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Computational Methods and Optimization for Numerical Analysis
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Computational Methods and Optimization for Numerical Analysis

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Algorithms for Multidisciplinary Applications".

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 37320

Special Issue Editors

Prof. Dr. Dunhui Xiao

E-Mail Website
Guest Editor
School of Mathematical Sciences, Tongji University, Shanghai 201804, China
Interests: AI; machine learning; model reduction; finite element analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shuai Li

E-Mail Website
Guest Editor
Faculty of Information Technology and Electrical Engineering, University of Oulu, 90570 Oulu, Finland
Interests: AI; machine learning; control algorithms; robotics; nonlinear optimization; control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Computational methods and optimization are widely used in science and engineering, such as physics, environment, mechanics, biology, data science, economics, finance, and so on. These problems are complex and highly nonlinear and difficult to predict. Over the last decade, computational problems have become popular and gained much attention due to the improved computer performance, computing methods, and the rapid development of data science technology. However, these developments also raise various issues and challenges, such as highly non-linearity, the curse of dimensionality, uncertainty, complexity, and so on. Therefore, it is urgent to respond to those challenges by developing new computational methods such as graph theory, optimization methods, algebra, uncertainty, data science or analysis, new differential equations solving methods, probability, and statistics methods.

This Special Issue deals with various computational methods in both science and engineering.

Prof. Dr. Dunhui Xiao
Prof. Dr. Shuai Li
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. Algorithms is an international peer-reviewed open access monthly 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 1600 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

  • graph theory
  • optimization
  • algebra
  • uncertainty
  • data science
  • differential equations
  • probability and statistics
  • computational methods

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Published Papers (20 papers)

