Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains
In this paper, we develop an efficient Hermite spectral-Galerkin method for nonlocal diffusion equations in unbounded domains. We show that the use of the Hermite basis can de-convolute the troublesome convolutional operations involved in the nonlocal Laplacian. As a result, the “stiffness” matrix c...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/168766 |
| _version_ | 1811689987860594688 |
|---|---|
| author | Li, Huiyuan Liu, Ruiqing Wang, Li-Lian |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Li, Huiyuan Liu, Ruiqing Wang, Li-Lian |
| author_sort | Li, Huiyuan |
| collection | NTU |
| description | In this paper, we develop an efficient Hermite spectral-Galerkin method for nonlocal diffusion equations in unbounded domains. We show that the use of the Hermite basis can de-convolute the troublesome convolutional operations involved in the nonlocal Laplacian. As a result, the “stiffness” matrix can be fast computed and assembled via the four-point stable recursive algorithm with O(N2) arithmetic operations. Moreover, the singular factor in a typical kernel function can be fully absorbed by the basis. With the aid of Fourier analysis, we can prove the convergence of the scheme. We demonstrate that the recursive computation of the entries of the stiffness matrix can be extended to the two-dimensional nonlocal Laplacian using the isotropic Hermite functions as basis functions. We provide ample numerical results to illustrate the accuracy and efficiency of the proposed algorithms. |
| first_indexed | 2024-10-01T05:56:50Z |
| format | Journal Article |
| id | ntu-10356/168766 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:56:50Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1687662023-06-19T04:26:31Z Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains Li, Huiyuan Liu, Ruiqing Wang, Li-Lian School of Physical and Mathematical Sciences Science::Mathematics Nonlocal diffusion Equation Spectral-Galerkin In this paper, we develop an efficient Hermite spectral-Galerkin method for nonlocal diffusion equations in unbounded domains. We show that the use of the Hermite basis can de-convolute the troublesome convolutional operations involved in the nonlocal Laplacian. As a result, the “stiffness” matrix can be fast computed and assembled via the four-point stable recursive algorithm with O(N2) arithmetic operations. Moreover, the singular factor in a typical kernel function can be fully absorbed by the basis. With the aid of Fourier analysis, we can prove the convergence of the scheme. We demonstrate that the recursive computation of the entries of the stiffness matrix can be extended to the two-dimensional nonlocal Laplacian using the isotropic Hermite functions as basis functions. We provide ample numerical results to illustrate the accuracy and efficiency of the proposed algorithms. 2023-06-19T04:26:31Z 2023-06-19T04:26:31Z 2022 Journal Article Li, H., Liu, R. & Wang, L. (2022). Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains. Numerical Mathematics, 15(4), 1009-1040. https://dx.doi.org/10.4208/nmtma.OA-2022-0007s 1004-8979 https://hdl.handle.net/10356/168766 10.4208/nmtma.OA-2022-0007s 2-s2.0-85144803698 4 15 1009 1040 en Numerical Mathematics © 2022 Global-Science Press. All rights reserved. |
| spellingShingle | Science::Mathematics Nonlocal diffusion Equation Spectral-Galerkin Li, Huiyuan Liu, Ruiqing Wang, Li-Lian Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains |
| title | Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains |
| title_full | Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains |
| title_fullStr | Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains |
| title_full_unstemmed | Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains |
| title_short | Efficient hermite spectral-galerkin methods for nonlocal diffusion equations in unbounded domains |
| title_sort | efficient hermite spectral galerkin methods for nonlocal diffusion equations in unbounded domains |
| topic | Science::Mathematics Nonlocal diffusion Equation Spectral-Galerkin |
| url | https://hdl.handle.net/10356/168766 |
| work_keys_str_mv | AT lihuiyuan efficienthermitespectralgalerkinmethodsfornonlocaldiffusionequationsinunboundeddomains AT liuruiqing efficienthermitespectralgalerkinmethodsfornonlocaldiffusionequationsinunboundeddomains AT wanglilian efficienthermitespectralgalerkinmethodsfornonlocaldiffusionequationsinunboundeddomains |