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Volume 12, Issue 2
Preconditioned CG Methods for a Variable-Coefficient Nonlocal Diffusion Model

Yu-Hong Ran & Min Yan

DOI: 10.4208/eajam.290921.230122

East Asian J. Appl. Math., 12 (2022), pp. 421-434.

Published online: 2022-02

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  • Abstract

A variable-coefficient nonlocal diffusion model is discretized by an improved fast collocation scheme. The resulting linear system has a symmetric positive definite Toeplitz-like coefficient matrix. The preconditioned CG methods with Toeplitz and circulant preconditioners are used for solving the discretized linear system. Numerical experiments demonstrate the effectiveness of the preconditioned CG methods.

  • Keywords

Nonlocal diffusion model, fast collocation method, Toeplitz matrix, CG method, preconditioner.

  • AMS Subject Headings

65F10, 65F15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-421, author = {Ran , Yu-Hong and Yan , Min}, title = {Preconditioned CG Methods for a Variable-Coefficient Nonlocal Diffusion Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {2}, pages = {421--434}, abstract = {

A variable-coefficient nonlocal diffusion model is discretized by an improved fast collocation scheme. The resulting linear system has a symmetric positive definite Toeplitz-like coefficient matrix. The preconditioned CG methods with Toeplitz and circulant preconditioners are used for solving the discretized linear system. Numerical experiments demonstrate the effectiveness of the preconditioned CG methods.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290921.230122}, url = {http://global-sci.org/intro/article_detail/eajam/20262.html} }
TY - JOUR T1 - Preconditioned CG Methods for a Variable-Coefficient Nonlocal Diffusion Model AU - Ran , Yu-Hong AU - Yan , Min JO - East Asian Journal on Applied Mathematics VL - 2 SP - 421 EP - 434 PY - 2022 DA - 2022/02 SN - 12 DO - http://doi.org/10.4208/eajam.290921.230122 UR - https://global-sci.org/intro/article_detail/eajam/20262.html KW - Nonlocal diffusion model, fast collocation method, Toeplitz matrix, CG method, preconditioner. AB -

A variable-coefficient nonlocal diffusion model is discretized by an improved fast collocation scheme. The resulting linear system has a symmetric positive definite Toeplitz-like coefficient matrix. The preconditioned CG methods with Toeplitz and circulant preconditioners are used for solving the discretized linear system. Numerical experiments demonstrate the effectiveness of the preconditioned CG methods.

Ran , Yu-Hong and Yan , Min. (2022). Preconditioned CG Methods for a Variable-Coefficient Nonlocal Diffusion Model. East Asian Journal on Applied Mathematics. 12 (2). 421-434. doi:10.4208/eajam.290921.230122
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