In most domain decomposition (DD) methods, a coarse grid solve is employed to provide the global coupling required to produce an optimal method. The total cost of a method can depend sensitively on the choice of the c...In most domain decomposition (DD) methods, a coarse grid solve is employed to provide the global coupling required to produce an optimal method. The total cost of a method can depend sensitively on the choice of the coaxse grid size H. In this paper, we give a simple analysis of this phenomenon for a model elliptic problem and a variant of Smith's vertex space domain decomposition method [11, 3]. We derive the optimal value Hopt which asymptotically minimises the total cost of method (number of floating point operations in the sequential case and execution time in the parallel case), for subdomain solvers with different complekities. Using the value of Hopt, we derive the overall complexity of the DD method, which can be significantly lower than that of the subdomain solver展开更多
文摘In most domain decomposition (DD) methods, a coarse grid solve is employed to provide the global coupling required to produce an optimal method. The total cost of a method can depend sensitively on the choice of the coaxse grid size H. In this paper, we give a simple analysis of this phenomenon for a model elliptic problem and a variant of Smith's vertex space domain decomposition method [11, 3]. We derive the optimal value Hopt which asymptotically minimises the total cost of method (number of floating point operations in the sequential case and execution time in the parallel case), for subdomain solvers with different complekities. Using the value of Hopt, we derive the overall complexity of the DD method, which can be significantly lower than that of the subdomain solver
