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Search results for: discrete green's function (dgf)

Accuracy of the discrete Green's function computations
PublicationThis paper discusses the accuracy of the discrete Green's function (DGF) computations. Recently closedform expression of the DGF and its efficient numerical implementation were presented which facilitate the DGF applications in FDTD simulations of radiation and scattering problems. By carefully comparing the DGF results to those of the FDTD simulation, one can make conclusions about the range of the applicability of the DGF for...

Acceleration of the discrete Green's function computations
PublicationResults of the acceleration of the 3D discrete Green's function (DGF) computations on the multicore processor are presented. The code was developed in the multiple precision arithmetic with use of the OpenMP parallel programming interface. As a result, the speedup factor of three orders of magnitude compared to the previous implementation was obtained thus applicability of the DGF in FDTD simulations was significantly improved.

FDTDCompatible Green's function based on scalar discrete Green's function and multidimensional Ztransform
PublicationIn this contribution, a new formulation of the discrete Green's function (DGF) is presented for the finitedifference timedomain (FDTD) grid. Recently, dyadic DGF has been derived from the impulse response of the discretized scalar wave equation (i.e., scalar DGF) with the use of the multidimensional Ztransform. Its software implementation is straightforward because only elementary functions are involved and a single function...

Windowing of the Discrete Green's Function for Accurate FDTD Computations
PublicationThe paper presents systematic evaluation of the applicability of parametric and nonparametric window functions for truncation of the discrete Green's function (DGF). This function is directly derived from the FDTD update equations, thus the FDTD method and its integral discrete formulation can be perfectly coupled using DGF. Unfortunately, the DGF computations require processor time, hence DGF has to be truncated with appropriate...

Hybridization of the FDTD method with use of the discrete Green's function
PublicationIn this contribution, a hybrid technique is presented which combines the finitedifference timedomain (FDTD) method and the discrete Green's function (DGF) formulation of this method. FDTD is a powerful technique for the analysis of complex penetrable objects but its application is not efficient when the computational domain includes many freespace cells. Therefore, the hybrid method was developed which is applicable to complex...

Accuracy of the Discrete Green's Function Formulation of the FDTD Method
PublicationThis paper reports an evaluation of the accuracy of the discrete Greens function (DGF) formulation of the finitedifference timedomain (FDTD) method. Recently, the closedform expression for the DGF and its efficient numerical implementation were presented, which facilitates applications of the DGF in FDTD simulations of radiation and scattering problems. So far, the accuracy of the DGF formulation of the FDTD method has been...

Applications of the discrete green's function in the finitedifference timedomain method
PublicationIn this paper, applications of the discrete Green's function (DGF) in the threedimensional (3D) finitedifference timedomain (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...

FDTD Simulations on Disjoint Domains with the Use of Discrete Green's Function Diakoptics
PublicationA discrete Green's function (DGF) approach to couple disjoint domains in the finitedifference timedomain (FDTD) grid is developed. In this method, totalfield/scatteredfield (TFSF) FDTD domains are associated with simulated objects whereas the interaction between them is modeled with the use of the DGF propagator. Hence, source and scatterer are simulated in separate domains and updating of vacuum cells, being of little interest,...

Recurrence scheme for FDTDcompatible discrete Green's function derived based on properties of Gauss hypergeometric function
PublicationIn this paper, the formulation of onedimensional FDTD (Finitedifference timedomain)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 timestep size and can be implemented using standard numerical...

Discrete Green's function approach to disjoint domain simulations in 3D FDTD method
PublicationA discrete Green’s function (DGF) approach to couple 3D FDTD subdomains is developed. The totalfield/scatteredfield subdomains are simulated using the explicit FDTD method whilst interaction between them is computed as a convolution of the DGF with equivalent current sources measured over Huygens surfaces. In the developed method, the DGF waveforms are truncated using the Hann’s window. The error varies in the range 65 to 40...

Exact modal absorbing boundary condition for waveguide simulations  discrete Green's function approach
PublicationA modal absorbing boundary condition (ABC) based on the discrete Green's function (DGF) is introduced and applied for termination of waveguides simulated by means of the finitedifference timedomain (FDTD) method. The differences between the developed approach and implementations already demonstrated in the literature are presented. By applying DGF, a consistent theoretical approach to modal ABC in the FDTD method is obtained....

Parallel Implementation of the Discrete Green's Function Formulation of the FDTD Method on a Multicore Central Processing Unit
PublicationParallel implementation of the discrete Green's function formulation of the finitedifference timedomain (DGFFDTD) method was developed on a multicore central processing unit. DGFFDTD avoids computations of the electromagnetic field in freespace cells and does not require domain termination by absorbing boundary conditions. Computed DGFFDTD solutions are compatible with the FDTD grid enabling the perfect hybridization of FDTD...

