The Composite Grid Method for Singular Problems of Partial Differential Equations
Partial differential equations are crucial in scientific computing, and this paper will consider some of the problems of partial differential equation singularities. The Composite Mesh Method (CGM) is a new and improved numerical method for solving partial differential equations based on existing nu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/15/3385 |
| _version_ | 1797586360447533056 |
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| author | Hai Ye Yajun Xie |
| author_facet | Hai Ye Yajun Xie |
| author_sort | Hai Ye |
| collection | DOAJ |
| description | Partial differential equations are crucial in scientific computing, and this paper will consider some of the problems of partial differential equation singularities. The Composite Mesh Method (CGM) is a new and improved numerical method for solving partial differential equations based on existing numerical methods for finite elements. The method has two meshes over the entire domain—a coarse and a fine set. The two sets of meshes generated by Mesh3 are separate in their respective regions and do not nest or interact. This method improves the accuracy of solving the numerical solution of partial differential equations. This paper discusses the CGM method based on the Finite Element Program Generator (FEPG) and uses it to simulate several singular problems. The numerical simulation results show that the proposed method can obtain more satisfactory simulation results for global problems and use a smaller number of computational generations than the general finite element method. |
| first_indexed | 2024-03-11T00:22:11Z |
| format | Article |
| id | doaj.art-1fd31110d02447b8beceeac0de954ab8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:22:11Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1fd31110d02447b8beceeac0de954ab82023-11-18T23:15:58ZengMDPI AGMathematics2227-73902023-08-011115338510.3390/math11153385The Composite Grid Method for Singular Problems of Partial Differential EquationsHai Ye0Yajun Xie1Department of Mathematics and Physics, Fujian Health College, Fuzhou 350101, ChinaSchool of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202, ChinaPartial differential equations are crucial in scientific computing, and this paper will consider some of the problems of partial differential equation singularities. The Composite Mesh Method (CGM) is a new and improved numerical method for solving partial differential equations based on existing numerical methods for finite elements. The method has two meshes over the entire domain—a coarse and a fine set. The two sets of meshes generated by Mesh3 are separate in their respective regions and do not nest or interact. This method improves the accuracy of solving the numerical solution of partial differential equations. This paper discusses the CGM method based on the Finite Element Program Generator (FEPG) and uses it to simulate several singular problems. The numerical simulation results show that the proposed method can obtain more satisfactory simulation results for global problems and use a smaller number of computational generations than the general finite element method.https://www.mdpi.com/2227-7390/11/15/3385partial differential equationscomposite grid methodfinite element methodnumerical simulation |
| spellingShingle | Hai Ye Yajun Xie The Composite Grid Method for Singular Problems of Partial Differential Equations Mathematics partial differential equations composite grid method finite element method numerical simulation |
| title | The Composite Grid Method for Singular Problems of Partial Differential Equations |
| title_full | The Composite Grid Method for Singular Problems of Partial Differential Equations |
| title_fullStr | The Composite Grid Method for Singular Problems of Partial Differential Equations |
| title_full_unstemmed | The Composite Grid Method for Singular Problems of Partial Differential Equations |
| title_short | The Composite Grid Method for Singular Problems of Partial Differential Equations |
| title_sort | composite grid method for singular problems of partial differential equations |
| topic | partial differential equations composite grid method finite element method numerical simulation |
| url | https://www.mdpi.com/2227-7390/11/15/3385 |
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