Previous Issue
Volume 24, June

Table of Contents

Math. Comput. Appl., Volume 24, Issue 3 (September 2019)

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Order results
Result details
Select all
Export citation of selected articles as:
Open AccessFeature PaperArticle
Geometric Modeling and 3D Printing Using Recursively Generated Point Cloud
Math. Comput. Appl. 2019, 24(3), 83; https://doi.org/10.3390/mca24030083 (registering DOI) - 17 Sep 2019
Abstract
Previous studies have reported that a recursive process called the point cloud creation algorithm (PCA) that generates a point cloud is useful for reverse engineering a planner shape. This study elucidates the characteristics of the parameters used in the recursive process as well [...] Read more.
Previous studies have reported that a recursive process called the point cloud creation algorithm (PCA) that generates a point cloud is useful for reverse engineering a planner shape. This study elucidates the characteristics of the parameters used in the recursive process as well as its ability in geometric modeling and 3D printing of 3D shapes. In the recursive process, three constants (center point, initial distance, and initial angle) and two variables (instantaneous distance and instantaneous rotational angle) are employed. The shape-modeling characteristics of the constants and variables are elucidated using some commonly used shapes (straight-line, circle, ellipses, spiral, astroid, S-shape, and leaf-shape). In addition, the shape-modeling capability of the recursive process as a whole is quantified using two parameters called the radius of curvature and aesthetic value. Moreover, an illustrative example that shows the efficacy of the recursive process in virtual and physical prototyping of a relatively complex 3D object is presented. The results show that reverse engineering performed by the recursive-process-created point cloud is free from computational complexity compared to reverse engineering performed by the 3D-scanner-created point cloud. As such, the outcomes of this study enrich the field of reverse engineering. Full article
(This article belongs to the Section Engineering)
Open AccessFeature PaperArticle
Variation Rate to Maintain Diversity in Decision Space within Multi-Objective Evolutionary Algorithms
Math. Comput. Appl. 2019, 24(3), 82; https://doi.org/10.3390/mca24030082 - 13 Sep 2019
Viewed by 126
Abstract
The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations’ approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in [...] Read more.
The performance of a multi-objective evolutionary algorithm (MOEA) is in most cases measured in terms of the populations’ approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals of their populations in decision space. This, however, represents a potential shortcoming in certain applications as in many cases one can obtain the same or very similar qualities (measured in objective space) in several ways (measured in decision space). Hence, a high diversity in decision space may represent valuable information for the decision maker for the realization of a given project. In this paper, we propose the Variation Rate, a heuristic selection strategy that aims to maintain diversity both in decision and objective space. The core of this strategy is the proper combination of the averaged distance applied in variable space together with the diversity mechanism in objective space that is used within a chosen MOEA. To show the applicability of the method, we propose the resulting selection strategies for some of the most representative state-of-the-art MOEAs and show numerical results on several benchmark problems. The results demonstrate that the consideration of the Variation Rate can greatly enhance the diversity in decision space for all considered algorithms and problems without a significant loss in the approximation qualities in objective space. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
Show Figures

Figure 1

Open AccessArticle
Hydrodynamic and Acoustic Performance Analysis of Marine Propellers by Combination of Panel Method and FW-H Equations
Math. Comput. Appl. 2019, 24(3), 81; https://doi.org/10.3390/mca24030081 - 09 Sep 2019
Viewed by 144
Abstract
The noise emitted by ships is one of the most important noises in the ocean, and the propeller noise is one of the major components of the ship noise. Measuring the propeller noise in a laboratory, despite the high accuracy and good reliability, [...] Read more.
The noise emitted by ships is one of the most important noises in the ocean, and the propeller noise is one of the major components of the ship noise. Measuring the propeller noise in a laboratory, despite the high accuracy and good reliability, has high costs and is very time-consuming. For this reason, the calculation of propeller noise using numerical methods has been considered in recent years. In this study, the noise of a propeller in non-cavitating conditions is calculated by the combination of the panel method (boundary element method) and solving the Ffowcs Williams-Hawkings (FW-H) equations. In this study, a panel method code is developed, and the results are validated by the experimental results of the model tests carried out in the cavitation tunnel of the Sharif University of Technology. Software for numerical calculation of propeller noise, based on FW-H equations, is also developed and the results are validated by experimental results. This study shows that the results of the panel method code have good agreement with experimental results, and that the maximum error of this code for the thrust and torque coefficients is 4% and 7%, respectively. The results of the FW-H noise code are also in good agreement with the experimental data. Full article
Show Figures

