Chebyshev pseudospectral solution of the Stokes equations using finite element preconditioning
Journal of Computational Physics
Applied Numerical Mathematics - Spectral multi-domain methods
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Journal of Computational Physics
Fourier analysis of finite element preconditioned collocation schemes
SIAM Journal on Scientific and Statistical Computing
Preconditioning Chebyshev Spectral Collocation Method for Elliptic Partial Differential Equations
SIAM Journal on Numerical Analysis
Preconditioning Chebyshev Spectral Collocation by Finite-Difference Operators
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Stokes eigenmodes in square domain and the stream function-vorticity correlation
Journal of Computational Physics
The optimal 3-node preconditioner of the d2dx2 Fourier and Chebyshev spectral operators
Journal of Computational Physics
Anelastic Stokes Eigenmodes in Infinite Channel
Journal of Scientific Computing
Hi-index | 31.45 |
The low-order (3-node) Finite Volume (FV) preconditioning technique is considered for its efficiency to spectrally solve the L[u]=d^2udx^2=f problem. The Fourier spectrum of the associated preconditioning operator is analytically determined and compared with the known Fourier spectra of the corresponding Finite Difference (FD) and Finite Element (FE) preconditioning operators. Moreover, following what was done in [P. Haldenwang, G. Labrosse, S. Abboudi, M.O. Deville, Chebyshev 3-d spectral and 2-d pseudospectral solvers for the Helmholtz equation, J. Comput. Phys. 55 (1984) 115-128] for the FD case, the FE and FV preconditioning operator Chebyshev spectra are analytically determined, first without reference to boundary conditions, and then confirmed when Dirichlet boundary conditions are imposed. The convergence of the Chebyshev towards the Fourier spectra is established. All this analysis leads to conclude that the best of the known lowest-order preconditioners is provided by the piecewise-linear Finite Volume scheme.