A New Iterative Chebyshev Spectral Method for Solving the Elliptic Equation ∇ • (σ∇u) ≈ ƒ

✍ Scribed by Shengkai Zhao; Matthew J. Yedlin

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 323 KB
• Volume: 113
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1994.1131

✦ Synopsis

We present a new iterative Chebyshev spectral method for solving the elliptic equation (\nabla \cdot(\sigma \nabla u)=f). We rewrite the equation in the form of a Poisson's equation (\nabla^{2} u=(f-\nabla u \cdot \nabla \sigma) / \sigma). In each iteration we compute the right-hand side terms from the guess values first. Then we solve the resultant Poisson equation by a direct method to obtain the updated values. Three numerical examples are presented. For the same number of iterations, the accuracy of the present method is about 6-8 orders better than the Chebyshev spectral multigrid method. On a SPARC Station 2 computer, the CPU time of the new method is about one-third of the Chebyshev spectral multigrid method. To obtain the same accuracy, the CPU time of the present method is about one-tenth of the Chebyshev spectral muitigrid method. (C) 1994 Academic Press, Inc.