Holomorphic embedding method for large-scale reverse osmosis desalination optimization
Abstract Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. Herein we propose a fast and flexible holomorphic embedding-based method to solve nonlinear differential eq...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | Communications Engineering |
| Online Access: | https://doi.org/10.1038/s44172-025-00343-3 |
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| _version_ | 1832571670648324096 |
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| author | Junzhi Chen Tao Wang Jiu Luo Hongbo Chen Yi Heng |
| author_facet | Junzhi Chen Tao Wang Jiu Luo Hongbo Chen Yi Heng |
| author_sort | Junzhi Chen |
| collection | DOAJ |
| description | Abstract Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. Herein we propose a fast and flexible holomorphic embedding-based method to solve nonlinear differential equations quickly, and further apply it to handle the industrial application of reverse osmosis desalination. Without solving nonlinear differential equations at each discrete point by a traditional small-step iteration approach, the proposed method determines the solution through an approximation function or approximant within segmented computational domain independently. The results of solving more than 11 million of nonlinear differential equations with various design parameters for the reverse osmosis desalination process indicate that the fast and flexible holomorphic embedding-based method is six-fold faster than several typical solvers in computational efficiency with the same level of accuracy. The proposed computational method in this work has great application potential in engineering design. |
| format | Article |
| id | doaj-art-97c56e6ef381438594f911bd32f6d664 |
| institution | Kabale University |
| issn | 2731-3395 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Communications Engineering |
| spelling | doaj-art-97c56e6ef381438594f911bd32f6d6642025-02-02T12:27:04ZengNature PortfolioCommunications Engineering2731-33952025-01-01411910.1038/s44172-025-00343-3Holomorphic embedding method for large-scale reverse osmosis desalination optimizationJunzhi Chen0Tao Wang1Jiu Luo2Hongbo Chen3Yi Heng4School of Computer Science and Engineering, Sun Yat-sen UniversitySchool of Computer Science and Engineering, Sun Yat-sen UniversitySchool of Future Science and Engineering, Soochow UniversitySchool of Systems Science and Engineering, Sun Yat-sen UniversitySchool of Computer Science and Engineering, Sun Yat-sen UniversityAbstract Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. Herein we propose a fast and flexible holomorphic embedding-based method to solve nonlinear differential equations quickly, and further apply it to handle the industrial application of reverse osmosis desalination. Without solving nonlinear differential equations at each discrete point by a traditional small-step iteration approach, the proposed method determines the solution through an approximation function or approximant within segmented computational domain independently. The results of solving more than 11 million of nonlinear differential equations with various design parameters for the reverse osmosis desalination process indicate that the fast and flexible holomorphic embedding-based method is six-fold faster than several typical solvers in computational efficiency with the same level of accuracy. The proposed computational method in this work has great application potential in engineering design.https://doi.org/10.1038/s44172-025-00343-3 |
| spellingShingle | Junzhi Chen Tao Wang Jiu Luo Hongbo Chen Yi Heng Holomorphic embedding method for large-scale reverse osmosis desalination optimization Communications Engineering |
| title | Holomorphic embedding method for large-scale reverse osmosis desalination optimization |
| title_full | Holomorphic embedding method for large-scale reverse osmosis desalination optimization |
| title_fullStr | Holomorphic embedding method for large-scale reverse osmosis desalination optimization |
| title_full_unstemmed | Holomorphic embedding method for large-scale reverse osmosis desalination optimization |
| title_short | Holomorphic embedding method for large-scale reverse osmosis desalination optimization |
| title_sort | holomorphic embedding method for large scale reverse osmosis desalination optimization |
| url | https://doi.org/10.1038/s44172-025-00343-3 |
| work_keys_str_mv | AT junzhichen holomorphicembeddingmethodforlargescalereverseosmosisdesalinationoptimization AT taowang holomorphicembeddingmethodforlargescalereverseosmosisdesalinationoptimization AT jiuluo holomorphicembeddingmethodforlargescalereverseosmosisdesalinationoptimization AT hongbochen holomorphicembeddingmethodforlargescalereverseosmosisdesalinationoptimization AT yiheng holomorphicembeddingmethodforlargescalereverseosmosisdesalinationoptimization |