Article ID Journal Published Year Pages File Type
521126 Journal of Computational Physics 2011 12 Pages PDF
Abstract

It is shown in [G. Labrosse, The piecewise-linear Finite Volume scheme: the best known lowest-order preconditioner for the d2dx2 Chebyshev spectral operator, J. Comput. Phys. 228 (2009) 4491–4509] that the piecewise-linear Finite Volume (FV) approximation is the best preconditioner of the L[u]≡d2udx2=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.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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