Figure 1

Open AccessArticle
Improved Differential Evolution Algorithm for Flexible Job Shop Scheduling Problems
Math. Comput. Appl. 2019, 24(3), 80; https://doi.org/10.3390/mca24030080 - 06 Sep 2019
Viewed by 144
Abstract
This research project aims to study and develop the differential evolution (DE) for use in solving the flexible job shop scheduling problem (FJSP). The development of algorithms were evaluated to find the solution and the best answer, and this was subsequently compared to [...] Read more.
This research project aims to study and develop the differential evolution (DE) for use in solving the flexible job shop scheduling problem (FJSP). The development of algorithms were evaluated to find the solution and the best answer, and this was subsequently compared to the meta-heuristics from the literature review. For FJSP, by comparing the problem group with the makespan and the mean relative errors (MREs), it was found that for small-sized Kacem problems, value adjusting with “DE/rand/1” and exponential crossover at position 2. Moreover, value adjusting with “DE/best/2” and exponential crossover at position 2 gave an MRE of 3.25. For medium-sized Brandimarte problems, value adjusting with “DE/best/2” and exponential crossover at position 2 gave a mean relative error of 7.11. For large-sized Dauzere-Peres and Paulli problems, value adjusting with “DE/best/2” and exponential crossover at position 2 gave an MRE of 4.20. From the comparison of the DE results with other methods, it was found that the MRE was lower than that found by Girish and Jawahar with the particle swarm optimization (PSO) method (7.75), which the improved DE was 7.11. For large-sized problems, it was found that the MRE was lower than that found by Warisa (1ST-DE) method (5.08), for which the improved DE was 4.20. The results further showed that basic DE and improved DE with jump search are effective methods compared to the other meta-heuristic methods. Hence, they can be used to solve the FJSP. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
Show Figures

Figure 1

Open AccessArticle
Tensors in Newtonian Physics and the Foundations of Classical Continuum Mechanics
Math. Comput. Appl. 2019, 24(3), 79; https://doi.org/10.3390/mca24030079 - 03 Sep 2019
Viewed by 142
Abstract
In the Newtonian approach to mechanics, the concepts of objective tensors of various ranks and types are introduced. The tough classification of objective tensors is given, including tensors of material and spatial types. The diagrams are constructed for non-degenerate (“analogous”) relations between tensors [...] Read more.
In the Newtonian approach to mechanics, the concepts of objective tensors of various ranks and types are introduced. The tough classification of objective tensors is given, including tensors of material and spatial types. The diagrams are constructed for non-degenerate (“analogous”) relations between tensors of one and the same (any) rank, and of various types of objectivity. Mappings expressing dependence between objective tensor processes of various ranks and types are considered. The fundamental concept of frame-independence of such mappings is introduced as being inherent to constitutive relations of various physical and mechanical properties in the Newtonian approach. The criteria are established for such frame-independence. The mathematical restrictions imposed on the frame-independent mappings by the objectivity types of connected tensors are simultaneously revealed. The absence of such restrictions is established exclusively for mappings and equations linking tensors of material types. Using this, a generalizing concept of objective differentiation of tensor processes in time, and a new concept of objective integration, are introduced. The axiomatic construction of the generalized theory of stress and strain tensors in continuum mechanics is given, which leads to the emergence of continuum classes and families of new tensor measures. The axioms are proposed and a variant of the general theory of constitutive relations of mechanical properties of continuous media is constructed, generalizing the known approaches by Ilyushin and Noll, taking into account the possible presence of internal kinematic constraints and internal body-forces in the body. The concepts of the process image and the properties of the five-dimensional Ilyushin’s isotropy are generalized on the range of finite strains. Full article
(This article belongs to the Special Issue Related Problems of Continuum Mechanics)
Open AccessFeature PaperArticle
Pool-Based Genetic Programming Using Evospace, Local Search and Bloat Control
Math. Comput. Appl. 2019, 24(3), 78; https://doi.org/10.3390/mca24030078 - 29 Aug 2019
Viewed by 320
Abstract
This work presents a unique genetic programming (GP) approach that integrates a numerical local search method and a bloat-control mechanism within a distributed model for evolutionary algorithms known as EvoSpace. The first two elements provide a directed search operator and a way to [...] Read more.
This work presents a unique genetic programming (GP) approach that integrates a numerical local search method and a bloat-control mechanism within a distributed model for evolutionary algorithms known as EvoSpace. The first two elements provide a directed search operator and a way to control the growth of evolved models, while the latter is meant to exploit distributed and cloud-based computing architectures. EvoSpace is a Pool-based Evolutionary Algorithm, and this work is the first time that such a computing model has been used to perform a GP-based search. The proposal was extensively evaluated using real-world problems from diverse domains, and the behavior of the search was analyzed from several different perspectives. The results show that the proposed approach compares favorably with a standard approach, identifying promising aspects and limitations of this initial hybrid system. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization)
Show Figures

