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Wyniki wyszukiwania dla: MICKENS-TYPE FINITE-DIFFERENCE SCHEME
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublikacjaDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Dane BadawczeThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Dane BadawczeThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Dane BadawczePresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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Dataset of phase portraits of the fractional prey-predator model with Holling type-II interaction (without predator harvesting)
Dane BadawczeThe need for a fractional generalization of a given classical model is often due to new behaviors which cannot be taken into account by the model. In this situation, it can be useful to look for a fractional deformation of the initial system, trying to fit the fractional exponent of differentiation in order to catch properly the data.
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublikacjaIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublikacjaIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Finite-difference time-domain analyses of active cloaking for electrically-large objects
PublikacjaInvisibility cloaking devices constitute a unique and potentially disruptive technology, but only if they can work over broad bandwidths for electrically-large objects. So far, the only known scheme that allows for broadband scattering cancellation from an electrically-large object is based on an active implementation where electric and magnetic sources are deployed over a surface surrounding the object, but whose ‘switching on’...
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Lax-Wendroff and McCormack Schemes for Numerical Simulation of Unsteady Gradually and Rapidly Varied Open Channel Flow
PublikacjaTwo explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free...
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Recurrence scheme for FDTD-compatible discrete Green's function derived based on properties of Gauss hypergeometric function
PublikacjaIn this paper, the formulation of one-dimensional FDTD (Finite-difference time-domain)-compatible discrete Green's function (DGF) is derived based on the Gauss hypergeometric function (GHF). The properties of GHF make it possible to derive the recurrence scheme only in the time domain for the DGF generation. Furthermore, this recurrence scheme is valid for any stable time-step size and can be implemented using standard numerical...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublikacjaWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublikacjaIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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A Fortran-95 algorithm to solve the three-dimensional Higgs boson equation in the de Sitter space-time
Dane BadawczeA numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space-time is designed. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0,1)U(1,2], which considers a generalized potential and a time-dependent diffusion...
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublikacjaThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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Coupled Urban Areas Inundation Model with Interaction Between Storm Water System and Surface Flow - Case Study of Sea Level Impact on Seaside Areas Flooding
PublikacjaInundations are becoming more frequent than ever. What is connected with increasing area of impervious surface in cities. This makes predicting urban flooding and its scale especially important. At the seaside we observe additional conditions such as sea level that makes accurate numerical modelling of issue even harder. With complex approach to the matter which is simultaneous calculation of storm water conduit flow and overland...
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublikacjaThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublikacjaWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublikacjaIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Straightened characteristics of McKendrick-von Foerster equation
PublikacjaWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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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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Numerical solutions for blood flow in elastic vessels
PublikacjaWe consider the differential–algebraic system for the blood flow and pressure in the systemic arteries. By the operator splitting method, we transform the system into the hyperbolic one, introduce the bicharacteristics, and perform the time–space nonuniform discretization, obtaining the innovative difference scheme. Our results are illustrated with numerical experiments.
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Coupled nonlinear Schrödinger equations in optic fibers theory
PublikacjaIn this paper a detailed derivation and numerical solutions of CoupledNonlinear Schr¨odinger Equations for pulses of polarized electromagnetic wavesin cylindrical fibers has been reviewed. Our recent work has been compared withsome previous ones and the advantage of our new approach over other methods hasbeen assessed. The novelty of our approach lies is an attempt to proceed withoutloss of information within the frame of basic...
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Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations
PublikacjaThe paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not...
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Inverse Flood Routing Using Simplified Flow Equations
PublikacjaThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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A fast high-resolution 3-D Finite Difference Time-Domain scheme with macromodels.
PublikacjaZaprezentowano szybki trójwymiarowy wysokorozdzielczy algorytm różnic skończonych w dziedzinie czasu. Zwiększona rozdzielczość osiągnięta została poprzez połączenie standardowego schematu FDTD z makromodelami silnie zagęszczonych objętości stworzonych przez zastosowanie redukcji rzędu modelu. Nowy schemat FDTD z makromodelami jest wyprowadzony. Koszt numeryczny nowej metody jest wyestymowany. Doskonałe wyniki zostały zaobserwowane...
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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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The finite-difference simulation of x-rays propagation through a system of lenses
PublikacjaThe propagation of X-ray waves through an optical system consisting of 33 aluminum X-ray refractive lenses is considered. For solving the problem, a finite-difference method is suggested and investigated. It is shown that very small steps of the difference grid are necessary for reliable computation of propagation of X-ray waves through the system of lenses. It is shown that the wave phase is a function very quickly increasing...
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Augmented speed control scheme of dual induction motors with mutual flux angle control loop
PublikacjaThis paper proposes an augmented speed control scheme of dual induction motors fed by a five-leg voltage source inverter (VSI) with a common/shared-leg. An additional control loop is proposed here and based on the mutual flux angle – the difference between flux angular positions of the IMs. The main purpose of this research is to minimize the energy losses in the common inverter leg by controlling the mutual flux angle, at equal...
