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Mathematical and Computational Applications — Open Access Journal

Mathematical and Computational Applications (ISSN 2297-8747; ISSN 1300-686X for printed edition) is an international peer-reviewed open access journal on the applications of the mathematical and/or computational techniques published quarterly online by MDPI from Volume 21 Issue 1 (2016).

Open Access - free for readers, with article processing charges (APC) paid by authors or their institutions.
High visibility: Indexed in Inspec (IET) and MathSciNet (AMS).
Rapid publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 18 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the second half of 2018).
Recognition of reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Testimonials: See what our authors say about MCA.

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Latest Articles

Open AccessArticle

Spectral Element Method Modeling of Eddy Current Losses in High-Frequency Transformers

by Koen Bastiaens, Mitrofan Curti, Dave C. J. Krop, Sultan Jumayev and Elena A. Lomonova

Math. Comput. Appl. 2019, 24(1), 28; https://doi.org/10.3390/mca24010028 - 21 February 2019

Abstract

This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre–Gauss–Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem. Full article

Open AccessArticle

Trustworthiness in Modeling Unreinforced and Reinforced T-Joints with Finite Elements

by Slimane Ouakka and Nicholas Fantuzzi

Math. Comput. Appl. 2019, 24(1), 27; https://doi.org/10.3390/mca24010027 - 20 February 2019

Abstract

As required by regulations, Finite Element Analyses (FEA) can be used to investigate the behavior of joints which might be complex to design due to the presence of geometrical and material discontinuities. The static behavior of such problems is mesh dependent, thus these results must be calibrated by using laboratory tests or reference data. Once the Finite Element (FE) model is correctly setup, the same settings can be used to study joints for which no reference is available. The present work analyzes the static strength of reinforced T-joints and sheds light on the following aspects: shell elements are a valid alternative to solid modeling; the best combination of element type and mesh density for several configurations is shown; the ultimate static strength of joints can be predicted, as well as when mechanical properties are roughly introduced for some FE topologies. The increase in strength of 12 unreinforced and reinforced (with collar or doubler plate) T-joints subjected to axial brace loading is studied. The present studies are compared with the literature and practical remarks are given in the conclusion section. Full article

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Open AccessArticle

Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

by Sergey A. Davydov, Andrei V. Zemskov and Elena R. Akhmetova

Math. Comput. Appl. 2019, 24(1), 26; https://doi.org/10.3390/mca24010026 - 19 February 2019

Abstract

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes. Full article

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Open AccessFeature PaperArticle

On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces

by Hovik Matevossian

Math. Comput. Appl. 2019, 24(1), 25; https://doi.org/10.3390/mca24010025 - 18 February 2019

Abstract

We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet–Steklov-type and Steklov-type biharmonic problems in the exterior of a compact [...] Read more.

{| x |}^{a}

. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions. Full article

Open AccessArticle

Exact Two-Dimensional Analytical Calculations for Magnetic Field, Electromagnetic Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface Inset Permanent Magnet Machines

by AmirAbbas Vahaj, Akbar Rahideh, Hossein Moayed-Jahromi and AliReza Ghaffari

Math. Comput. Appl. 2019, 24(1), 24; https://doi.org/10.3390/mca24010024 - 17 February 2019

Abstract

This paper presents a two-dimensional analytical model of outer rotor permanent magnet machines equipped with surface inset permanent magnets. To obtain the analytical model, the whole model is divided into the sub-domains, according to the magnetic properties and geometries. Maxwell equations in each sub-domain are expressed and analytically solved. By using the boundary/interface conditions between adjacent sub-regions, integral coefficients in the general solutions are obtained. At the end, the analytically calculated results of the air-gap magnetic flux density, electromagnetic torque, unbalanced magnetic force (UMF), back-electromotive force (EMF) and inductances are verified by comparing them with those obtained from finite element method (FEM). One of the merits of this method in comparison with the numerical model is the capability of rapid calculation with the highest precision, which made it suitable for optimization problems. Full article

Open AccessArticle

An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation

by Dmitry Tarlakovskii and Andrei Zemskov

Math. Comput. Appl. 2019, 24(1), 23; https://doi.org/10.3390/mca24010023 - 6 February 2019

Abstract

This article considers an unsteady elastic diffusion model of Euler–Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum to formulate the problem. A model of unsteady bending for the elastic diffusive Euler–Bernoulli beam was obtained using Hamilton’s variational principle. The Laplace transform on time and the Fourier series expansion by the spatial coordinate were used to solve the obtained problem. Full article

Open AccessArticle

Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach

by Kalyan Das, M. N. Srinivas, V. Madhusudanan and Sandra Pinelas

Math. Comput. Appl. 2019, 24(1), 22; https://doi.org/10.3390/mca24010022 - 5 February 2019

