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Volume 18, Issue 3
New Extrapolation Modulus-Based Economical Cascadic Multigrid Method for Variational Inequality Problems with Nonlinear Source Terms

Xin Lu & Chenliang Li

DOI: 10.4208/nmtma.OA-2024-129

Numer. Math. Theor. Meth. Appl., 18 (2025), pp. 575-597.

Published online: 2025-09

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  • Abstract

In this paper, we combine a new extrapolation formula with a cascadic multigrid method to solve variational inequality problems with nonlinear source terms. We construct a new extrapolation modulus-based cascadic multigrid method and a new extrapolation modulus-based economical cascadic multigrid method. Based on a new formula for controlling the number of iterations, the convergence is analyzed. Numerical experiments demonstrate the effectiveness of the proposed methods.

  • Keywords

Variational inequality, nonlinear source terms, new extrapolation modulus-based cascadic multigrid method, new extrapolation modulus-based economical cascadic multigrid method, iterative step control formula.

  • AMS Subject Headings

65F10, 65N55, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-18-575, author = {Lu , Xin and Li , Chenliang}, title = {New Extrapolation Modulus-Based Economical Cascadic Multigrid Method for Variational Inequality Problems with Nonlinear Source Terms}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2025}, volume = {18}, number = {3}, pages = {575--597}, abstract = {

In this paper, we combine a new extrapolation formula with a cascadic multigrid method to solve variational inequality problems with nonlinear source terms. We construct a new extrapolation modulus-based cascadic multigrid method and a new extrapolation modulus-based economical cascadic multigrid method. Based on a new formula for controlling the number of iterations, the convergence is analyzed. Numerical experiments demonstrate the effectiveness of the proposed methods.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-129}, url = {http://global-sci.org/intro/article_detail/nmtma/24319.html} }
TY - JOUR T1 - New Extrapolation Modulus-Based Economical Cascadic Multigrid Method for Variational Inequality Problems with Nonlinear Source Terms AU - Lu , Xin AU - Li , Chenliang JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 575 EP - 597 PY - 2025 DA - 2025/09 SN - 18 DO - http://doi.org/10.4208/nmtma.OA-2024-129 UR - https://global-sci.org/intro/article_detail/nmtma/24319.html KW - Variational inequality, nonlinear source terms, new extrapolation modulus-based cascadic multigrid method, new extrapolation modulus-based economical cascadic multigrid method, iterative step control formula. AB -

In this paper, we combine a new extrapolation formula with a cascadic multigrid method to solve variational inequality problems with nonlinear source terms. We construct a new extrapolation modulus-based cascadic multigrid method and a new extrapolation modulus-based economical cascadic multigrid method. Based on a new formula for controlling the number of iterations, the convergence is analyzed. Numerical experiments demonstrate the effectiveness of the proposed methods.

Lu , Xin and Li , Chenliang. (2025). New Extrapolation Modulus-Based Economical Cascadic Multigrid Method for Variational Inequality Problems with Nonlinear Source Terms. Numerical Mathematics: Theory, Methods and Applications. 18 (3). 575-597. doi:10.4208/nmtma.OA-2024-129
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