New techniques for designing a finite difference domain decomposition algorithm for the two- and three-dimensional heat equations

Abstract

New techniques are presented for designing a finite difference domain decomposition algorithm for the two- and three-dimensional heat equations. The basic procedure is to define the finite difference schemes at the interface grid points with a smaller time step and a larger mesh spacing h¯. The stability region of the algorithm is expanded Jd ² times compared with the classical explicit scheme, and a better error bound of the numerical solutions is obtained when r¯=1/6. Numerical experiments are also presented.

Keywords:

• Compute
• Finite element
• Finite difference
• Domain decomposition
• Algorithm

Acknowledgements

The author gives sincere thanks to Professor Hongxing Rui and the referees for their useful advice. Supported by the National Natural Science Foundation of China (10471079) and the Research Fund of the Doctoral Program of High Education of the State Education Ministry of China (20020422019).