Abstract

In this paper, stochastic analysis of a diseased prey–predator system involving adaptive back-stepping control is studied. The system was investigated for its dynamical behaviours, such as boundedness and local stability analysis. The global stability of the system was derived using the Lyapunov function. The uniform persistence condition for the system is obtained. The proposed system was studied with adaptive back-stepping control, and it is proved that the system stabilizes to its steady state in nonlinear feedback control. The value of the system is described mostly by the environmental stochasticity in the form of Gaussian white noise. We also established some conditions for oscillations of all positive solutions of the delayed system. Numerical simulations are illustrated, and sustained our analytical findings. We concluded that controlled harvesting on the susceptible and infected prey is able to control prey infection. Full article

Open AccessArticle

Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

by Christian Kasumo

Math. Comput. Appl. 2019, 24(1), 21; https://doi.org/10.3390/mca24010021 - 2 February 2019

Abstract

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard a Black–Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton–Jacobi–Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed individual claim amount distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price. Full article

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Open AccessFeature PaperArticle

Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

by Benjamin Brands, Denis Davydov, Julia Mergheim and Paul Steinmann

Math. Comput. Appl. 2019, 24(1), 20; https://doi.org/10.3390/mca24010020 - 1 February 2019

Abstract

The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE

^{2}

method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the [...] Read more.

The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE

^{2}

method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss–Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE

^{2}

framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies. Full article

Open AccessArticle

High-Order Methods Applied to Nonlinear Magnetostatic Problems

by Léo A. J. Friedrich, Mitrofan Curti, Bart L. J. Gysen and Elena A. Lomonova

Math. Comput. Appl. 2019, 24(1), 19; https://doi.org/10.3390/mca24010019 - 29 January 2019

Abstract

This paper presents a comparison between two high-order modeling methods for solving magnetostatic problems under magnetic saturation, focused on the extraction of machine parameters. Two formulations are compared, the first is based on the Newton-Raphson approach, and the second successively iterates the local remanent magnetization and the incremental reluctivity of the nonlinear soft-magnetic material. The latter approach is more robust than the Newton-Raphson method, and uncovers useful properties for the fast and accurate calculation of incremental inductance. A novel estimate for the incremental inductance relying on a single additional computation is proposed to avoid multiple nonlinear simulations which are traditionally operated with finite difference linearization or spline interpolation techniques. Fast convergence and high accuracy of the presented methods are demonstrated for the force calculation, which demonstrates their applicability for the design and analysis of electromagnetic devices. Full article

Open AccessFeature PaperArticle

Data Pruning of Tomographic Data for the Calibration of Strain Localization Models

by William Hilth, David Ryckelynck and Claire Menet

Math. Comput. Appl. 2019, 24(1), 18; https://doi.org/10.3390/mca24010018 - 28 January 2019

Abstract

The development and generalization of Digital Volume Correlation (DVC) on X-ray computed tomography data highlight the issue of long-term storage. The present paper proposes a new model-free method for pruning experimental data related to DVC, while preserving the ability to identify constitutive equations (i.e., closure equations in solid mechanics) reflecting strain localizations. The size of the remaining sampled data can be user-defined, depending on the needs concerning storage space. The proposed data pruning procedure is deeply linked to hyper-reduction techniques. The DVC data of a resin-bonded sand tested in uniaxial compression is used as an illustrating example. The relevance of the pruned data was tested afterwards for model calibration. A Finite Element Model Updating (FEMU) technique coupled with an hybrid hyper-reduction method aws used to successfully calibrate a constitutive model of the resin bonded sand with the pruned data only. Full article

Open AccessFeature PaperArticle

Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

by Clément Olivier, David Ryckelynck and Julien Cortial

Math. Comput. Appl. 2019, 24(1), 17; https://doi.org/10.3390/mca24010017 - 28 January 2019

Abstract

This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients. Full article

Open AccessArticle

On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity

by Maria Korovina, Ilya Smirnov and Vladimir Smirnov

Math. Comput. Appl. 2019, 24(1), 16; https://doi.org/10.3390/mca24010016 - 28 January 2019

Abstract

The re-quantization method—one of the resurgent analysis methods of current importance—is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse Laplace–Borel transform is solved for a particular type of functions with holomorphic coefficients that exponentially grow at zero. Two examples of constructing the uniform asymptotics at infinity for the second- and forth-order differential equations with the help of the re-quantization method and the result obtained in this study are considered. Full article

Open AccessArticle

A Novel Air Quality Monitoring Unit Using Cloudino and FIWARE Technologies

by Yolanda Raquel Baca Gómez, Hugo Estrada Esquivel, Alicia Martínez Rebollar and Daniel Villanueva Vásquez