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21 pages, 2828 KiB  
Article
Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis
by Sebastiano Fichera, Gregorio Mariggiò, Mauro Corrado and Giulio Ventura
Algorithms 2023, 16(6), 290; https://doi.org/10.3390/a16060290 - 04 Jun 2023
Viewed by 1140
Abstract
The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable [...] Read more.
The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable results. In this scope, equivalent polynomials represent an effective method to circumvent the problem while exploiting the standard Gauss quadrature rule to exactly integrate polynomials times step function. Certain scenarios, however, might require the integration of polynomials times two step functions (i.e., problems in which branching cracks, kinking cracks or crack junctions within a single finite element occur). In this context, the use of equivalent polynomials has been investigated by the authors, and an algorithm to exactly integrate arbitrary polynomials times two Heaviside step functions in quadrilateral domains has been developed and is presented in this paper. Moreover, the algorithm has also been implemented into a software library (DD_EQP) to prove its precision and effectiveness and also the proposed method’s ease of implementation into any existing computational software or framework. The presented algorithm is the first step towards the numerical integration of an arbitrary number of discontinuities in quadrilateral domains. Both the algorithm and the library have a wide application range, in addition to fracture mechanics, from mathematical computing of complex geometric regions, to computer graphics and computational mechanics. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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60 pages, 14142 KiB  
Article
On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
by Adnan Alhaj Hasan, Aleksey A. Kvasnikov, Dmitriy V. Klyukin, Anton A. Ivanov, Alexander V. Demakov, Dmitry M. Mochalov and Sergei P. Kuksenko
Algorithms 2023, 16(4), 200; https://doi.org/10.3390/a16040200 - 07 Apr 2023
Viewed by 3221
Abstract
This paper focuses on antenna modeling using wire-grid and surface triangulation as two of the most commonly used MoM-based approaches in this field. A comprehensive overview is provided for each of them, including their history, applications, and limitations. The mathematical background of these [...] Read more.
This paper focuses on antenna modeling using wire-grid and surface triangulation as two of the most commonly used MoM-based approaches in this field. A comprehensive overview is provided for each of them, including their history, applications, and limitations. The mathematical background of these approaches is briefly presented. Two working algorithms were developed and described in detail, along with their implementations using acceleration techniques. The wire-grid-based algorithm enables modeling of arbitrary antenna solid structures using their equivalent grid of wires according to a specific modeling recommendation proposed in earlier work. On the other hand, the surface triangulation-based algorithm enables calculation of antenna characteristics using a novel excitation source model. Additionally, a new mesh generator based on the combined use of the considered algorithms is developed. These algorithms were used to estimate the characteristics of several antenna types with different levels of complexity. The algorithms computational complexities were also obtained. The results obtained using these algorithms were compared with those obtained using the finite difference time domain numerical method, as well as those calculated analytically and measured. The analysis and comparisons were performed on the example of a rectangle spiral, a spiral, rounded bow-tie planar antennas, biconical, and horn antennas. Furthermore, the validity of the proposed algorithms is verified using the Monte Carlo methodology. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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14 pages, 843 KiB  
Article
Apollonian Packing of Circles within Ellipses
by Carlo Santini, Fabio Mangini and Fabrizio Frezza
Algorithms 2023, 16(3), 129; https://doi.org/10.3390/a16030129 - 24 Feb 2023
Viewed by 1555
Abstract
The purpose of a circle packing procedure is to fill up a predefined, geometrical, closed contour with a maximum finite number of circles. The subject has received considerable attention in pure and applied sciences and has proved to be highly effective in connection [...] Read more.
The purpose of a circle packing procedure is to fill up a predefined, geometrical, closed contour with a maximum finite number of circles. The subject has received considerable attention in pure and applied sciences and has proved to be highly effective in connection with many a problem in logistics and technology. The well-known Apollonian circle packing achieves the packing of an infinite number of mutually tangent smaller circles of decreasing radii, internal or tangent to the outer boundary. Algorithms are available in the literature for the packing of equal-radius circles within an ellipse for global optimization purposes. In this paper, we propose a new algorithm for the Apollonian packing of circles within an ellipse, based on fundamental numerical methods, granting suitable speed, accuracy and stability. The novelty of the proposed approach consists in its applicability to the Apollonian packing of circles within a generic, closed, convex contour, if the parametrization of its outer boundary is given. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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15 pages, 574 KiB  
Article
Learning Data for Neural-Network-Based Numerical Solution of PDEs: Application to Dirichlet-to-Neumann Problems