Hybrid Technique Combining the FDTD Method and Its Convolution Formulation Based on the Discrete Green's Function
PublicationIn this letter, a technique combining the finitedifference timedomain (FDTD) method and its formulation based on the discrete Green's function (DGF) is presented. The hybrid method is applicable to inhomogeneous dielectric structures that are mutually coupled with wire antennas. The method employs the surface equivalence theorem in the discrete domain to separate the problem into a dielectric domain simulated using the FDTD method...

Analysis of radiation and scattering problems with the use of hybrid techniques based on the discrete Green's function formulation of the FDTD method
PublicationIn this contribution, simulation scenarios are presented which take advantage of the hybrid techniques based on the discrete Green's function formulation of the finitedifference timedomain (DGFFDTD) method. DGFFDTD solutions are compatible with the finitedifference grid and can be applied for perfect hybridization of the FDTD method. The following techniques are considered: (i) DGFFDTD for antenna simulations, (ii) DGFbased...

Analytical Expression for the TimeDomain Discrete Green's Function of a Plane Wave Propagating in the 2D FDTD Grid
PublicationIn this letter, a new closedform expression for the timedomain discrete Green's function (DGF) of a plane wave propagating in the 2D finitedifference timedomain (FDTD) grid is derived. For the sake of its verification, the timedomain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2D totalfield/scatteredfield (TFSF) FDTD simulations. Such an implementation of...

Application of the discrete Green's functionbased antenna simulations for excitation of the totalfield/scatteredfield interface in the FDTD method
PublicationIn this article, the discrete Green's function formulation of the finitedifference timedomain (DGFFDTD) method is proposed for simulation of wire antennas irradiating inhomogeneous dielectric scatterers. Surface equivalence theorem in the discrete domain is used to separate the problem into an inhomogeneous domain and a wire antenna that are simulated with the use of FDTD and DGFFDTD, respectively. Then, the excitation of the...

Fast implementation of FDTDcompatible green's function on multicore processor
PublicationIn this letter, numerically efficient implementation of the finitedifference time domain (FDTD)compatible Green's function on a multicore processor is presented. Recently, closedform expression of this discrete Green's function (DGF) was derived, which simplifies its application in the FDTD simulations of radiation and scattering problems. Unfortunately, the new DGF expression involves binomial coefficients, whose computations...

Implementation of FDTDCompatible Green's Function on Graphics Processing Unit
PublicationIn this letter, implementation of the finitedifference time domain (FDTD)compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closedform expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision...

A New Expression for the 3D Dyadic FDTDCompatible Green's Function Based on Multidimensional ZTransform
PublicationIn this letter, a new analytic expression for the timedomain discrete Green's function (DGF) is derived for the 3D finitedifference timedomain (FDTD) grid. The derivation employs the multidimensional Ztransform and the impulse response of the discretized scalar wave equation (i.e., scalar DGF). The derived DGF expression involves elementary functions only and requires the implementation of a single function in the multipleprecision...

Implementation of FDTDcompatible Green's function on heterogeneous CPUGPU parallel processing system
PublicationThis paper presents an implementation of the FDTDcompatible Green's function on a heterogeneous parallel processing system. The developed implementation simultaneously utilizes computational power of the central processing unit (CPU) and the graphics processing unit (GPU) to the computational tasks best suited to each architecture. Recently, closedform expression for this discrete Green's function (DGF) was derived, which facilitates...

Acceleration of the Discrete Green’s Function Formulation of the FDTD Method Based on Recurrence Schemes
PublicationIn this paper, we investigate an acceleration of the discrete Green's function (DGF) formulation of the FDTD method (DGFFDTD) with the use of recurrence schemes. The DGFFDTD method allows one to compute FDTD solutions as a convolution of the excitation with the DGF kernel. Hence, it does not require to execute a leapfrog timestepping scheme in a whole computational domain for this purpose. Until recently, the DGF generation...

Analytical Expression for the TimeDomain Green's Function of a Discrete Plane Wave Propagating in the 3D FDTD Grid
PublicationIn this paper, a closedform expression for the timedomain dyadic Green’s function of a discrete plane wave (DPW) propagating in a 3D finitedifference timedomain (FDTD) grid is derived. In order to verify our findings, the timedomain implementation of the DPWinjection technique is developed with the use of the derived expression for 3D totalfield/scatteredfield (TFSF) FDTD simulations. This implementation requires computations...

