A cell structure implementation of the multigrid method for the two-dimensional diffusion equation
To solve the two-dimensional diffusion equation using the finite difference method, we propose a simple MATLAB implementation of the multigrid method. The diffusion equation plays a fundamental role in modeling many significant physical phenomena and is ubiquitous in many governing equations. Some e...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2025-01-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0247042 |
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| author | Yongho Choi Youngjin Hwang Soobin Kwak Seokjun Ham Jyoti Hyundong Kim Junseok Kim |
| author_facet | Yongho Choi Youngjin Hwang Soobin Kwak Seokjun Ham Jyoti Hyundong Kim Junseok Kim |
| author_sort | Yongho Choi |
| collection | DOAJ |
| description | To solve the two-dimensional diffusion equation using the finite difference method, we propose a simple MATLAB implementation of the multigrid method. The diffusion equation plays a fundamental role in modeling many significant physical phenomena and is ubiquitous in many governing equations. Some examples include the reaction–diffusion equations, the convection–diffusion equations, and others. These equations often lack analytical solutions or pose extreme challenges in finding them. Therefore, numerical techniques are indispensable for obtaining practical and accurate approximations for these equations. The multigrid method is known for its computational efficiency and effectiveness as an iterative technique for solving the discretized diffusion equation. Due to its popularity, the multigrid method has been implemented in several programming languages, such as Python, Java, C++, C, Fortran, and others. However, it is not easy for beginners to understand the implementation of the multigrid method due to its complex data structures and recursive routines. To resolve these difficulties, we develop a straightforward MATLAB implementation of the two-dimensional diffusion equation using a cell structure in MATLAB. This work provides an accessible and efficient framework for understanding and applying the multigrid method, thereby simplifying its implementation for researchers and practitioners. |
| format | Article |
| id | doaj-art-a947646f4dcb426ea496cb086a2042a9 |
| institution | Kabale University |
| issn | 2158-3226 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj-art-a947646f4dcb426ea496cb086a2042a92025-02-03T16:40:41ZengAIP Publishing LLCAIP Advances2158-32262025-01-01151015019015019-1110.1063/5.0247042A cell structure implementation of the multigrid method for the two-dimensional diffusion equationYongho Choi0Youngjin Hwang1Soobin Kwak2Seokjun Ham3Jyoti4Hyundong Kim5Junseok Kim6Department of Computer and Information Engineering, Daegu University, Gyeongsan-si, Gyeongsangbuk-do 38453, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaThe Institute of Basic Science, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics and Physics, Gangneung-Wonju National University, Gangneung 25457, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaTo solve the two-dimensional diffusion equation using the finite difference method, we propose a simple MATLAB implementation of the multigrid method. The diffusion equation plays a fundamental role in modeling many significant physical phenomena and is ubiquitous in many governing equations. Some examples include the reaction–diffusion equations, the convection–diffusion equations, and others. These equations often lack analytical solutions or pose extreme challenges in finding them. Therefore, numerical techniques are indispensable for obtaining practical and accurate approximations for these equations. The multigrid method is known for its computational efficiency and effectiveness as an iterative technique for solving the discretized diffusion equation. Due to its popularity, the multigrid method has been implemented in several programming languages, such as Python, Java, C++, C, Fortran, and others. However, it is not easy for beginners to understand the implementation of the multigrid method due to its complex data structures and recursive routines. To resolve these difficulties, we develop a straightforward MATLAB implementation of the two-dimensional diffusion equation using a cell structure in MATLAB. This work provides an accessible and efficient framework for understanding and applying the multigrid method, thereby simplifying its implementation for researchers and practitioners.http://dx.doi.org/10.1063/5.0247042 |
| spellingShingle | Yongho Choi Youngjin Hwang Soobin Kwak Seokjun Ham Jyoti Hyundong Kim Junseok Kim A cell structure implementation of the multigrid method for the two-dimensional diffusion equation AIP Advances |
| title | A cell structure implementation of the multigrid method for the two-dimensional diffusion equation |
| title_full | A cell structure implementation of the multigrid method for the two-dimensional diffusion equation |
| title_fullStr | A cell structure implementation of the multigrid method for the two-dimensional diffusion equation |
| title_full_unstemmed | A cell structure implementation of the multigrid method for the two-dimensional diffusion equation |
| title_short | A cell structure implementation of the multigrid method for the two-dimensional diffusion equation |
| title_sort | cell structure implementation of the multigrid method for the two dimensional diffusion equation |
| url | http://dx.doi.org/10.1063/5.0247042 |
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