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Computational Methods and Applications for Numerical Analysis, 2nd Edition
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Computational Methods and Applications for Numerical Analysis, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 3139

Special Issue Editors

Dr. Fajie Wang

E-Mail Website
Guest Editor
College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
Interests: computational mechanics; numerical analysis; boundary element method; meshless method; acoustic propagation; heat and mass transfer
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ji Lin

E-Mail Website
Guest Editor
College of Mechanics and Materials, Hohai University, Nanjing 211100, China
Interests: solid mechanics; computational mechanics; meshless method; wave propagation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are delighted to announce the second volume of our Special Issue on "Computational Methods and Applications for Numerical Analysis". Building upon the success of the first volume, we aim to continue exploring the innovative computational methods and their diverse applications in numerical analysis

The scope encompasses a wide range of areas, including theory, algorithms, programming, coding, numerical simulation, and novel applications of computational techniques in engineering, science, and related disciplines. Contributions may explore various computational methods within applied mathematics and mechanics, including (but not limited to) finite element methods, finite difference methods, finite volume methods, meshless and particle methods, peridynamics, molecular dynamics, interpolation, approximation, optimization, quadrature methods, numerical linear algebra, and numerical methods for ordinary and partial differential equations. The goal is to showcase research that addresses real-world challenges and demonstrates the effectiveness of computational approaches for solving problems across scientific and engineering domains.

Researchers are encouraged to submit papers that include cutting-edge computational methods, novel algorithms, and successful applications in various fields, which will help advance the field of numerical analysis and its impact on scientific research and technological advancements.

Potential topics include (but are not limited to):

  • Computational methods.
  • Numerical analysis.
  • Finite element methods.
  • Finite difference methods.
  • Finite volume methods.
  • Meshless and particle methods.
  • Neural network algorithm.
  • High-performance computing techniques.
  • Optimization.
  • Interpolation.
  • Approximation.
  • Adaptive analysis.
  • Error estimation.
  • Convergence analysis.

We look forward to receiving your contributions.

Dr. Fajie Wang
Prof. Dr. Ji Lin
Guest Editors

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.

Related Special Issue

Published Papers (4 papers)

