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Wyniki wyszukiwania dla: COMPUTATIONAL ELECTROMAGNETICS, ELECTROMAGNETIC PROPAGATION, MAXWELL’S EQUATIONS, FRACTIONAL CALCULUS
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublikacjaIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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Simulation of Wave Propagation in Media Described by Fractional-Order Models
PublikacjaIn this paper, algorithms for simulation of the wave propagation in electromagnetic media described by fractional-order (FO) models (FOMs) are presented. Initially, fractional calculus and FO Maxwell's equations are introduced. The problem of the wave propagation is formulated for media described by FOMs. Then, algorithms for simulation of the non-monochromatic wave propagation are presented which employ computations in the time...
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Signal propagation in electromagnetic media described by fractional-order models
PublikacjaIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublikacjaIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublikacjaThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublikacjaIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublikacjaIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Systems of Nonlinear Fractional Differential Equations
PublikacjaUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
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Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative
PublikacjaIn this paper, wave propagation is considered in a medium described by a fractional-order model, which is formulated with the use of the two-sided fractional derivative of Ortigueira and Machado. Although the relation of the derivative to causality is clearly specified in its definition, there is no obvious relation between causality of the derivative and causality of the transfer function induced by this derivative. Hence, causality...
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Functional delay fractional equations
PublikacjaIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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GENERAL DYNAMIC PROJECTING OF MAXWELL EQUATIONS
PublikacjaA complete – system of Maxwell equations is splitting into independent subsystems by means of a special dynamic projecting technique. The technique relies upon a direct link between field components that determine correspondent subspaces. The explicit form of links and corresponding subspace evolution equations are obtained in conditions of certain symmetry, it is illustrated by examples of spherical and quasi-one-dimensional waves.
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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Simulation of Signal Propagation Along Fractional-Order Transmission Lines
PublikacjaIn this paper, the simulation method of signal propagation along fractional-order (FO) transmission lines is presented. Initially, fractional calculus and the model of FO transmission line are introduced. Then, the algorithm allowing for simulation of the nonmonochromatic wave propagation along FO transmission lines is presented. It employs computations in the frequency domain, i.e., an analytical excitation is transformed to the...
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Boundary problems for fractional differential equations
PublikacjaIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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Electromagnetic-based derivation of fractional-order circuit theory
PublikacjaIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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Fractional differential equations with causal operators
PublikacjaWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF NONLINEAR FRACTIONAL INTEGRAL EQUATIONS
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Some applications of fractional order calculus
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Object oriented grid computing for computational electromagnetics
PublikacjaArtykuł opisuje bibliotekę WiCommGrid napisaną w języku java, która realizuje ideę wymiany informacji pomiędzy węzłami środowiska rozproszonego z zastosowaniem programowania zorientowanego obiektowo. Biblioteka ta przystosowana jest do współdziałania z wieloma systemami operacyjnymi oraz z rożnym środowiskiem sprzętowym. Zbudowaną aplikację zastosowano do zrównoleglonych obliczeń rozkładu pola elektromagnetycznego w oparciu o algorytm...
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublikacjaIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Theoretical and computational analysis of nonlinear fractional integro-differential equations via collocation method
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublikacjaWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Reduced order models in computational electromagnetics (in memory of Ruediger Vahldieck)
PublikacjaThis paper reviews research of Ruediger Vahldieck's group and the group at the Gdansk University of Technology in the area of model order reduction techniques for accelerating full-wave simulations. The applications of reduced order models to filter design as well as of local and nested(multilevel) macromodels for solving 3D wave equations and wave-guiding problems using finite difference and finite element methods are discussed.
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublikacjaIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Modelling heat transfer in heterogeneous media using fractional calculus
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Modeling Heat Transfer in Heterogeneous Media Using Fractional Calculus
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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublikacjaThe paper presents research on the approximation of variable-order fractional operators by recurrent neural networks. The research focuses on two basic variable-order fractional operators, i.e., integrator and differentiator. The study includes variations of the order of each fractional operator. The recurrent neural network architecture based on GRU (Gated Recurrent Unit) cells functioned as a neural approximation for selected...
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublikacjaIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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Multimodal Genetic Algorithm with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublikacjaIn this contribution, a new genetic-algorithm-based method of finding roots and poles of a complex function of a complex variable is presented. The algorithm employs the phase analysis of the function to explore the complex plane with the use of the genetic algorithm. Hence, the candidate regions of root and pole occurrences are selected and verified with the use of discrete Cauchy's argument principle. The algorithm is evaluated...
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Fractional differential equations with deviating arguments
PublikacjaDla równań różniczkowych typu ułamkowego, zostały podane warunki dostateczne na istnienie jednego rozwiązania lub rozwiazań ekstremalnych. Nierówności różniczkowe są też doskutowane.
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Fractional Calculus Evaluation of Hyaluronic Acid Crosslinking in a Nanoscopic Part of Articular Cartilage Model System
PublikacjaThis work presents a study of the mechanism of physical crosslinking of hyaluronic acid in the presence of common phospholipids in synovial joint organ systems. Molecular dynamic simulations have been executed to understand the formation of hyaluronan networks at various phospholipid concentrations. The results of the simulations suggest that the mechanisms exhibit subdiffusion characteristics. Transportation quantities derive...
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Very accurate time propagation of coupled Schrödinger equations for femto- and attosecond physics and chemistry, with C++ source code
PublikacjaIn this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schrödinger equations with a time-dependent Hamiltonian. It can be used to describe time-dependent processes in molecular systems after excitation by femto- and attosecond laser pulses. It also works with an arbitrary user supplied Hamiltonian and can be used...
