@Article{IJNAM-15-1-2,
author = {Zhi-Wei, Fang and Shen, Jie and Sun, Hai-Wei},
title = {Preconditioning Techniques in Chebyshev Collocation Method for Elliptic Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2018},
volume = {15},
number = {1-2},
pages = {277--287},
abstract = {<p style="text-align: justify;">When one approximates elliptic equations by the spectral collocation method on the Chebyshev-Gauss-Lobatto (CGL) grid, the resulting coefficient matrix is dense and ill-conditioned. It is known that a good preconditioner, in the sense that the preconditioned system becomes well conditioned, can be constructed with finite difference on the CGL grid. However, there is a lack of an efficient solver for this preconditioner in multi-dimension. A modified preconditioner based on the approximate inverse technique is constructed in this paper. The computational cost of each iteration in solving the preconditioned system is $\mathcal{O}(\ell N_x N_y log N_x)$, where $N_x$, $N_y$ are the grid sizes in each direction and $\ell$ is a small integer. Numerical examples are given to demonstrate the efficiency of the proposed preconditioner.</p>},
issn = {2617-8710},
doi = {https://doi.org/2018-IJNAM-10568},
url = {https://global-sci.com/article/83112/preconditioning-techniques-in-chebyshev-collocation-method-for-elliptic-equations}
}