Domain decomposition algorithm based on the group explicit formula for the heat equation

Abstract

A finite difference domain decomposition algorithm (DDA) for solving the heat equation in parallel is presented. In this procedure, interface values between subdomains are calculated by the group explicit formula, whereas interior values of subdomains are determined by the classical implicit scheme. The stability and convergence for this DDA are proved. The stability bound of the procedure is derived to be eight times that of the classical explicit scheme. Though the truncation error at the interface is O(τ + h), L ²-error is proved to be O(τ + h ²). Numerical examples confirm the second-order convergence and indicate that the stability condition is sharp. A comparison of the numerical errors of this procedure with other known methods is also included.

Keywords:

• Finite difference method
• Domain decomposition
• Heat equations
• Parallel computing

Acknowledgements

The project is supported by the Special Funds for Major State Basic Research Projects G1999032801, the National Natural Science Foundation of China (No. 19932010), the Foundation of CAEP and the special foundation of Nankai University.