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On Radar DoA Estimation and Tilted Rotating Electronically Scanned Arrays
PublikacjaWe consider DoA estimation in a monopulse radar system employing a tilted rotating array. We investigate the case of nonzero steering angles, in which case the mapping between the target’s azimuth and elevation in the global coordinate system and their counterparts in the array local coordinate system becomes increasingly nonlinear and coupled. Since estimating the azimuth using coherently integrated signals might be difficult because...
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Optimizing the computation of a parallel 3D finite difference algorithm for graphics processing units
PublikacjaThis paper explores the possibilities of using a graphics processing unit for complex 3D finite difference computation via MUSTA‐FORCE and WENO algorithms. We propose a novel algorithm based on the new properties of CUDA surface memory optimized for 2D spatial locality and compare it with 3D stencil computations carried out via shared memory, which is currently considered to be the best approach. A case study was performed for...
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Applications of the discrete green's function in the finite-difference time-domain method
PublikacjaIn this paper, applications of the discrete Green's function (DGF) in the three-dimensional (3-D) finite-difference time-domain (FDTD) method are presented. The FDTD method on disjoint domains was developed employing DGF to couple the subdomains as well as to compute the electromagnetic field outside these subdomains. Hence, source and scatterer are simulated in separate subdomains and updating of vacuum cells, being of little...
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The finite difference methods of computation of X-rays propagation through a system of many lenses
PublikacjaThe propagation of X-ray waves through an optical system consisting of many beryllium X-ray refrac- tive lenses is considered. In order to calculate the propagation of electromagnetic in the optical sys- tem, two differential equations are considered. First equation for an electric field of a monochromatic wave and the second equation derived for complex phase of the same electric The propagation of X-ray waves through an optical system...
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Finite-difference analysis of a loaded hemispherical resonator
PublikacjaPrzedstawiono analizę osiowo symetrycznej struktury otwartego rezonatora he-misferycznego zawierającego warstwowe ośrodki dielektryczne. W analizie wy-korzystano metodę różnic skończonych w dziedzinie częstotliwości (FDFD). Wcelu osiągnięcia wysokiej dokładności obliczeń zastosowano zaawansowane me-tody modelowania warunków brzegowych i granicznych.
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Data obtained by numerical simulation for X-ray focusing using a finite difference method
Dane BadawczeThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied.
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Simple and accurate field interpolation in finite difference methods
PublikacjaW artykule wprowadzono nową metodę interpolacji pól w metodzie różnic skończonych. Metoda jest prosta i daje wyniki bardziej dokładne niż w przypadku interpolacji liniowej. Proponowana metoda interpolacji może zostać użyta do poprawienia dokładności takich metod, jak subgridding.
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Application of hybrid finite-difference mode-matching method to analysis of structures loaded with axially-symmetrical posts
PublikacjaW artykule przedstawiono nową metodę hybrydową do analizy układów falowodowych zawierających dowolne konfiguracje obiektów osiowo-symetrycznych. Metoda oparta jest na połączeniu metody różnic skończonych, metody dopasowania rodzajów oraz iteracyjnej procedury rozpraszania. W pracy przedstawiono badania zbieżności metody. Uzyskane wyniki numeryczne porównano z wynikami odniesienia. Duża zgodność wyników potwierdziła poprawność opracowanego...
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Efficient finite difference analysis of microstructured optical fibers [on line]
PublikacjaW pracy przedstawiono nową technikę numerycznej analizy mikrostruktur światłowodowych. Technika ta polega na połączeniu metody różnic skończonych i dyskretnych rozwinięć funkcyjnych. Pozwala to na zmniejszenie rozmiaru macierzy powstających przy analizie problemu, a jednocześnie na bezpośrednią implementację radiacyjnych warunków brzegowych. Testy algorytmu przeprowadzono dla kilku wybranych struktur, uzyskując bardzo dobrą zgodność...
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Finite difference approximations for nonlinear first order partial differential equations
PublikacjaKlasyczne rozwiązania nieliniowych równań różniczkowych o pochodnych cząst-kowych pierwszego rzędu są aproksymowane za pomocą równań quasiliniowych uk-ładów równań różniczkowych. Dowód zbieżności wykorzystuje metody porównawcze
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3-D finite-difference time-domain modelling of ground penetrating radar for identification of rebars in complex reinforced concrete structures
PublikacjaThis paper presents numerical and experimental investigations to identify reinforcing bars using the ground penetrating radar (GPR) method. A novel element of the paper is the inspection of different arrangements of reinforcement bars. Two particular problems, i.e. detection of few adjacent transverse bars and detection of a longitudinal bar located over or under transverse reinforcement, have been raised. An attention was also...
