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Preconditioning spectral element schemes for definite and indefinite problems

✍ Scribed by Yair Shapira; Moshe Israeli; Avram Sidi; Uzi Zrahia

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
65 KB
Volume
15
Category
Article
ISSN
0749-159X

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✦ Synopsis

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.

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