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Research

20 pages, 2900 KiB  
Article
Intelligent Low-Consumption Optimization Strategies: Economic Operation of Hydropower Stations Based on Improved LSTM and Random Forest Machine Learning Algorithm
by Hong Pan, Jie Yang, Yang Yu, Yuan Zheng, Xiaonan Zheng and Chenyang Hang
Mathematics 2024, 12(9), 1292; https://doi.org/10.3390/math12091292 - 24 Apr 2024
Viewed by 193
Abstract
The economic operation of hydropower stations has the potential to increase water use efficiency. However, there are some challenges, such as the fixed and unchangeable flow characteristic curve of the hydraulic turbines, and the large number of variables in optimal load distribution, which [...] Read more.
The economic operation of hydropower stations has the potential to increase water use efficiency. However, there are some challenges, such as the fixed and unchangeable flow characteristic curve of the hydraulic turbines, and the large number of variables in optimal load distribution, which limit the progress of research. In this paper, we propose a new optimal method of the economic operation of hydropower stations based on improved Long Short-Term Memory neural network (I-LSTM) and Random Forest (RF) algorithm. Firstly, in order to accurately estimate the water consumption, the LSTM model’s hyperparameters are optimized using improved particle swarm optimization, and the I-LSTM method is proposed to fit the flow characteristic curve of the hydraulic turbines. Secondly, the Random Forest machine learning algorithm is introduced to establish a load-distribution model with its powerful feature extraction and learning ability. To improve the accuracy of the load-distribution model, we use the K-means algorithm to cluster the historical data and optimize the parameters of the Random Forest model. A Hydropower Station in China is selected for a case study. It is shown that (1) the I-LSTM method fits the operating characteristics under various working conditions and actual operating characteristics of hydraulic turbines, ensuring that they are closest to the actual operating state; (2) the I-LSTM method is compared with Support Vector Machine (SVM), Extreme Learning Machine (ELM) and Long Short-Term Memory neural network (LSTM). The prediction results of SVM have a large error, but compared with ELM and LSTM, MSE is reduced by about 46% and 38% respectively. MAE is reduced by about 25% and 21%, respectively. RMSE is reduced by about 27% and 24%, respectively; (3) the RF algorithm performs better than the traditional dynamic programming algorithm in load distribution. With the passage of time and the increase in training samples, the prediction accuracy of the Random Forest model has steadily improved, which helps to achieve optimal operation of the units, reducing their average total water consumption by 1.24%. This study provides strong support for the application of intelligent low-consumption optimization strategies in hydropower fields, which can bring higher economic benefits and resource savings to renewable energy production. Full article
(This article belongs to the Special Issue Computational Methods and Applications for Numerical Analysis, 2nd Edition)
19 pages, 8027 KiB  
Article
Dynamic Behavior of a 10 MW Floating Wind Turbine Concrete Platform under Harsh Conditions
by Xiaocui Chen, Qirui Wang, Yuquan Zhang and Yuan Zheng
Mathematics 2024, 12(3), 412; https://doi.org/10.3390/math12030412 - 26 Jan 2024
Viewed by 655
Abstract
To ensure the safe and stable operation of a 10 MW floating wind turbine concrete platform under harsh sea conditions, the fluid–structure coupling theory was used to apply wind, wave, and current loads to a concrete semi-submersible floating platform, and strength analysis was [...] Read more.
To ensure the safe and stable operation of a 10 MW floating wind turbine concrete platform under harsh sea conditions, the fluid–structure coupling theory was used to apply wind, wave, and current loads to a concrete semi-submersible floating platform, and strength analysis was performed to calculate its stress and deformation under environmental loads. Moreover, the safety factor and fatigue life prediction of the platform were also conducted. The results indicated that the incident angles of the environmental loads had a significant impact on motion response in the surge, sway, pitch, and yaw directions. As the incident angles increased, the motion response in the surge and pitch directions gradually decreased, the motion response in the sway direction gradually increased, and the yaw motion response showed a trend of first increasing and then decreasing. In addition, the maximum stress of the floating platform under harsh sea conditions was 12.718 MPa, mainly concentrated at the connection of the middle column and pontoon and the connection of the heave plate and Y-shaped pontoon, which meets the use strength requirements. However, the stress concentration zone exhibited a significantly shorter fatigue life with a magnitude of 106. This implies a higher susceptibility to fatigue damage and the potential occurrence of structural failure. This research holds paramount significance in ensuring the safe and stable operation of floating wind turbine platforms, particularly under harsh sea conditions. Full article
(This article belongs to the Special Issue Computational Methods and Applications for Numerical Analysis, 2nd Edition)
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18 pages, 8825 KiB  
Article
Numerical Investigation on Suction Flow Control Technology for a Blunt Trailing Edge Hydrofoil
by Peng Yang, Chiye Zhang, Hongyeyu Yan, Yifan Ren, Changliang Ye, Yaguang Heng and Yuan Zheng
Mathematics 2023, 11(16), 3618; https://doi.org/10.3390/math11163618 - 21 Aug 2023
Viewed by 745
Abstract
The generation of hydro-mechanical resonance is related to the transition of the boundary layer and the development of vortex shedding. The application effect of suction control in hydrodynamics is equally deserving of consideration as an active control technique in aerodynamics. This study examines [...] Read more.
The generation of hydro-mechanical resonance is related to the transition of the boundary layer and the development of vortex shedding. The application effect of suction control in hydrodynamics is equally deserving of consideration as an active control technique in aerodynamics. This study examines how suction control affects the flow field of the NACA0009 blunt trailing edge hydrofoil using the γ transition model. Firstly, the accuracy of the numerical method is checked by performing a three-dimensional hydrofoil numerical simulation. Based on this, three-dimensional hydrofoil suction control research is conducted. According to the results, the suction control increases the velocity gradient in the boundary layer and delays the position of transition. The frequency of vortex shedding in the wake region lowers, and the peak value of velocity fluctuation declines. The hydrofoil hydrodynamic performance may be successfully improved with a proper selection of the suction coefficient via research of the suction coefficient and suction position on the flow field around the hydrofoil. The lift/drag ratio goes up as the suction coefficient goes up. The boundary layer displacement thickness and momentum thickness are at their lowest points, and the velocity fluctuation amplitude in the wake region is at its lowest point as the suction coefficient Cμ = 0.003. When the suction slots are at the leading edge, the momentum loss in the boundary layer is minimal and the velocity fluctuation in the wake zone is negligible. Full article
(This article belongs to the Special Issue Computational Methods and Applications for Numerical Analysis, 2nd Edition)
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9 pages, 270 KiB  
Article
A New Efficient Method for Absolute Value Equations
by Peng Guo, Javed Iqbal, Syed Muhammad Ghufran, Muhammad Arif, Reem K. Alhefthi and Lei Shi
Mathematics 2023, 11(15), 3356; https://doi.org/10.3390/math11153356 - 31 Jul 2023
Cited by 1 | Viewed by 879
Abstract
In this paper, the two-step method is considered with the generalized Newton method as a predictor step. The three-point Newton–Cotes formula is taken as a corrector step. The proposed method’s convergence is discussed in detail. This method is very simple and therefore very [...] Read more.
In this paper, the two-step method is considered with the generalized Newton method as a predictor step. The three-point Newton–Cotes formula is taken as a corrector step. The proposed method’s convergence is discussed in detail. This method is very simple and therefore very effective for solving large systems. In numerical analysis, we consider a beam equation, transform it into a system of absolute value equations and then use the proposed method to solve it. Numerical experiments show that our method is very accurate and faster than already existing methods. Full article
(This article belongs to the Special Issue Computational Methods and Applications for Numerical Analysis, 2nd Edition)
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