Figure 1

Open AccessArticle
Direct Power Control Optimization for Doubly Fed Induction Generator Based Wind Turbine Systems
Math. Comput. Appl. 2019, 24(3), 77; https://doi.org/10.3390/mca24030077 - 26 Aug 2019
Viewed by 339
Abstract
This study presents an intelligent metaheuristics-based design procedure for the Proportional-Integral (PI) controllers tuning in the direct power control scheme for 1.5 MW Doubly Fed Induction Generator (DFIG) based Wind Turbine (WT) systems. The PI controllers’ gains tuning is formulated as a constrained [...] Read more.
This study presents an intelligent metaheuristics-based design procedure for the Proportional-Integral (PI) controllers tuning in the direct power control scheme for 1.5 MW Doubly Fed Induction Generator (DFIG) based Wind Turbine (WT) systems. The PI controllers’ gains tuning is formulated as a constrained optimization problem under nonlinear and non-smooth operational constraints. Such a formulated tuning problem is efficiently solved by means of the proposed Thermal Exchange Optimization (TEO) algorithm. To evaluate the effectiveness of the introduced TEO metaheuristic, an empirical comparison study with the homologous particle swarm optimization, genetic algorithm, harmony search algorithm, water cycle algorithm, and grasshopper optimization algorithm is achieved. The proposed TEO algorithm is ensured to perform several desired operational characteristics of DFIG for the active/reactive power and DC-link voltage simultaneously. This is performed by solving a multi-objective function optimization problem through a weighted-sum approach. The proposed control strategy is investigated in MATLAB/environment and the results proved the capabilities of the proposed control system in tracking and control under different scenarios. Moreover, a statistical analysis using non-parametric Friedman and Bonferroni–Dunn’s tests demonstrates that the TEO algorithm gives very competitive results in solving global optimization problems in comparison to the other reported metaheuristic algorithms. Full article
Show Figures

Figure 1

Open AccessFeature PaperArticle
Comparison of Splitting Methods for Deterministic/Stochastic Gross–Pitaevskii Equation
Math. Comput. Appl. 2019, 24(3), 76; https://doi.org/10.3390/mca24030076 - 20 Aug 2019
Viewed by 388
Abstract
In this paper, we discuss the different splitting approaches to numerically solve the Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einstein condensate (BEC). This system is formed of coupled mean-field equations, which are based on coupled Gross–Pitaevskii equations. We consider conservative [...] Read more.
In this paper, we discuss the different splitting approaches to numerically solve the Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einstein condensate (BEC). This system is formed of coupled mean-field equations, which are based on coupled Gross–Pitaevskii equations. We consider conservative finite-difference schemes and spectral methods for the spatial discretisation. Furthermore, we apply implicit or explicit time-integrators and combine these schemes with different splitting approaches. The numerical solutions are compared based on the conservation of the L 2 -norm with the analytical solutions. The advantages of the novel splitting methods for large time-domains are based on the asymptotic conservation of the solution of the soliton’s applications. Furthermore, we have the benefit of larger local time-steps and therefore obtain faster numerical schemes. Full article
(This article belongs to the Section Engineering)
Show Figures

Figure 1

Open AccessArticle
Overlapping Multi-Domain Spectral Method for Conjugate Problems of Conduction and MHD Free Convection Flow of Nanofluids over Flat Plates
Math. Comput. Appl. 2019, 24(3), 75; https://doi.org/10.3390/mca24030075 - 05 Aug 2019
Viewed by 366
Abstract
An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal [...] Read more.
An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag–water nanofluid has higher skin friction and surface temperature than the Cu–water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement. Full article
Show Figures

Figure 1

Open AccessArticle
2D Hybrid Steady-State Magnetic Field Model for Linear Induction Motors
Math. Comput. Appl. 2019, 24(3), 74; https://doi.org/10.3390/mca24030074 - 25 Jul 2019
Viewed by 374
Abstract
This paper presents a 2D hybrid steady-state magnetic field model, capable of accurately modeling the electromagnetic behavior in a linear induction motor, including primary slotting, finite yoke length, and longitudinal end-effects by primary motion. This model integrates a complex harmonic modeling technique with [...] Read more.
This paper presents a 2D hybrid steady-state magnetic field model, capable of accurately modeling the electromagnetic behavior in a linear induction motor, including primary slotting, finite yoke length, and longitudinal end-effects by primary motion. This model integrates a complex harmonic modeling technique with a discretized magnetic equivalent circuit model. The Fourier model is applied to regions with homogeneous material properties, e.g., air regions and the track of the motor, while the magnetic equivalent circuit (MEC) approach is used for the regions containing non-homogeneous material properties, e.g., the primary of the linear induction motor (LIM). By only meshing the domains containing highly-permeable materials, the computational effort is reduced in comparison with the finite element method (FEM). The model is applied to a double-layer single-sided LIM, and the resulting thrust and normal forces show an excellent agreement with respect to finite element analysis and measurement data. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
Show Figures

