Efficient Chebyshev-Petrov-Galerkin method for solving second-order equations

Journal of Scientific Computing

Volumn 34, Issue 2, 2008, Pages 113-126

  Elbarbary, Elsayed M E ^a  

^a Ain Shams University   (Egypt)

Author keywords

Chebyshev polynomials; Direct solvers; Petrov Galerkin method; Second order elliptic equations; Sparse matrices

Indexed keywords

CHEBYSHEV POLYNOMIALS; DIRECT SOLVERS; ELLIPTIC PROBLEMS; ORTHOGONALITY PROPERTY; SPARSE MATRICES;

BOUNDARY CONDITIONS; POLYNOMIALS; PROBLEM SOLVING;

CHEBYSHEV APPROXIMATION;

EID: 38349016923     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-007-9161-9     Document Type: Article

References (12)

1. Auteri, F., Quartapelle, L.: Galerkin-Legendre spectral method for the vorticity and stream functions. J. Comput. Phys. 149, 306-332 (1999)
2. Auteri, F., Quartapelle, L.: Galerkin-Legendre spectral method for the 3D Helmholtz equation. J. Comput. Phys. 161, 454-483 (2000)
3. Auteri, F., Parolini, N., Quartapelle, L.: Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers. J. Comput. Phys. 185, 427-444 (2003)
4. Doha, E.H., Abd-Elhameed, W.: Efficient spectral-Galerkin algorithms for direct solution of second-order equations using ultraspherical polynomials. SIAM J. Sci. Comput. 24, 548-571 (2002)
5. Ghoreishi, F., Hosseini, S.M.: The tau method and a new preconditioner. J. Comput. Appl. Math. 163, 351-379 (2004)
6. Haidvogel, D.B., Zang, T.A.: The accurate solution of Poisson's equation by expansion in Chebyshev polynomials. J. Comput. Phys. 30, 167-180 (1979)
7. Hesthaven, J.S.: Integration preconditioning of pseudospectral operators. I. Basic linear operators. SIAM J. Numer. Anal. 35, 1571-1593 (1998)
8. Hesthaven, J.S., Gottlieb, S., Gottlieb, D.: Spectral Methods for Time-Dependent Problems. Cambridge University Press, Cambridge (2007)
9. Khalifa, A.K., Elbarbary, E.M.E., Abd-Elrazek, M.A.: Chebyshev expansion method for solving second and fourth order elliptic equations. App. Math. Comput. 135, 307-318 (2003)
10. Shen, J.: Efficient spectral-Galerkin method I. Direct solvers of second and fourth order equations by using Legendre polynomials. SIAM J. Sci. Comput. 15, 1489-1505 (1994)
11. Shen, J.: Efficient spectral-Galerkin method II. Direct solvers of second and fourth order equations by using Chebyshev polynomials. SIAM J. Sci. Comput. 16, 74-87 (1995)
12. Szegö, G.: Orthogonal Polynomials, 4th edn. Colloquium Publication, vol. 23. American Mathematical Society, Providence (1975)