A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations
Inhomogeneous elliptical inclusions with partial differential equations have aroused appreciable concern in many disciplines. In this paper, a pseudo-spectral collocation method, based on Fourier basis functions, is proposed for the numerical solutions of two- (2D) and three-dimensional (3D) inhomog...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/296 |
| _version_ | 1797486430887346176 |
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| author | Xiao Wang Juan Wang Xin Wang Chujun Yu |
| author_facet | Xiao Wang Juan Wang Xin Wang Chujun Yu |
| author_sort | Xiao Wang |
| collection | DOAJ |
| description | Inhomogeneous elliptical inclusions with partial differential equations have aroused appreciable concern in many disciplines. In this paper, a pseudo-spectral collocation method, based on Fourier basis functions, is proposed for the numerical solutions of two- (2D) and three-dimensional (3D) inhomogeneous elliptic boundary value problems. We describe how one can improve the numerical accuracy by making some extra “reconstruction techniques” before applying the traditional Fourier series approximation. After the particular solutions have been obtained, the resulting homogeneous equation can then be calculated using various boundary-type methods, such as the method of fundamental solutions (MFS). Using Fourier basis functions, one does not need to use large matrices, making accrual computations relatively fast. Three benchmark numerical examples involving Poisson, Helmholtz, and modified-Helmholtz equations are presented to illustrate the applicability and accuracy of the proposed method. |
| first_indexed | 2024-03-09T23:33:08Z |
| format | Article |
| id | doaj.art-63a1ac5412c540399d5d4a36cdfd42d8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:33:08Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-63a1ac5412c540399d5d4a36cdfd42d82023-11-23T17:05:15ZengMDPI AGMathematics2227-73902022-01-0110329610.3390/math10030296A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential EquationsXiao Wang0Juan Wang1Xin Wang2Chujun Yu3School of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaSchool of Foreign Languages, Qingdao University, Qingdao 266071, ChinaDirectly Affiliated College, Shandong Open University, Jinan 250014, ChinaInhomogeneous elliptical inclusions with partial differential equations have aroused appreciable concern in many disciplines. In this paper, a pseudo-spectral collocation method, based on Fourier basis functions, is proposed for the numerical solutions of two- (2D) and three-dimensional (3D) inhomogeneous elliptic boundary value problems. We describe how one can improve the numerical accuracy by making some extra “reconstruction techniques” before applying the traditional Fourier series approximation. After the particular solutions have been obtained, the resulting homogeneous equation can then be calculated using various boundary-type methods, such as the method of fundamental solutions (MFS). Using Fourier basis functions, one does not need to use large matrices, making accrual computations relatively fast. Three benchmark numerical examples involving Poisson, Helmholtz, and modified-Helmholtz equations are presented to illustrate the applicability and accuracy of the proposed method.https://www.mdpi.com/2227-7390/10/3/296inhomogeneous elliptical inclusionsmeshless methodcollocation methodFourier collocation methodFourier basis functionsmethod of fundamental solutions |
| spellingShingle | Xiao Wang Juan Wang Xin Wang Chujun Yu A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations Mathematics inhomogeneous elliptical inclusions meshless method collocation method Fourier collocation method Fourier basis functions method of fundamental solutions |
| title | A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations |
| title_full | A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations |
| title_fullStr | A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations |
| title_full_unstemmed | A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations |
| title_short | A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations |
| title_sort | pseudo spectral fourier collocation method for inhomogeneous elliptical inclusions with partial differential equations |
| topic | inhomogeneous elliptical inclusions meshless method collocation method Fourier collocation method Fourier basis functions method of fundamental solutions |
| url | https://www.mdpi.com/2227-7390/10/3/296 |
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