Pub Date : 2024-02-01DOI: 10.1051/wujns/2024291013
Jiping Song, Tianqi Luo, Lei Lei
The study delves into multiplicative contractions, exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings. Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces. It is noted that a metric can induce a multiplicative metric, and conversely, a multiplicative metric can give a rise to a metric on a nonempty set. As an application, another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.
{"title":"Common Fixed Points for Multiplicative Contractions in Multiplicative Metric Spaces","authors":"Jiping Song, Tianqi Luo, Lei Lei","doi":"10.1051/wujns/2024291013","DOIUrl":"https://doi.org/10.1051/wujns/2024291013","url":null,"abstract":"The study delves into multiplicative contractions, exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings. Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces. It is noted that a metric can induce a multiplicative metric, and conversely, a multiplicative metric can give a rise to a metric on a nonempty set. As an application, another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140468139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-01DOI: 10.1051/wujns/2024291059
Zhongjian Wu, Junyan Li
In recent years, numerical weather forecasting has been increasingly emphasized. Variational data assimilation furnishes precise initial values for numerical forecasting models, constituting an inherently nonlinear optimization challenge. The enormity of the dataset under consideration gives rise to substantial computational burdens, complex modeling, and high hardware requirements. This paper employs the Dual-Population Particle Swarm Optimization (DPSO) algorithm in variational data assimilation to enhance assimilation accuracy. By harnessing parallel computing principles, the paper introduces the Parallel Dual-Population Particle Swarm Optimization (PDPSO) Algorithm to reduce the algorithm processing time. Simulations were carried out using partial differential equations, and comparisons in terms of time and accuracy were made against DPSO, the Dynamic Weight Particle Swarm Algorithm (PSOCIWAC), and the Time-Varying Double Compression Factor Particle Swarm Algorithm (PSOTVCF). Experimental results indicate that the proposed PDPSO outperforms PSOCIWAC and PSOTVCF in convergence accuracy and is comparable to DPSO. Regarding processing time, PDPSO is 40% faster than PSOCIWAC and PSOTVCF and 70% faster than DPSO.
{"title":"Variational Data Assimilation Method Using Parallel Dual Populations Particle Swarm Optimization Algorithm","authors":"Zhongjian Wu, Junyan Li","doi":"10.1051/wujns/2024291059","DOIUrl":"https://doi.org/10.1051/wujns/2024291059","url":null,"abstract":"In recent years, numerical weather forecasting has been increasingly emphasized. Variational data assimilation furnishes precise initial values for numerical forecasting models, constituting an inherently nonlinear optimization challenge. The enormity of the dataset under consideration gives rise to substantial computational burdens, complex modeling, and high hardware requirements. This paper employs the Dual-Population Particle Swarm Optimization (DPSO) algorithm in variational data assimilation to enhance assimilation accuracy. By harnessing parallel computing principles, the paper introduces the Parallel Dual-Population Particle Swarm Optimization (PDPSO) Algorithm to reduce the algorithm processing time. Simulations were carried out using partial differential equations, and comparisons in terms of time and accuracy were made against DPSO, the Dynamic Weight Particle Swarm Algorithm (PSOCIWAC), and the Time-Varying Double Compression Factor Particle Swarm Algorithm (PSOTVCF). Experimental results indicate that the proposed PDPSO outperforms PSOCIWAC and PSOTVCF in convergence accuracy and is comparable to DPSO. Regarding processing time, PDPSO is 40% faster than PSOCIWAC and PSOTVCF and 70% faster than DPSO.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140467976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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