The optimal 3-node preconditioner of the Fourier and Chebyshev spectral operators

✍ Scribed by G. Labrosse; A. Redondo

• Book ID: 104021005
• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 431 KB
• Volume: 230
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2010.09.016

✦ Synopsis

It is shown in [G. Labrosse, The piecewise-linear Finite Volume scheme: the best known lowest-order preconditioner for the d 2 dx 2 Chebyshev spectral operator, J. Comput. Phys. 228 (2009) 4491-4509] that the piecewise-linear Finite Volume (FV) approximation is the best preconditioner of the L½u d 2 u dx 2 ¼ f Fourier and Chebyshev solvers compared to the corresponding 3-node Finite Difference (FD) and Finite Element (FE) approximations. The present paper reports about a 3-node preconditioner which, constructed from an appropriate linear combination of these FD, FE and FV approximations, is significantly better than the FV approximation. It is shown to be optimal.