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A higher order transversely deformable shell-type spectral finite element for dynamic analysis of isotropic structures
PublikacjaThis paper deals with certain aspects related to the dynamic behaviour of isotropic shell-like structures analysed by the use of a higher order transversely deformable shell-type spectral finite element newly formulated and the approach known as the Time-domain Spectral Finite Element Method (TD-SFEM). Although recently this spectral approach is reported in the literature as a very powerful numerical tool used to solve various...
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Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches
PublikacjaThis paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite...
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A simple finite difference approach using unstructured meshes from FEM mesh generators.
PublikacjaPrezentujemy metodologię używania dwuwymiarowych różnic skończonych wykorzystujących siatki trójkątne z metody FEM. Określiliśmy wyrażenia opisujące pierwsząi drugą pochodną w oparciu o wartości pól w saśiednich punktach. Metodę przetestowaliśmy na strukturze rezonatora z prostokątnym rdzeniem dielektrycznym.
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Improving the accuracy of subgridding scheme in finite differences method based on Legendre polynomials expansion
PublikacjaIn this article the Legendre polynomials have been used to interpolate the field at the boundary of the meshes of different densities. The numerical verification of the proposed technique has been carried out in frequency domain. It has been shown that the accuracy of the presented method is very high and stable - the error monotonically decreases as a function of the refinement factor.
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Efficient Multiscale Finite Difference Frequency Domain Analysis Using Multiple Macromodels with Compressed Boundaries
PublikacjaW niniejszym artykule zaprezentowany został nowatorski pomysł na zmniejszenie numerycznej złożoności metody różnic skończonych przy użyciu wielu makromodeli. Skuteczność techniki macromodelingu zależy od liczby portów modelu. Aby zwiększyć efektywność algorytmu, próbki pola na granicy makromodeli są zastępowane przez amplitudy wielomianów Legendre'a. Przedefiniowanie problemu w taki sposób powoduje znaczną redukcję czasu analizy....
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Approximate analytical boundary conditions for efficient finite difference frequency domain simulations in cylindrical coordinates
PublikacjaW artykule zaprezentowano prostą technikę analizy rezonatora otwartego. Algorytm łączy w sobie metodę różnic skończonych i rozwinięć funkcyjnych , umożliwiając implementację warunków brzegowych symulujących otwartą przestrzeń. Metoda testowana była w analizie rezonatorów o różnych wymiarach,a otrzymane wyniki dobrze zgadzały się z rezultatami innych metod.
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A new conformal radiation boundary condition for high accuracy finite difference analysis of open waveguides
PublikacjaW publikacji zaprezentowano nowe warunki brzegowe przeznaczone dla precyzyjnej analizy otwartych prowadnic falowych metodą różnic skończonych. Praca zawiera również liczne przykłady zastosowania proponowanej techniki oraz porównanie otrzymanych rezultatów numerycznych z wynikami otrzymywanymi przy użyciu innych metod.
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Projection framework for hybrid methods derived from finite difference operators in time and frequency domain
PublikacjaW artykule przedstawiono ogólną koncepcję tworzenia algorytmów hybrydowych na bazie operatorowego sformułowania metody różnic skończonych. Wykorzystano koncepcję projekcji ortogonalnej w przestrzeni skończeniewymiarowej w celu modyfilacji pierwotnego sformułowania.
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Analysis of waveguide junctions containing axially-symetrical posts using hybrid finite-difference mode-matching technique
PublikacjaArtykuł opisuję hybrydową metodę analizy złącz falowodowych zawierających osiowo-symetryczne obiekty rozpraszające. Metoda jest oparta na metodzie dopasowania rodzajów oraz metodzie różnic skończonych w dziedzinie częstotliwości.
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Hybrid finite-difference/mode-matching method for analysis of scattering from arbitrary configuration of rotationally-symmetrical posts
PublikacjaW artykule przedstawiona została metoda hybrydowa pozwalająca na analizę zjawiska rozpraszania od dowolnej konfiguracji obiektów o osiowej symetrii. Proponowana metoda oparta jest na reprezentacji obiektu lub dowolnej konfiguracji obiektów poprzez zastępczy obiekt kulisty ze znanymi warunkami brzegowymi. W analizie pojedynczego obiektu wykorzystana została metoda hybrydowa stanowiąca połączenie metody różnic skończonych z metodą...
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Application of a hybrid finite difference-mode matching method to the analysis of circular cavities loaded with cylindrical metallic objects
PublikacjaW artykule przedstawiono badania rezonatorów cylindrycznych zawierających obiekty cylindryczne o dowolnym przekroju poprzecznym z wykorzystaniem metody hybrydowej stanowiącej połączenie metody różnic skończonych z metodą dopasowania rodzajów. W ramach badań określono częstotliwości rezonansowe dla wybranych struktur rezonatorów. Wyniki numeryczne zostały zweryfikowane eksperymentalnie.