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Numerical Computation, Data Analysis and Software in Mathematics and Engineering,...
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Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: closed (20 May 2025) | Viewed by 5077

Special Issue Editor

Prof. Dr. Yumin Cheng

E-Mail Website
Guest Editor
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China
Interests: numerical analysis; applied mathematics; computational mathematics; computational mechanics; civil and structural engineering; CAE software
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of the previous successful Special Issue “Numerical Computation, Data Analysis and Software in Mathematics and Engineering” in the MDPI journal Mathematics.

In recent years, mathematical models, numerical methods and data analyses have been paid more attention. After the finite element method, the meshless method has been another effective tool for solving science and engineering problems. Numerical methods, such as the finite element method, boundary element method and meshless method, have played important roles in numerical simulations of complicated problems in science, engineering and society fields. Various numerical methods have been presented for solving problems in different fields, and the corresponding computational efficiency, accuracy and convergence have also been studied. With the development of big data, a numerical simulation based on data analysis or big data will be an important direction for science and engineering computation. Furthermore, deep learning is also a new effective approach for analyzing the properties of new materials.

In this Special Issue, we particularly take an interest in manuscripts that report the relevance of numerical computation and data analysis for mathematical and engineering problems. The Special Issue will become an international forum for researchers to summarize the most recent developments of numerical simulations and data analysis within the last five years, especially for new problems. Moreover, manuscripts on the mathematical theories of numerical computation and data analysis for complicated science, engineering or social problems are welcome. We are also interested in the development of the corresponding aspects based on big data, including the corresponding theory, numerical method and the applications.

Software is an important part of numerical computation and data analysis in mathematics and engineering. This Special Issue also concerns the developments of the software of numerical methods, including the finite element method, boundary element method and meshless method, and the methods for data analysis.

Prof. Dr. Yumin Cheng
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • numerical method
  • numerical simulation
  • finite element method
  • boundary element method
  • meshless method
  • mathematical model
  • data analysis
  • software

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Related Special Issue

Published Papers (6 papers)