by Ferenc Izsák and Taki Eddine Djebbar
Algorithms 2023, 16(2), 111; https://doi.org/10.3390/a16020111 - 14 Feb 2023
Cited by 2 | Viewed by 1291
Abstract
We propose neural-network-based algorithms for the numerical solution of boundary-value problems for the Laplace equation. Such a numerical solution is inherently mesh-free, and in the approximation process, stochastic algorithms are employed. The chief challenge in the solution framework is to generate appropriate learning [...] Read more.
We propose neural-network-based algorithms for the numerical solution of boundary-value problems for the Laplace equation. Such a numerical solution is inherently mesh-free, and in the approximation process, stochastic algorithms are employed. The chief challenge in the solution framework is to generate appropriate learning data in the absence of the solution. Our main idea was to use fundamental solutions for this purpose and make a link with the so-called method of fundamental solutions. In this way, beyond the classical boundary-value problems, Dirichlet-to-Neumann operators can also be approximated. This problem was investigated in detail. Moreover, for this complex problem, low-rank approximations were constructed. Such efficient solution algorithms can serve as a basis for computational electrical impedance tomography. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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23 pages, 823 KiB  
Article
Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
by Predrag S. Stanimirović, Bilall I. Shaini, Jamilu Sabi’u, Abdullah Shah, Milena J. Petrović, Branislav Ivanov, Xinwei Cao, Alena Stupina and Shuai Li
Algorithms 2023, 16(2), 64; https://doi.org/10.3390/a16020064 - 18 Jan 2023
Cited by 2 | Viewed by 1795
Abstract
This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction [...] Read more.
This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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16 pages, 309 KiB  
Article
A Symbolic Method for Solving a Class of Convolution-Type Volterra–Fredholm–Hammerstein Integro-Differential Equations under Nonlocal Boundary Conditions
by Efthimios Providas and Ioannis Nestorios Parasidis
Algorithms 2023, 16(1), 36; https://doi.org/10.3390/a16010036 - 07 Jan 2023
Viewed by 1152
Abstract
Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurate measurements of the true state than classical (local) initial [...] Read more.
Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurate measurements of the true state than classical (local) initial and boundary conditions. Closed-form solutions are always desirable, not only because they are more efficient, but also because they can be valuable benchmarks for validating approximate and numerical procedures. This paper presents a direct operator method for solving, in closed form, a class of Volterra–Fredholm–Hammerstein-type integro-differential equations under nonlocal boundary conditions when the inverse operator of the associated Volterra integro-differential operator exists and can be found explicitly. A technique for constructing inverse operators of convolution-type Volterra integro-differential operators (VIDEs) under multipoint and integral conditions is provided. The proposed methods are suitable for integration into any computer algebra system. Several linear and nonlinear examples are solved to demonstrate the effectiveness of the method. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
19 pages, 3304 KiB  
Article
On the Numerical Treatment of the Temporal Discontinuity Arising from a Time-Varying Point Mass Attachment on a Waveguide
by George D. Manolis and Georgios I. Dadoulis
Algorithms 2023, 16(1), 26; https://doi.org/10.3390/a16010026 - 03 Jan 2023
Viewed by 1229
Abstract
A vibrating pylon, modeled as a waveguide, with an attached point mass that is time-varying poses a numerically challenging problem regarding the most efficient way for eigenvalue extraction. The reason is three-fold, starting with a heavy mass attachment that modifies the original eigenvalue [...] Read more.
A vibrating pylon, modeled as a waveguide, with an attached point mass that is time-varying poses a numerically challenging problem regarding the most efficient way for eigenvalue extraction. The reason is three-fold, starting with a heavy mass attachment that modifies the original eigenvalue problem for the stand-alone pylon, plus the fact that the point attachment results in a Dirac delta function in the mixed-type boundary conditions, and finally the eigenvalue problem becomes time-dependent and must be solved for a sequence of time steps until the time interval of interests is covered. An additional complication is that the eigenvalues are now complex quantities. Following the formulation of the eigenvalue problem as a system of first-order, time-dependent matrix differential equations, two eigenvalue extraction methods are implemented and critically examined, namely the Laguerre and the QR algorithms. The aim of the analysis is to identify the most efficient technique for interpreting time signals registered at a given pylon as a means for detecting damage, a procedure which finds application in structural health monitoring of civil engineering infrastructure. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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14 pages, 1145 KiB  
Article
On a Hypothetical Model with Second Kind Chebyshev’s Polynomial–Correction: Type of Limit Cycles, Simulations, and Possible Applications
by Nikolay Kyurkchiev and Anton Iliev
Algorithms 2022, 15(12), 462; https://doi.org/10.3390/a15120462 - 06 Dec 2022
Cited by 16 | Viewed by 1437
Abstract
