STUDY OF PARALLEL ITERATIVE ALGORITHMS WITH ACCELERATE CONVERGENCE FOR SOLVING ONE-DIMENSION IMPLICIT DIFFERENCE EQUATIONS

摘要

This paper focuses on the solution to implicit difference equations, which are very difficult to compute in parallel for one-dimension diffusion equation. For improving the convergent rates and the properties of gradual-approach convergence of segment-classic-implicit-iterative (SCII) and segment-Crank-Nicolson-iterative (SCNI) algorithms realizing efficient iterative computation in parallel by segmenting grid domains, SCII and SCNI algorithms with accelerate convergence are studied and improved through inserting classic implicit schemes and Crank-Nicolson schemes into them respectively. The SCII and SCNI algorithms with accelerate convergence, which can be decomposed into smaller strictly tri-diagonally dominant subsystems, are solved by using double-sweep algorithm. In the present paper, general structures of SCII and SCNI algorithms with accelerate convergence are constructed with matrix forms. The convergent rates are estimated and properties of gradual-approach convergence about one-dimension diffusion equation are described by splitting coefficient matrix in detail. These algorithms improve the convergent rates in iteration while make the properties of gradual-approach convergence reach two rank. The efficiency of computation is greatly enhanced. Numerical computations employing SCII and SCNI algorithms with accelerate convergence are made on SGL/Challenge L with 8 CPUs as examples. Theoretical analyses and numerical exemplifications show that the parallel iterative algorithms with accelerate convergence for solving one-dimension diffusion equations are more efficient in computation and have much better convergent rates and properties of gradual-approach convergence.