Acceleration of the DGFFDTD method on GPU using the CUDA technology
PublicationWe present a parallel implementation of the discrete Green's function formulation of the finitedifference timedomain (DGFFDTD) method on a graphics processing unit (GPU). The compute unified device architecture (CUDA) parallel computing platform is applied in the developed implementation. For the sake of example, arrays of YagiUda antennas were simulated with the use of DGFFDTD on GPU. The efficiency of parallel computations...

Parallel implementation of the DGFFDTD method on GPU Using the CUDA technology
PublicationThe discrete Green's function (DGF) formulation of the finitedifference timedomain method (FDTD) is accelerated on a graphics processing unit (GPU) by means of the Compute Unified Device Architecture (CUDA) technology. In the developed implementation of the DGFFDTD method, a new analytic expression for dyadic DGF derived based on scalar DGF is employed in computations. The DGFFDTD method on GPU returns solutions that are compatible...

Electromagnetic Problems Requiring HighPrecision Computations
PublicationAn overview of the applications of multipleprecision arithmetic in CEM was presented in this paper for the first time. Although doubleprecision floatingpoint arithmetic is sufficient for most scientific computations, there is an expanding body of electromagnetic problems requiring multipleprecision arithmetic. Software libraries facilitating these computations were described, and investigations requiring multipleprecision...

OpenSource Coprocessor for Integer Multiple Precision Arithmetic
PublicationThis paper presents an opensource digital circuit of the coprocessor for an integer multipleprecision arithmetic (MPA). The purpose of this coprocessor is to support a central processing unit (CPU) by offloading computations requiring integer precision higher than 32/64 bits. The coprocessor is developed using the very high speed integrated circuit hardware description language (VHDL) as an intellectual property (IP) core. Therefore,...

Closed forms of the Green's function and the generalized Green's function for the Helmholtz operator on the Ndimensional unit sphere
PublicationPokazano, że funkcję Greena dla operatora Helmholtza na Nwymiarowej sferze jednostkowej można wyrazić przez funcję Gegenbauera pierwszego rodzaju. W tych przypadkach, w których funkcja Greena nie istnieje, skonstruowano uogólnioną funkcję Greena.

Green's function for the wavized Maxwell fisheye problem
PublicationRozpatrzono niezależne od czasu skalarne równanie falowe dla ośrodka typu ''rybie oko'' Maxwella w przestrzeni R^N (N >=2). Pokazano, że równanie to posiada unikalne własności transformacyjne względem inwersji w pewnej klasie hipersfer. Wykorzystano ten fakt do znalezienia zamkniętej postaci funkcji Greena, oraz uogólnionej funkcji Greena, dla wyjściowego równania.

Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized DiracCoulomb Green function
PublicationThe Sturmian expansion of the generalized DiracCoulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive a closedform expression for the magnetizability of an arbitrary discrete state of the relativistic oneelectron atom with a pointlike, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric...

Closedform expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac–Coulomb Green function
PublicationWe present analytical derivation of the closedform expression for the dipole magnetic shielding constant of a Dirac oneelectron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Ze. Calculations are...

Secondorder Stark effect and polarizability of a relativistic twodimensional hydrogenlike atom in the ground state
PublicationThe secondorder Stark effect for a planar Dirac oneelectron atom in the ground state is analyzed within the framework of the RayleighSchrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized DiracCoulomb Green's function. A closedform analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_{2}$...

The modelling method of discretecontinuous systems
PublicationThe paper introduces a method of discretecontinuous systems modelling. In the proposed method a threedimensional system is divided into finite elements in only two directions, with the third direction remaining continuous. The thus obtained discretecontinuous model is described by a set of partial differential equations. General difference equations of discrete system are obtained using the rigid finite element method. The limit...

Implementation of the Boundary Element Method to TwoDimensional Heat Transfer with Thermal Bridge Effects
PublicationThe work presents an application of the boundary element method applied to a twodimensional conductive heat transfer. The algorithm of the method is explained and its advantages are outlined. Green's function as a fundamental solution for Poisson's equation in two dimensions was used and the direct approach was applied. The presented results concern building construction elements as typical cases of thermal bridges. Some properties...

Dyskretnociągła metoda modelowania układów dynamicznych
PublicationW artykule przedstawiono oryginalną metodę modelowania układów dyskretnociągłych. Metoda polega na dyskretyzowaniu układu trójwymiarowego jedynie w dwóch wybranych kierunkach. W trzecim z kierunków układ pozostaje ciągły. Otrzymany w ten sposób model jest modelem dyskretnociągłym. Opisany jest za pomocą równań różniczkowych cząstkowych. Ogólne równania różnicowe układu dyskretnego otrzymano, wykorzystując metodę sztywnych elementów...