In this article, we explore a new extended Lienard-type planar system with “corrections” of the second kind Chebyshev’s polynomial Un. The number and type of limit cycles are also studied. The discussion on the y(t)—component of the [...] Read more.
In this article, we explore a new extended Lienard-type planar system with “corrections” of the second kind Chebyshev’s polynomial Un. The number and type of limit cycles are also studied. The discussion on the y(t)—component of the solution of the Lienard system is connected to searching for the solution of the synthesis of filters and electrical circuits. Numerical experiments, depicting our outcomes using CAS MATHEMATICA, are presented. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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13 pages, 1205 KiB  
Article
Modular Stability Analysis of a Nonlinear Stochastic Fractional Volterra IDE
by Azam Ahadi, Zahra Eidinejad, Reza Saadati and Donal O’Regan
Algorithms 2022, 15(12), 459; https://doi.org/10.3390/a15120459 - 05 Dec 2022
Viewed by 1155
Abstract
We define a new control function to approximate a stochastic fractional Volterra IDE using the concept of modular-stability. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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26 pages, 9148 KiB  
Article
Consistency and Convergence Properties of 20 Recent and Old Numerical Schemes for the Diffusion Equation
by Ádám Nagy, János Majár and Endre Kovács
Algorithms 2022, 15(11), 425; https://doi.org/10.3390/a15110425 - 10 Nov 2022
Cited by 5 | Viewed by 1699
Abstract
We collected 20 explicit and stable numerical algorithms for the one-dimensional transient diffusion equation and analytically examined their consistency and convergence properties. Most of the methods used have been constructed recently and their truncation errors are given in this paper for the first [...] Read more.
We collected 20 explicit and stable numerical algorithms for the one-dimensional transient diffusion equation and analytically examined their consistency and convergence properties. Most of the methods used have been constructed recently and their truncation errors are given in this paper for the first time. The truncation errors contain the ratio of the time and space steps; thus, the algorithms are conditionally consistent. We performed six numerical tests to compare their performance and try to explain the observed accuracies based on the truncation errors. In one of the experiments, the diffusion coefficient is supposed to change strongly in time, where a nontrivial analytical solution containing the Kummer function was successfully reproduced. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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31 pages, 1483 KiB  
Article
Stable Evaluation of 3D Zernike Moments for Surface Meshes
by Jérôme Houdayer and Patrice Koehl
Algorithms 2022, 15(11), 406; https://doi.org/10.3390/a15110406 - 31 Oct 2022
Cited by 1 | Viewed by 2532
Abstract
The 3D Zernike polynomials form an orthonormal basis of the unit ball. The associated 3D Zernike moments have been successfully applied for 3D shape recognition; they are popular in structural biology for comparing protein structures and properties. Many algorithms have been proposed for [...] Read more.
The 3D Zernike polynomials form an orthonormal basis of the unit ball. The associated 3D Zernike moments have been successfully applied for 3D shape recognition; they are popular in structural biology for comparing protein structures and properties. Many algorithms have been proposed for computing those moments, starting from a voxel-based representation or from a surface based geometric mesh of the shape. As the order of the 3D Zernike moments increases, however, those algorithms suffer from decrease in computational efficiency and more importantly from numerical accuracy. In this paper, new algorithms are proposed to compute the 3D Zernike moments of a homogeneous shape defined by an unstructured triangulation of its surface that remove those numerical inaccuracies. These algorithms rely on the analytical integration of the moments on tetrahedra defined by the surface triangles and a central point and on a set of novel recurrent relationships between the corresponding integrals. The mathematical basis and implementation details of the algorithms are presented and their numerical stability is evaluated. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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28 pages, 19642 KiB  
Article
Testing Some Different Implementations of Heat Convection and Radiation in the Leapfrog-Hopscotch Algorithm
by Ali Habeeb Askar, Issa Omle, Endre Kovács and János Majár
Algorithms 2022, 15(11), 400; https://doi.org/10.3390/a15110400 - 29 Oct 2022
Cited by 5 | Viewed by 1658
Abstract
Based on many previous experiments, the most efficient explicit and stable numerical method to solve heat conduction problems is the leapfrog-hopscotch scheme. In our last paper, we made a successful attempt to solve the nonlinear heat conduction–convection–radiation equation. Now, we implement the convection [...] Read more.
Based on many previous experiments, the most efficient explicit and stable numerical method to solve heat conduction problems is the leapfrog-hopscotch scheme. In our last paper, we made a successful attempt to solve the nonlinear heat conduction–convection–radiation equation. Now, we implement the convection and radiation terms in several ways to find the optimal implementation. The algorithm versions are tested by comparing their results to 1D numerical and analytical solutions. Then, we perform numerical tests to compare their performance when simulating heat transfer of the two-dimensional surface and cross section of a realistic wall. The latter case contains an insulator layer and a thermal bridge. The stability and convergence properties of the optimal version are analytically proved as well. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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11 pages, 452 KiB  
