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Fast artificial boundary method for the heat equation on unbounded domains with strip tails.
- Source :
-
Journal of Computational & Applied Mathematics . Jun2023, Vol. 425, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- We propose a fast numerical algorithm for the multi-dimensional heat equation on unbounded domains with strips tails. The artificial boundary method is used to confine the computational domains. By applying BDF2 for the time discretization and performing the Z transform, we derive an exact semi-discrete artificial boundary condition which contains the discrete temporal convolution and the surface Laplacian operator. Based on the best relative Chebyshev approximation of the square-root function, we design a fast algorithm to approximate and localize the exact semi-discrete artificial boundary condition. The spatial discretization is realized by the Galerkin finite element method with a special boundary treatment. A complete error estimate for the fully discrete problems is performed, and numerical tests are presented to demonstrate the accuracy and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 425
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 161953649
- Full Text :
- https://doi.org/10.1016/j.cam.2022.115032