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Research

18 pages, 5587 KiB  
Article
The Determinants of Commercial Land Leases in the Non-Central Districts of a Large City in China: Data Analysis from the Government–Market Perspective
by Jing Cheng
Mathematics 2025, 13(10), 1595; https://doi.org/10.3390/math13101595 - 13 May 2025
Viewed by 129
Abstract
Based on the data of the non-central districts in Shanghai, this paper investigates the determinants of the commercial land leases of district governments from the government–market perspective and how these determinants affect the price and area of commercial land leasing. A kernel density [...] Read more.
Based on the data of the non-central districts in Shanghai, this paper investigates the determinants of the commercial land leases of district governments from the government–market perspective and how these determinants affect the price and area of commercial land leasing. A kernel density analysis is used to analyze the agglomeration degree and density distribution of commercial land leasing. The variables are considered as the factors impacting commercial land leases based on a literature review and land development in Shanghai. The mathematical models used for multiple linear regression for the leased price and area of the influencing factors of commercial land leases from the perspective of the government and market are proposed. The results show that Shanghai’s multi-center development strategy aims to optimize the city’s commercial layout by developing the key areas of non-central districts. The construction area and plot ratio of land; the distances from the land to the city center, district center, airports, the nearest middle schools, the nearest park, and the nearest industrial zone; and the quantity of subway stations and highways affect commercial land leases. Policies are proposed to improve commercial land lease efficiency, make more suitable land planning strategies, and optimize urban spatial structures. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)
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22 pages, 7805 KiB  
Article
Seismic Performance of a Novel Precast Shear Wall with Mixed Wet and Dry Steel Plate–Bolt Connections: A Finite Element Study
by Qiang Du, Zhaoxi Ma, Yiyun Zhu, Geng Chen and Yue Zhao
Mathematics 2025, 13(7), 1168; https://doi.org/10.3390/math13071168 - 2 Apr 2025
Viewed by 293
Abstract
This paper proposes a hybrid steel plate–bolt dry and wet jointing method, where the dry jointing part is a steel plate–bolt connector joint and the wet jointing part is a cast-in-place concrete. The novel precast concrete shear wall (PCW) combines the advantages of [...] Read more.
This paper proposes a hybrid steel plate–bolt dry and wet jointing method, where the dry jointing part is a steel plate–bolt connector joint and the wet jointing part is a cast-in-place concrete. The novel precast concrete shear wall (PCW) combines the advantages of both dry and wet connections. A steel plate–bolt dry–wet hybrid connection shear wall model was developed using the finite element method, and a low circumferential reciprocating load was applied to the PCW. By analyzing the force and deformation characteristics of the wall, the results showed that the failure mode of novel PCWs was bending-shear failure. Compared to the concrete wall (CW), the yield load, peak load, and ductile displacement coefficient were 6.55%, 7.56%, and 21.49% higher, respectively, demonstrating excellent seismic performance. By extending the wall parameters, it was found that the increased strength of the novel PCW concrete slightly improved the load-bearing capacity, and the ductility coefficient was greatly reduced. As the axial compression ratio increased from 0.3 to 0.4, the wall ductility decreased by 22.85%. Increasing the reinforcement rate of edge-concealed columns resulted in a severe reduction in ultimate displacement and ductility. By extending the connector parameters, it was found that there was an increased number of steel joints, a severe reduction in ductility, enlarged distribution spacing, weld hole plugging and bolt yielding, reduced anchorage performance, and weakening of the steel plate section, which reduced the load-bearing capacity and initial stiffness of the wall, with little effect on ductility. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)
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25 pages, 2086 KiB  
Article
Evaluation Model for Indoor Comprehensive Environmental Comfort Based on the Utility Function Method
by Xiaona Fan and Yiyun Zhu
Mathematics 2025, 13(6), 1000; https://doi.org/10.3390/math13061000 - 19 Mar 2025
Viewed by 190
Abstract
Indoor environmental comfort is closely related to human health and well-being. This study aimed to establish a quantitative evaluation model for indoor comprehensive environmental comfort based on multiple physical environmental parameters. Firstly, based on the subjective evaluation characteristics of indoor environmental comfort and [...] Read more.
Indoor environmental comfort is closely related to human health and well-being. This study aimed to establish a quantitative evaluation model for indoor comprehensive environmental comfort based on multiple physical environmental parameters. Firstly, based on the subjective evaluation characteristics of indoor environmental comfort and the principles of a multi-factor comprehensive evaluation, a comprehensive environmental comfort evaluation method utilizing the utility function approach was proposed. Secondly, subjective questionnaires and objective measurements were conducted in the indoor physical environment of rural dwellings in the Guanzhong Plain. The Kano model was employed to quantitatively analyze the influence of individual environmental comfort factors on the comprehensive environmental comfort based on the survey results. The findings revealed that thermal, lighting, and acoustic environments were the key influencing factors, while air quality was considered a non-key factor. Furthermore, quantitative relationships between environmental comfort and individual parameters were established, and the weights of individual environmental factors were determined using the analytic hierarchy process and the entropy weight method, based on the perspective of categorizing functional rooms and usage time periods. Finally, a quantitative evaluation model for indoor comprehensive environmental comfort was proposed that considered the one-vote veto characteristics and differentiated demands. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)
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23 pages, 4303 KiB  
Article
Adaptive Transit Signal Priority Control for Traffic Safety and Efficiency Optimization: A Multi-Objective Deep Reinforcement Learning Framework
