A modified domain decomposition spectral collocation method for parabolic partial differential equations

Wei-Hua Luo; Liang Yin; Jun Guo; Wei-Hua Luo; Liang Yin; Jun Guo

doi:10.3934/nhm.2024041

Networks and Heterogeneous Media

2024, Volume 19, Issue 3: 923-939. doi: 10.3934/nhm.2024041

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Research article

A modified domain decomposition spectral collocation method for parabolic partial differential equations

1.
School of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, P.R. China
2.
Laboratory of Numerical Simulation of Sichuan Provincial Universities, Neijiang Normal University, Neijiang, Sichuan, 641000, P.R. China
3.
College of Mechanical Engineering, Hunan University of Arts and Science, Changde, Hunan, 415000, P.R. China
4.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, 610225, P.R. China

Received: 15 July 2024 Revised: 26 August 2024 Accepted: 10 September 2024 Published: 14 September 2024

In this paper, utilizing Legendre polynomials as the basis functions in both space and time, we present a modified domain decomposition spectral method for 2-dimensional parabolic partial differential equations. For solving the obtained linear/nonlinear algebraic equations, a dimension expanding preconditioner is applied employing the obtained saddle construction of the coefficient matrix. Numerical examples are given to show the performance of the presented method and the efficiency of the preconditioner.
- domain decomposition,
- spectral collocation method,
- preconditioner,
- parabolic PDE
Citation: Wei-Hua Luo, Liang Yin, Jun Guo. A modified domain decomposition spectral collocation method for parabolic partial differential equations[J]. Networks and Heterogeneous Media, 2024, 19(3): 923-939. doi: 10.3934/nhm.2024041

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Abstract

In this paper, utilizing Legendre polynomials as the basis functions in both space and time, we present a modified domain decomposition spectral method for 2-dimensional parabolic partial differential equations. For solving the obtained linear/nonlinear algebraic equations, a dimension expanding preconditioner is applied employing the obtained saddle construction of the coefficient matrix. Numerical examples are given to show the performance of the presented method and the efficiency of the preconditioner.

References

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