Math. Comput. Appl. 2019, 24(1), 15; https://doi.org/10.3390/mca24010015 - 24 January 2019

Abstract

Smart City applications aim to improve the quality of life of citizens. Applying technologies of the Internet of Things (IoT) to urban environments is considered as a key of the development of smart cities. In this context, air pollution is one of the most important factors affecting the quality of life and the health of the increasing urban population of industrial societies. For this reason, it is essential to develop applications that allow citizens monitoring the concentration of pollutants and avoid places with high levels of pollution. Due to the increasing use of IoT in different areas, there are arising platforms which deal with the challenges IoT implies, such as FIWARE, which provides technologies to facilitate the development of IoT applications. In this paper, an Air Quality Monitoring Unit using Cloudino and Arduino devices and FIWARE technologies is presented. Through Cloudino and Arduino, the monitoring unit gather data from various sensors and transforms the data in a FIWARE data model. Then, the measurements are sent to the Orion Context Broker (OCB), which is a software component provided by FIWARE. The Orion Context Broker allows to manage and publish the data to be consumed by users and applications. Full article

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Open AccessArticle

A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript

by Luis Acedo

Math. Comput. Appl. 2019, 24(1), 14; https://doi.org/10.3390/mca24010014 - 23 January 2019

Abstract

Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze the underlying structure of an ancient and complex manuscript, known as the Voynich manuscript, which remains undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscripts, we train the network by means of the

α

and

β

-pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices to compare with known languages concerning the frequency of consonant andvowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript. Full article

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Open AccessArticle

Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems

by Francisco Solis

Math. Comput. Appl. 2019, 24(1), 13; https://doi.org/10.3390/mca24010013 - 18 January 2019

Abstract

In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, [...] Read more.

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Open AccessArticle

Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process

by Imelda Trejo, Hristo Kojouharov and Benito Chen-Charpentier

Math. Comput. Appl. 2019, 24(1), 12; https://doi.org/10.3390/mca24010012 - 17 January 2019

Abstract

A new mathematical model is presented to study the effects of macrophages on the bone fracture healing process. The model consists of a system of nonlinear ordinary differential equations that represents the interactions among classically and alternatively activated macrophages, mesenchymal stem cells, osteoblasts, and pro- and anti-inflammatory cytokines. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. Numerical simulations are also presented to support the theoretical results, and to monitor the evolution of a broken bone for different types of fractures under various medical interventions. The model can be used to guide clinical experiments and to explore possible medical treatments that accelerate the bone fracture healing process, either by surgical interventions or drug administrations. Full article

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Open AccessEditorial

Acknowledgement to Reviewers of MCA in 2018

by MCA Editorial Office

Math. Comput. Appl. 2019, 24(1), 11; https://doi.org/10.3390/mca24010011 - 16 January 2019

Abstract

Rigorous peer-review is the corner-stone of high-quality academic publishing [...] Full article

Open AccessArticle

Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

by Raghda A. M. Attia, Dianchen Lu and Mostafa M. A. Khater

Math. Comput. Appl. 2019, 24(1), 10; https://doi.org/10.3390/mca24010010 - 16 January 2019

Abstract

This paper studies the nonlinear fractional undamped Duffing equation. The Duffing equation is one of the fundamental equations in engineering. The geographical areas of this model represent chaos, relativistic energy-momentum, electrodynamics, and electromagnetic interactions. These properties have many benefits in different science fields. The equation depicts the energy of a point mass, which is well thought out as a periodically-forced oscillator. We employed twelve different techniques to the nonlinear fractional Duffing equation to find explicit solutions and approximate solutions. The stability of the solutions was also examined to show the ability of our obtained solutions in the application. The main goals here were to apply a novel computational method (modified auxiliary equation method) and compare the novel method with other methods via the solutions that were obtained by each of these methods. Full article

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Open AccessFeature PaperArticle

Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation

by Amanda Carreño, Luca Bergamaschi, Angeles Martinez, Antoni Vidal-Ferrándiz, Damian Ginestar and Gumersindo Verdú

Math. Comput. Appl. 2019, 24(1), 9; https://doi.org/10.3390/mca24010009 - 15 January 2019

Abstract

In nuclear engineering, the

λ

In nuclear engineering, the

λ

-modes associated with the neutron diffusion equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied. Full article

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Numerical and Evolutionary Optimization Guest Editors: Adriana Lara, Marcela Quiroz, Efrén Mezura-Montes, Oliver Schütze
Deadline: 1 March 2019

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Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics Guest Editors: Felix Fritzen, David Ryckelynck
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Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications Guest Editor: Nicholas Fantuzzi
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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert