large-scale problems, it is difficult to solve the coarse problem of a coarse grid correction since the size of the coarse problem increases in proportion to the number of subdomains (i.e., the size of the original problem). Other preconditioners with a coarse grid correction have the same problem. To overcome this problem, use of a new preconditioner, namely, incomplete balancing domain decomposition with a diagonal-scaling (IBDD-DIAG) method is proposed in this study. The method is based on the BDD method, and constructed by an incomplete balancing preconditioner and a simplified diagonal-scaling preconditioner. Moreover, it is parallelized by the hierarchical domain decomposition method. To evaluate this new approach, some computational examples of large-scale problems are demonstrated.