Article
Computational Modeling of Lymph Filtration and Absorption in the Lymph Node by Boundary Integral Equations
by Alexey Setukha and Rufina Tretiakova
Algorithms 2022, 15(10), 388; https://doi.org/10.3390/a15100388 - 21 Oct 2022
Cited by 2 | Viewed by 1464
Abstract
We develop a numerical method for solving three-dimensional problems of fluid filtration and absorption in a piecewise homogeneous medium by means of boundary integral equations. This method is applied to a simulation of the lymph flow in a lymph node. The lymph node [...] Read more.
We develop a numerical method for solving three-dimensional problems of fluid filtration and absorption in a piecewise homogeneous medium by means of boundary integral equations. This method is applied to a simulation of the lymph flow in a lymph node. The lymph node is considered as a piecewise homogeneous domain containing porous media. The lymph flow is described by Darcy’s law. Taking into account the lymph absorption, we propose an integral representation for the velocity and pressure fields, where the lymph absorption imitates the lymph outflow from a lymph node through a system of capillaries. The original problem is reduced to a system of boundary integral equations, and a numerical algorithm for solving this system is provided. We simulate the lymph velocity and pressure as well as the total lymph flux. The method is verified by comparison with experimental data. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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22 pages, 1822 KiB  
Article
Stability and Convergence Analysis of a Domain Decomposition FE/FD Method for Maxwell’s Equations in the Time Domain
by Mohammad Asadzadeh and Larisa Beilina
Algorithms 2022, 15(10), 337; https://doi.org/10.3390/a15100337 - 20 Sep 2022
Cited by 5 | Viewed by 1455
Abstract
Stability and convergence analyses for the domain decomposition finite element/finite difference (FE/FD) method are presented. The analyses are developed for a semi-discrete finite element scheme for time-dependent Maxwell’s equations. The explicit finite element schemes in different settings of the spatial domain are constructed [...] Read more.
Stability and convergence analyses for the domain decomposition finite element/finite difference (FE/FD) method are presented. The analyses are developed for a semi-discrete finite element scheme for time-dependent Maxwell’s equations. The explicit finite element schemes in different settings of the spatial domain are constructed and a domain decomposition algorithm is formulated. Several numerical examples validate convergence rates obtained in the theoretical studies. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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11 pages, 355 KiB  
Article
Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design
by Masaaki Nagahara, Yu Iwai and Noboru Sebe
Algorithms 2022, 15(9), 322; https://doi.org/10.3390/a15090322 - 09 Sep 2022
Cited by 1 | Viewed by 1690
Abstract
In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. [...] Read more.
In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
27 pages, 1604 KiB  
Article
Adaptive Piecewise Poly-Sinc Methods for Ordinary Differential Equations
by Omar Khalil, Hany El-Sharkawy, Maha Youssef and Gerd Baumann
Algorithms 2022, 15(9), 320; https://doi.org/10.3390/a15090320 - 08 Sep 2022
Cited by 2 | Viewed by 1763
Abstract
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the [...] Read more.
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the adaptive piecewise Poly-Sinc method to function approximation, for which we derived an a priori error estimate for our adaptive method and showed its exponential convergence in the number of iterations. In this work, we show the exponential convergence in the number of iterations of the a priori error estimate obtained from the piecewise collocation method, provided that a good estimate of the exact solution of the ordinary differential equation at the Sinc points exists. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary differential equations. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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26 pages, 7996 KiB  
Article
Optimal Motorcycle Engine Mount Design Parameter Identification Using Robust Optimization Algorithms
by Adel Younis, Fadi AlKhatib and Zuomin Dong
Algorithms 2022, 15(8), 271; https://doi.org/10.3390/a15080271 - 03 Aug 2022
Viewed by 2755
Abstract
Mechanical vibrations have a significant impact on ride comfort; the driver is constantly distracted as a result. Volumetric engine inertial unbalances and road profile irregularities create mechanical vibrations. The purpose of this study is to employ optimization algorithms to identify structural elements that [...] Read more.