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Existence results to delay fractional differential equations with nonlinear boundary conditions
PublikacjaPraca dotyczy problemów brzegowych dla ułamkowych równań różniczkowych z opóźnionym argumentem. Podano warunki dostateczne na istnienie rozwiązań ekstremalnych takich zagadnień.
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Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublikacjaThis paper presents results concerning numerical solutions to a fractional neutron point kinetics model for a nuclear reactor. The paper discusses and expands on results presented in (Espinosa-Paredes et al., 2011). The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and a numerical solution using the Edwards’ method was proposed (Edwards et al., 2002). The mathematical model...
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Initial value problems for neutral fractional differential equations involving a Riemann-Liouville derivative
PublikacjaBadano równania neutralne typu ułamkowego z odchylonym argumentem. Podano warunki dostateczne na istnienie jednego rozwiązania.
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GPU-Accelerated LOBPCG Method with Inexact Null-Space Filtering for Solving Generalized Eigenvalue Problems in Computational Electromagnetics Analysis with Higher-Order FEM
PublikacjaThis paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact nullspace filtering approach to find eigenvalues in electromagnetics analysis with higherorder FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from...
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Multimodal Particle Swarm Optimization with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublikacjaIn this paper, a new meta-heuristic method of finding roots and poles of a complex function of a complex variable is presented. The algorithm combines an efficient space exploration provided by the particle swarm optimization (PSO) and the classification of root and pole occurrences based on the phase analysis of the complex function. The method initially generates two uniformly distributed populations of particles on the complex...
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublikacjaAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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A Note on Fractional Curl Operator
PublikacjaIn this letter, we demonstrate that the fractional curl operator, widely used in electromagnetics since 1998, is essentially a rotation operation of components of the complex Riemann–Silberstein vector representing the electromagnetic field. It occurs that after the wave decomposition into circular polarisations, the standard duality rotation with the angle depending on the fractional order is applied to the left-handed basis vector...
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Fractional Order Dynamic Positioning Controller
PublikacjaImproving the performance of Dynamic Positioning System in such applications as station keeping, position mooring and slow speed references tracking requires improving the position and heading control precision. These goals can be achieved through the improvement of the ship control system. Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control...
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Krylov Space Iterative Solvers on Graphics Processing Units
PublikacjaCUDA architecture was introduced by Nvidia three years ago and since then there have been many promising publications demonstrating a huge potential of Graphics Processing Units (GPUs) in scientific computations. In this paper, we investigate the performance of iterative methods such as cg, minres, gmres, bicg that may be used to solve large sparse real and complex systems of equations arising in computational electromagnetics.
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Variable Order Differential Models of Bone Remodelling * *This work was supported by FCT, through IDMEC, under LAETA, projects UID/EMS/50022/2013, BoneSys, joint Polish-Portuguese project Modelling and controlling cancer evolution using fractional calculus, PERSEIDS (PTDC/EMS-SIS/0642/2014) and IF/00653/2012
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Scattering by parallel cylindrical posts with conducting strips. W: Pro- gress in electromagnetics research. Ed. J.A. Kong. Cambridge, Massachusett/ USA/: EMW Publ.**2003 s. 305-333, 18 rys. 5 tabl. bibliogr. 14 poz. Electromagnetic Waves. PIER [nr] 43. Rozpraszanie na równoległych metalizowanych obiektach cylindrycznych.
PublikacjaRozwinięto teorię rozpraszania fali elektromagnetycznej w obszarach otwar-tych i zamkniętych na metalizowanych obiektach cylindrycznych przy użyciuzmodyfikowanej procedury iteracyjnej i metody dopasowania rodzajów. W wynikuanalizy uzyskano pole rozproszone w przypadku struktur otwartych oraz odpo-wiedzi częstotliwościowe współczynników odbicia i transmisji w prostokąt-nych złączach falowodowych. Obrót i przemieszczenie...
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Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid
PublikacjaThis paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...
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Directed electromagnetic pulse dynamics: projecting operators method
PublikacjaIn this article, we consider a one-dimensional model of electromagnetic pulse propagation in isotropic media, takinginto account a nonlinearity of the third order. We introduce a method for Maxwell's equation transformation on thebasis of a complete set of projecting operators. The operators correspond to wave dispersion branches including thedirection of propagation. As the simplest result of applying the method, we derive a system...
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Local dynamics of fluids and dielectrics as the foundation of signal-carrying wave properties
PublikacjaThis paper develops an original approach to fundamental problems of classical linear acoustics and electromagnetics, proving a crucial role of doubly-dynamic local properties of a propagation medium in supporting wave-like fields able to carry information signals. The proof is composed of two steps concerning, subsequently, fluid acoustics and dielectric electromagnetics. The first step consists in complementing a common, practically...
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A review on analytical models of brushless permanent magnet machines
PublikacjaThis study provides an in-depth investigation of the use of analytical and numerical methods in analyzing electrical machines. Although numerical models such as the finite-element method (FEM) can handle complex geometries and saturation effects, they have significant computational burdens, are time-consuming, and are inflexible when it comes to changing machine geometries or input values. Analytical models based on magnetic equivalent...
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Finite element matrix generation on a GPU
PublikacjaThis paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The performance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core...
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Multimode systems of nonlinear equations: derivation, integrability, and numerical solutions
PublikacjaWe consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearityinto account. We develop a method for transforming Maxwell's equations based on a complete set ofprojection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with thepropagation direction taken into account. The most important result of applying the method is a systemof equations describing the...
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Fractional problems with advanced arguments
PublikacjaThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...