Zerorange potentials for Dirac particles: Boundstate problems
PublicationA model in which a massive Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zerorange potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor wave function to certain limiting conditions at the potential centers. Each of these conditions is parametrized by a $2\times2$ Hermitian matrix (or, equivalently, a real scalar and a...

Simulation of Wave Propagation in Media Described by FractionalOrder Models
PublicationIn this paper, algorithms for simulation of the wave propagation in electromagnetic media described by fractionalorder (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 nonmonochromatic wave propagation are presented which employ computations in the time...

Multimodal Genetic Algorithm with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublicationIn this contribution, a new geneticalgorithmbased 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...

Numerical Test for Stability Evaluation of DiscreteTime Systems
PublicationIn this paper, a new numerical test for stability evaluation of discretetime systems is presented. It is based on modern rootfinding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For statespace discretetime models, the developed test...

Algorytmy Optymalizacji Dyskretnej  ed. 2021/2022
eLearning CoursesIn realworld applications, many important practical problems are NPhard, therefore it is expedient to consider not only the optimal solutions of NPhard optimization problems, but also the solutions which are “close” to them (nearoptimal solutions). So, we can try to design an approximation algorithm that efficiently produces a nearoptimal solution for the NPhard problem. In many cases we can even design approximation algorithms...

Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discretetime case
PublicationThis paper addresses the problem of modelbased global stability analysis of discretetime Takagi–Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the classical common quadratic Lyapunov...

Scalar and Vector acoustic fields and sources: a new look
PublicationA study of fundamental problems of the wavefields that are the reaction of fluid continuum on two kinds of primary actions in fluid, then on two kinds of elementary point sources, is presented in this paper, based on the assumption of the physical duality of linear fluid mechanics and the formal symmetry of mathematical description. The two fundamental wavefields generated in fluid by physical point sources are discussed in detail,...

Firing map of an almost periodic input function
PublicationIn mathematical biology and the theory of electric networks the firing map of an integrateandfire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...

A DISCRETECONTINUOUS METHOD OF MECHANICAL SYSTEM MODELLING
PublicationThe paper describes a discretecontinuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a threedimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discretecontinuous model is described...

Numerical modeling of the combustion in a labscale pulverizedcoal fired combustion chamber
PublicationThis work presents results of numerical modeling of the combustion process inside a labscale droptube chamber, designed to investigate the slagging properties of the flue ashes, created through the solid fuel firing. Interaction between turbulence and chemistry is accounted by use of probability density function (PDF). FLUENT inputs for nonpremixed combustion chemistry modeling are defined. A discrete second phase of the coal...

Numerical modeling of the combustion in a labscale pulverizedcoal fired combustion chamber
PublicationThis work presents results of numerical modeling of the combustion process inside a labscale droptube chamber, designed to investigate the slagging properties of the flue ashes, created through the solid fuel firing. Interaction between turbulence and chemistry is accounted by use of probability density function (PDF). FLUENT inputs for nonpremixed combustion chemistry modeling are defined. A discrete second phase of the coal...

Frequency and time domain characteristics of digital control of electric vehicle inwheel drives
PublicationInwheel electric drives are promising as actuators in active safety systems of electric and hybrid vehicles. This new function requires dedicated control algorithms, making it essential to deliver models that reflect better the wheeltorque control dynamics of electric drives. The timing of digital control events, whose importance is stressed in current research, still lacks an analytical description allowing for modeling its...

Stability analysis of interconnected discretetime fractionalorder LTI statespace systems
PublicationIn this paper, a stability analysis of interconnected discretetime fractionalorder (FO) linear timeinvariant (LTI) statespace systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a nonpolynomial characteristic equation must be within the unit circle on the complex zplane. The obtained...

Testing Stability of Digital Filters Using Multimodal Particle Swarm Optimization with Phase Analysis
PublicationIn this paper, a novel metaheuristic method for evaluation of digital filter stability is presented. The proposed method is very general because it allows one to evaluate stability of systems whose characteristic equations are not based on polynomials. The method combines an efficient evolutionary algorithm represented by the particle swarm optimization and the phase analysis of a complex function in the characteristic equation....

Weak Stability of Centred Quadratic Stochastic Operators
PublicationWe consider the weak convergence of iterates of socalled centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vectorvalued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...

Magneticfieldinduced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized DiracCoulomb Green function
PublicationWe consider a Dirac oneelectron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized DiracCoulomb Green function we derive a closedform expression for the electric quadrupole moment induced...