An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation
In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better way of c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2111 |
| _version_ | 1797546684430942208 |
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| author | Mitică CRAUS Silviu-Dumitru PAVĂL |
| author_facet | Mitică CRAUS Silviu-Dumitru PAVĂL |
| author_sort | Mitică CRAUS |
| collection | DOAJ |
| description | In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better way of computing its numerical approximation could be of interest, given that the numerical analysis usually takes place on large input domains having more than one dimension. After introducing the general reaction-diffusion model, we discuss a numerical approximation scheme for the diffusion term, based on a finite difference method. In the next sections we propose two algorithms to solve the numerical approximation scheme, focusing on finding a way to improve the time performance. While the first algorithm (sequential) is used as a baseline for performance measurement, the second algorithm (parallel) is implemented using two different memory-sharing parallelization technologies: Open Multi-Processing (OpenMP) and CUDA. All the results were obtained by using the model in image processing applications such as image restoration and segmentation. |
| first_indexed | 2024-03-10T14:33:42Z |
| format | Article |
| id | doaj.art-1e9023c24b8241d882009115031cff3f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:33:42Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1e9023c24b8241d882009115031cff3f2023-11-20T22:22:56ZengMDPI AGMathematics2227-73902020-11-01812211110.3390/math8122111An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion EquationMitică CRAUS0Silviu-Dumitru PAVĂL1Faculty of Automatic Control and Computer Engineering, Technical University “Gh. Asachi”, Dimitrie Mangeron, 27, 700050 Iaşi, RomaniaFaculty of Automatic Control and Computer Engineering, Technical University “Gh. Asachi”, Dimitrie Mangeron, 27, 700050 Iaşi, RomaniaIn this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better way of computing its numerical approximation could be of interest, given that the numerical analysis usually takes place on large input domains having more than one dimension. After introducing the general reaction-diffusion model, we discuss a numerical approximation scheme for the diffusion term, based on a finite difference method. In the next sections we propose two algorithms to solve the numerical approximation scheme, focusing on finding a way to improve the time performance. While the first algorithm (sequential) is used as a baseline for performance measurement, the second algorithm (parallel) is implemented using two different memory-sharing parallelization technologies: Open Multi-Processing (OpenMP) and CUDA. All the results were obtained by using the model in image processing applications such as image restoration and segmentation.https://www.mdpi.com/2227-7390/8/12/2111nonlocal reaction-diffusion equationparallel processingimage processing |
| spellingShingle | Mitică CRAUS Silviu-Dumitru PAVĂL An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation Mathematics nonlocal reaction-diffusion equation parallel processing image processing |
| title | An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation |
| title_full | An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation |
| title_fullStr | An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation |
| title_full_unstemmed | An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation |
| title_short | An Accelerating Numerical Computation of the Diffusion Term in a Nonlocal Reaction-Diffusion Equation |
| title_sort | accelerating numerical computation of the diffusion term in a nonlocal reaction diffusion equation |
| topic | nonlocal reaction-diffusion equation parallel processing image processing |
| url | https://www.mdpi.com/2227-7390/8/12/2111 |
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