Figure 1

Open AccessArticle
A Novel Decision-Making Approach under Complex Pythagorean Fuzzy Environment
Math. Comput. Appl. 2019, 24(3), 73; https://doi.org/10.3390/mca24030073 - 24 Jul 2019
Cited by 1 | Viewed by 361
Abstract
A complex Pythagorean fuzzy set (CPFS) is an extension of a Pythagorean fuzzy set that is used to handle the vagueness with the degrees whose ranges are enlarged from real to complex subset with unit disc. In this research study, we propose the [...] Read more.
A complex Pythagorean fuzzy set (CPFS) is an extension of a Pythagorean fuzzy set that is used to handle the vagueness with the degrees whose ranges are enlarged from real to complex subset with unit disc. In this research study, we propose the innovative concept of complex Pythagorean fuzzy graphs (CPFGs). Further, we present the concepts of regular and edge regular graphs in a complex Pythagorean fuzzy environment. Moreover, we develop a complex Pythagorean fuzzy graph based multi-attribute decision making an approach to handling the situations in which the graphic structure of attributes is obscure. A numerical example concerning information technology improvement project selection is utilized to illustrate the availability of the developed approach. Full article
Show Figures

Figure 1

Open AccessTechnical Note
The Archimedes’ Constant, π Seen by Mechanical Engineers
Math. Comput. Appl. 2019, 24(3), 72; https://doi.org/10.3390/mca24030072 - 23 Jul 2019
Viewed by 419
Abstract
Probabilistic engineering mechanics is used to relate the value of π with one of the main parameters in fracture mechanics. It proposes an engineering method to obtain the value of it from engineering data without involving any geometrical Euclidian’s circle’s data measurement or [...] Read more.
Probabilistic engineering mechanics is used to relate the value of π with one of the main parameters in fracture mechanics. It proposes an engineering method to obtain the value of it from engineering data without involving any geometrical Euclidian’s circle’s data measurement or analysis. It is the first trial in studying the use of fracture mechanics to determine the value of ratio of circumference and diameter of Euclidean’s circles indirectly, and subsequently evaluate the number of the digits actually needed in fracture mechanics and engineering purposes. Full article
(This article belongs to the Section Engineering)
Show Figures

Figure 1

Open AccessArticle
Hedging Crop Yields Against Weather Uncertainties—A Weather Derivative Perspective
Math. Comput. Appl. 2019, 24(3), 71; https://doi.org/10.3390/mca24030071 - 19 Jul 2019
Viewed by 359
Abstract
The effects of weather on agriculture in recent years have become a major global concern. Hence, an effective weather risk management tool (i.e., weather derivatives) that can hedge crop yields against weather uncertainties is needed. However, most smallholder farmers and agricultural stakeholders are [...] Read more.
The effects of weather on agriculture in recent years have become a major global concern. Hence, an effective weather risk management tool (i.e., weather derivatives) that can hedge crop yields against weather uncertainties is needed. However, most smallholder farmers and agricultural stakeholders are unwilling to pay for the price of weather derivatives (WD) because of the presence of basis risks (product-design and geographical) in the pricing models. To eliminate product-design basis risks, a machine learning ensemble technique was used to determine the relationship between maize yield and weather variables. The results revealed that the most significant weather variable that affected the yield of maize was average temperature. A mean-reverting model with a time-varying speed of mean reversion, seasonal mean, and local volatility that depended on the local average temperature was then proposed. The model was extended to a multi-dimensional model for different but correlated locations. Based on these average temperature models, pricing models for futures, options on futures, and basket futures for cumulative average temperature and growing degree-days are presented. Pricing futures on baskets reduces geographical basis risk, as buyers have the opportunity to select the most appropriate weather stations with their desired weight preference. With these pricing models, farmers and agricultural stakeholders can hedge their crops against the perils of extreme weather. Full article
(This article belongs to the Section Natural Sciences)
Show Figures

