A new iterative Chebyshev spectral method for solving the elliptic equation [del] [center dot] ([sigma] [del]u) = f

Journal Article · Mon Aug 01 04:00:00 EDT 1994 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1006/jcph.1994.1131· OSTI ID:7048647

Zhao, Shengkai; Yedlin, M J ^[1]

---

1. Univ. of British Columbia, Vancouver (Canada)

We present a new iterative Chebyshev spectral method for solving the elliptic equation [del] [center dot] ([sigma] [del]u) = f. We rewrite the equation in the form of a Poisson's equation [del][sup 2]u = (f - [del]u [center dot] [del][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 sam 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 multigrid method. 17 refs., 5 figs., 3 tabs.

• OSTI ID: 7048647
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 113:2; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
EFFICIENCY
EQUATIONS
FLUID FLOW
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
SIMULATION