by Yuxuan Dong, Helai Huang, Gongquan Zhang and Jieling Jin
Mathematics 2024, 12(24), 3994; https://doi.org/10.3390/math12243994 - 19 Dec 2024
Cited by 3 | Viewed by 1398
Abstract
This study introduces a multi-objective deep reinforcement learning (DRL)-based adaptive transit signal priority control framework designed to enhance safety and efficiency in mixed-autonomy traffic environments. The framework utilizes real-time data from connected and automated vehicles (CAVs) to define states, actions, and rewards, with [...] Read more.
This study introduces a multi-objective deep reinforcement learning (DRL)-based adaptive transit signal priority control framework designed to enhance safety and efficiency in mixed-autonomy traffic environments. The framework utilizes real-time data from connected and automated vehicles (CAVs) to define states, actions, and rewards, with traffic conflicts serving as the safety reward and vehicle waiting times as the efficiency reward. Transit signal priority strategies are incorporated, assigning weights based on vehicle type and passenger capacity to balance these competing objectives. Simulation modeling, based on a real-world intersection in Changsha, China, evaluated the framework’s performance across multiple CAV penetration rates and weighting configurations. The results revealed that a 5:5 weight ratio for safety and efficiency achieved the best trade-off, minimizing delays and conflicts for all vehicle types. At a 100% CAV penetration rate, delays and conflicts were most balanced, with buses showing an average waiting time of 4.93 s and 0.4 conflicts per vehicle, and CAVs achieving 1.97 s and 0.49 conflicts per vehicle, respectively. In mixed traffic conditions, the framework performed best at a 75% CAV penetration rate, where buses, cars, and CAVs exhibited optimal efficiency and safety. Comparative analysis with fixed-time signal control and other DRL-based methods highlights the framework’s adaptability and robustness, supporting its application in managing mixed traffic and enabling intelligent transportation systems for future smart cities. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)
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18 pages, 2307 KiB  
Article
Spatial–Temporal-Correlation-Constrained Dynamic Graph Convolutional Network for Traffic Flow Forecasting
by Yajun Ge, Jiannan Wang, Bo Zhang, Fan Peng, Jing Ma, Chenyu Yang, Yue Zhao and Ming Liu
Mathematics 2024, 12(19), 3159; https://doi.org/10.3390/math12193159 - 9 Oct 2024
Viewed by 1104
Abstract
Accurate traffic flow prediction in road networks is essential for intelligent transportation systems (ITS). Since traffic data are collected from the road network with spatial topological and time series sequences, the traffic flow prediction is regarded as a spatial–temporal prediction task. With the [...] Read more.
Accurate traffic flow prediction in road networks is essential for intelligent transportation systems (ITS). Since traffic data are collected from the road network with spatial topological and time series sequences, the traffic flow prediction is regarded as a spatial–temporal prediction task. With the powerful ability to model the non-Euclidean data, the graph convolutional network (GCN)-based models have become the mainstream framework for traffic forecasting. However, existing GCN-based models either use the manually predefined graph structure to capture the spatial features, ignoring the heterogeneity of road networks, or simply perform 1-D convolution with fixed kernel to capture the temporal dependencies of traffic data, resulting in insufficient long-term temporal feature extraction. To solve those issues, a spatial–temporal correlation constrained dynamic graph convolutional network (STC-DGCN) is proposed for traffic flow forecasting. In STC-DGCN, a spatial–temporal embedding encoder module (STEM) is first constructed to encode the dynamic spatial relationships for road networks at different time steps. Then, a temporal feature encoder module with heterogeneous time series correlation modeling (TFE-HCM) and a spatial feature encoder module with dynamic multi-graph modeling (SFE-DCM) are designed to generate dynamic graph structures for effectively capturing the dynamic spatial and temporal correlations. Finally, a spatial–temporal feature fusion module based on a gating fusion mechanism (STM-GM) is proposed to effectively learn and leverage the inherent spatial–temporal relationships for traffic flow forecasting. Experimental results from three real-world traffic flow datasets demonstrate the superior performance of the proposed STC-DGCN compared with state-of-the-art traffic flow forecasting models. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)
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17 pages, 3915 KiB  
Article
The Potential Changes and Stereocilia Movements during the Cochlear Sound Perception Process
by Bin Liu, Junyi Liang, Wenjuan Yao and Chun Xu
Mathematics 2024, 12(16), 2470; https://doi.org/10.3390/math12162470 - 10 Aug 2024
Viewed by 1478
Abstract
Sound vibrations generate electrical signals called cochlear potentials, which can reflect cochlear stereocilia movement and outer hair cells (OHC) mechanical activity. However, because the cochlear structure is delicate and complex, it is difficult for existing measurement techniques to pinpoint the origin of potentials. [...] Read more.
Sound vibrations generate electrical signals called cochlear potentials, which can reflect cochlear stereocilia movement and outer hair cells (OHC) mechanical activity. However, because the cochlear structure is delicate and complex, it is difficult for existing measurement techniques to pinpoint the origin of potentials. This limitation in measurement capability makes it difficult to fully understand the contribution of stereocilia and transduction channels to cochlear potentials. In view of this, firstly, this article obtains the stereocilia movement generated by basilar membrane (BM) vibration based on the positional relationship between the various structures of the organ Corti. Secondly, Kirchhoff’s law is used to establish an electric field model of the cochlear cavity, and the stereocilia movement is embedded in the electric field by combining the gated spring model. Finally, a force-electric coupling mathematical model of the cochlea is established. The results indicated that the resistance variation between different cavities in the cochlea leads to a sharp tuning curve. As the displacement of the BM increased, the longitudinal potential along the cochlea continued to move toward the base. The decrease in stereocilia stiffness reduced the deflection angle, thereby reducing the transduction current and lymphatic potential. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 3rd Edition)
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