Figure 1

Open AccessFeature PaperArticle
Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation
Math. Comput. Appl. 2019, 24(3), 70; https://doi.org/10.3390/mca24030070 - 19 Jul 2019
Viewed by 583
Abstract
Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of the underlying details of the chosen sparse matrix storage format. In addition, to achieve good performance, several formats [...] Read more.
Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of the underlying details of the chosen sparse matrix storage format. In addition, to achieve good performance, several formats may need to be used in one program, requiring explicit selection and conversion between the formats. This can be both tedious and error-prone, especially for non-expert users. Motivated by these issues, we present a user-friendly and open-source sparse matrix class for the C++ language, with a high-level application programming interface deliberately similar to the widely-used MATLAB language. This facilitates prototyping directly in C++ and aids the conversion of research code into production environments. The class internally uses two main approaches to achieve efficient execution: (i) a hybrid storage framework, which automatically and seamlessly switches between three underlying storage formats (compressed sparse column, red-black tree, coordinate list) depending on which format is best suited and/or available for specific operations, and (ii) a template-based meta-programming framework to automatically detect and optimise the execution of common expression patterns. Empirical evaluations on large sparse matrices with various densities of non-zero elements demonstrate the advantages of the hybrid storage framework and the expression optimisation mechanism. Full article
Show Figures

Figure 1

Open AccessArticle
On the Modeling of Five-Layer Thin Prismatic Bodies
Math. Comput. Appl. 2019, 24(3), 69; https://doi.org/10.3390/mca24030069 - 11 Jul 2019
Viewed by 417
Abstract
Proceeding from three-dimensional formulations of initial boundary value problems of the three-dimensional linear micropolar theory of thermoelasticity, similar formulations of initial boundary value problems for the theory of multilayer thermoelastic thin bodies are obtained. The initial boundary value problems for thin bodies are [...] Read more.
Proceeding from three-dimensional formulations of initial boundary value problems of the three-dimensional linear micropolar theory of thermoelasticity, similar formulations of initial boundary value problems for the theory of multilayer thermoelastic thin bodies are obtained. The initial boundary value problems for thin bodies are also obtained in the moments with respect to systems of orthogonal polynomials. We consider some particular cases of formulations of initial boundary value problems. In particular, the statements of the initial-boundary value problems of the micropolar theory of K-layer thin prismatic bodies are considered. From here, we can easily get the statements of the initial-boundary value problems for the five-layer thin prismatic bodies. Full article
(This article belongs to the Special Issue Related Problems of Continuum Mechanics)
Open AccessFeature PaperArticle
Influence of a Modulated Parameter on Hantavirus Infection
Math. Comput. Appl. 2019, 24(3), 68; https://doi.org/10.3390/mca24030068 - 10 Jul 2019
Viewed by 463
Abstract
We study the dynamical behavior of a model commonly used to describe the infection of mice due to hantavirus (and, therefore, its possibility of propagation into human populations) when a parameter is changed in time. In particular, we study the situation when the [...] Read more.
We study the dynamical behavior of a model commonly used to describe the infection of mice due to hantavirus (and, therefore, its possibility of propagation into human populations) when a parameter is changed in time. In particular, we study the situation when the ecological conditions (e.g., climate benignity, food availability, and so on) change periodically in time. We show that the density of infected mice increases abruptly as the parameter crosses a critical value. We correlate such a situation with the observed sudden outbreaks of hantavirus. Finally, we discuss the possibility of preventing a hantavirus epidemic. Full article
(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
Show Figures

Figure 1

Open AccessFeature PaperReview
Permanent-Magnet Eddy-Current Losses: A Global Revision of Calculation and Analysis
Math. Comput. Appl. 2019, 24(3), 67; https://doi.org/10.3390/mca24030067 - 09 Jul 2019
Viewed by 562
Abstract
Eddy-current analysis is an important research field. This phenomenon occurs in multiple areas and has several applications: electromagnetic braking, repulsive effects, levitation, etc. Thereby, this paper is limited to eddy-current study in rotating electrical machines. In the design process, if the permanent-magnet (PM) [...] Read more.
Eddy-current analysis is an important research field. This phenomenon occurs in multiple areas and has several applications: electromagnetic braking, repulsive effects, levitation, etc. Thereby, this paper is limited to eddy-current study in rotating electrical machines. In the design process, if the permanent-magnet (PM) loss calculation is very important, the overheating due to eddy-currents must be taken into account. The content of this paper includes sources, calculation methods, reduction techniques, and thermal analysis of PM eddy-current losses. This review aims to act as a guide for the reader to learn about the different aspects and points to consider in studying the eddy-current. Full article
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
Show Figures

Figure 1

Previous Issue
Back to TopTop