Mechanical vibrations have a significant impact on ride comfort; the driver is constantly distracted as a result. Volumetric engine inertial unbalances and road profile irregularities create mechanical vibrations. The purpose of this study is to employ optimization algorithms to identify structural elements that contribute to vibration propagation and to provide optimal solutions for reducing structural vibrations induced by engine unbalance and/or road abnormalities in a motorcycle. The powertrain assembly, swing-arm assembly, and vibration-isolating mounts make up the vibration-isolating system. Engine mounts are used to restrict transferred forces to the motorbike frame owing to engine shaking or road irregularities. Two 12-degree-of-freedom (DOF) powertrain motorcycle engine systems (PMS) were modeled and examined for design optimization in this study. The first model was used to compute engine mount parameters by reducing the transmitted load through the mounts while only considering shaking loads, whereas the second model considered both shaking and road bump loads. In both configurations, the frame is infinitely stiff. The mount stiffness, location, and orientation are considered to be the design parameters. The purpose of this study is to employ computational methods to minimize the loads induced by shaking forces. To continue the optimization process, Grey Wolf Optimizer (GWO), a meta-heuristic swarm intelligence optimization algorithm inspired by grey wolves in nature, was utilized. To demonstrate GWO’s superior performance in PMS, other optimization methods such as a Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) were used for comparison. To minimize the engine’s transmitted force, GWO was employed to determine the optimal mounting design parameters. The cost and constraint functions were formulated and optimized, and promising results were obtained and documented. The vibration modes due to shaking and road loads were decoupled for a smooth ride. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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17 pages, 4219 KiB  
Article
Optimization of Compensation Network for a Wireless Power Transfer System in Dynamic Conditions: A Circuit Analysis Approach
by Manuele Bertoluzzo, Paolo Di Barba, Michele Forzan, Maria Evelina Mognaschi and Elisabetta Sieni
Algorithms 2022, 15(8), 261; https://doi.org/10.3390/a15080261 - 27 Jul 2022
Cited by 4 | Viewed by 1857
Abstract
The paper is focused on the optimization of the compensation network of a wireless power transfer system (WPTS) intended to operate in dynamic conditions. A laboratory prototype of a WPTS has been taken as a reference in this work, allowing for the experimental [...] Read more.
The paper is focused on the optimization of the compensation network of a wireless power transfer system (WPTS) intended to operate in dynamic conditions. A laboratory prototype of a WPTS has been taken as a reference in this work, allowing for the experimental data and all the numerical models here presented to reproduce the configuration of the existing device. The numerical model has been used to perform FEM analysis with variable relative positions of the emitting and receiving coil to simulate the movement in a ‘recharge while driving’ condition. Inductive lumped parameters, i.e., self and mutual inductances computed from FEM results, have been used for the optimal design of the compensation network necessary for the WPTS operation. The optimal design of the resonance circuits has been developed by defining objective functions, aiming to achieve these goals: transmitted power must be as constant as possible when the vehicle is in movement and the electrical efficiency must be satisfactory high in most of the coupling conditions. The performances of the optimized network are finally compared and discussed. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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15 pages, 11309 KiB  
Article
Vector Fitting–Cauchy Method for the Extraction of Complex Natural Resonances in Ground Penetrating Radar Operations
by Andres Gallego, Francisco Roman and Edwin Pineda
Algorithms 2022, 15(7), 235; https://doi.org/10.3390/a15070235 - 03 Jul 2022
Cited by 3 | Viewed by 2227
Abstract
In this paper, we obtain the Complex Natural Resonances of an object from the backscattered response in the frequency domain with a novel rational function approximation method based on both Vector Fitting and Cauchy methods. We determine the system order and an initial [...] Read more.
In this paper, we obtain the Complex Natural Resonances of an object from the backscattered response in the frequency domain with a novel rational function approximation method based on both Vector Fitting and Cauchy methods. We determine the system order and an initial set of poles, which are used as a basis for a rational function approximation. The results from the simulations and experiments show an improvement in the reconstructed signals and the accuracy of the CNRs calculated, with an increased tolerance to the critical Signal-to-Noise Ratio. This is being used in the problem of GPR landmine humanitarian detection in Colombia. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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12 pages, 546 KiB  
Article
Pulsed Electromagnetic Field Transmission through a Small Rectangular Aperture: A Solution Based on the Cagniard–DeHoop Method of Moments
by Martin Štumpf
Algorithms 2022, 15(6), 216; https://doi.org/10.3390/a15060216 - 20 Jun 2022
Cited by 1 | Viewed by 1933
Abstract
Pulsed electromagnetic (EM) field transmission through a relatively small rectangular aperture is analyzed with the aid of the Cagniard–deHoop method of moments (CdH-MoM). The classic EM scattering problem is formulated using the EM reciprocity theorem of the time-convolution type. The resulting TD reciprocity [...] Read more.
Pulsed electromagnetic (EM) field transmission through a relatively small rectangular aperture is analyzed with the aid of the Cagniard–deHoop method of moments (CdH-MoM). The classic EM scattering problem is formulated using the EM reciprocity theorem of the time-convolution type. The resulting TD reciprocity relation is then, under the assumption of piecewise-linear, space–time magnetic-current distribution over the aperture, cast analytically into the form of discrete time-convolution equations. The latter equations are subsequently solved via a stable marching-on-in-time scheme. Illustrative examples are presented and validated using a 3D numerical EM tool. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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