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Preconditioning spectral element schemes for definite and indefinite problems
Author(s) -
Shapira Yair,
Israeli Moshe,
Sidi Avram,
Zrahia Uzi
Publication year - 1999
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199909)15:5<535::aid-num1>3.0.co;2-r
Subject(s) - preconditioner , mathematics , finite element method , multigrid method , positive definite matrix , finite difference , mixed finite element method , boundary value problem , partial differential equation , mathematical analysis , linear system , eigenvalues and eigenvectors , physics , quantum mechanics , thermodynamics
Spectral element schemes for the solution of elliptic boundary value problems are considered. Preconditioning methods based on finite difference and finite element schemes are implemented. Numerical experiments show that inverting the preconditioner by a single multigrid iteration is most efficient and that the finite difference preconditioner is superior to the finite element one for both definite and indefinite problems. A multigrid preconditioner is also derived from the finite difference preconditioner and is found suitable for the CGS acceleration method. It is pointed out that, for the finite difference and finite element preconditioners, CGS does not always converge to the accurate algebraic solution. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 535–543, 1999