dr hab. inż. Tomasz Stefański
Employment
- Associate professor at Department of Decision Systems and Robotics
Publications
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total: 89
Catalog Publications
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FPGA Acceleration of Matrix-Assembly Phase of RWG-Based MoM
PublicationIn this letter, the field-programmable-gate-array accelerated implementation of matrix-assembly phase of the method of moments (MoM) is presented. The solution is based on a discretization of the frequency-domain mixed potential integral equation using the Rao-Wilton-Glisson basis functions and their extension to wire-to-surface junctions. To take advantage of the given hardware resources (i.e., Xilinx Alveo U200 accelerator card),...
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Implementation of Coprocessor for Integer Multiple Precision Arithmetic on Zynq Ultrascale+ MPSoC
PublicationRecently, we have opened the source code of coprocessor for multiple-precision arithmetic (MPA). In this contribution, the implementation and benchmarking results for this MPA coprocessor are presented on modern Zynq Ultrascale+ multiprocessor system on chip, which combines field-programmable gate array with quad-core ARM Cortex-A53 64-bit central processing unit (CPU). In our benchmark, a single coprocessor can be up to 4.5 times...
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Simulation of Wave Propagation in Media Described by Fractional-Order Models
PublicationIn 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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Multimodal Particle Swarm Optimization with Phase Analysis to Solve Complex Equations of Electromagnetic Analysis
PublicationIn 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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Analytical Methods for Causality Evaluation of Photonic Materials
PublicationWe comprehensively review several general methods and analytical tools used for causality evaluation of photonic materials. Our objective is to call to mind and then formulate, on a mathematically rigorous basis, a set of theorems which can answer the question whether a considered material model is causal or not. For this purpose, a set of various distributional theorems presented in literature is collected as the distributional...
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Implementation of Addition and Subtraction Operations in Multiple Precision Arithmetic
PublicationIn this paper, we present a digital circuit of arithmetic unit implementing addition and subtraction operations in multiple-precision arithmetic (MPA). This adder-subtractor unit is a part of MPA coprocessor supporting and offloading the central processing unit (CPU) in computations requiring precision higher than 32/64 bits. Although addition and subtraction operations of two n-digit numbers require O(n) operations, the efficient...
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Reduction of Computational Complexity in Simulations of the Flow Process in Transmission Pipelines
PublicationThe paper addresses the problem of computational efficiency of the pipe-flow model used in leak detection and identification systems. Analysis of the model brings attention to its specific structure, where all matrices are sparse. With certain rearrangements, the model can be reduced to a set of equations with tridiagonal matrices. Such equations can be solved using the Thomas algorithm. This method provides almost the same values...
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Application of the discrete Green's function-based antenna simulations for excitation of the total-field/scattered-field interface in the FDTD method
PublicationIn this article, the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) 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 DGF-FDTD, respectively. Then, the excitation of the...
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Analysis of coupled coplanar waveguide with ideal bonding wires between ground conductors
PublicationPrzedstawiono zmodyfikowaną analizę sprzężonych linii koplanarnych prowadzącą do uproszczenia procesu modelowania struktur wieloprzewodowych zawierających poprzecznie ułożone względem kierunku propagacji fali mostki dla wyrównania potencjałów na odseparowanych przestrzennie przewodach. Wyniki analizy teoretycznej zweryfikowano doświadczalnie uzyskując potwierdzenie poprawności zastosowanego podejścia.
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Analytical Expression for the Time-Domain Discrete Green's Function of a Plane Wave Propagating in the 2-D FDTD Grid
PublicationIn this letter, a new closed-form expression for the time-domain discrete Green's function (DGF) of a plane wave propagating in the 2-D finite-difference time-domain (FDTD) grid is derived. For the sake of its verification, the time-domain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2-D total-field/scattered-field (TFSF) FDTD simulations. Such an implementation of...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space 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 non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding 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 state-space discrete-time models, the developed test...
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A New Approach to Stability Evaluation of Digital Filters
PublicationIn this paper, a new numerical method of evaluating digital filter stability is presented. This approach is based on novel root-finding algorithms at the complex plane using the Delaunay triangulation and Cauchy's Argument Principle. The presented algorithm locates unstable zeros of the characteristic equation with their multiplicities. The proposed method is generic and can be applied to a vast range of systems. Verification of...
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Topological extraordinary optical transmission
PublicationΤhe incumbent technology for bringing light to the nanoscale, the near-field scanning optical microscope, has notoriously small throughput efficiencies of the order of 10^4-10^5 or less. We report on a broadband, topological, unidirectionally guiding structure, not requiring adiabatic tapering and, in principle, enabling near-perfect (∼100%) optical transmission through an unstructured single arbitrarily subdiffraction slit at...
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Recurrence scheme for FDTD-compatible discrete Green's function derived based on properties of Gauss hypergeometric function
PublicationIn 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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Analysis of single-ground-plane coplanar waveguide
PublicationW pracy przedstawion metodę analizy rodziny koplanarnych linii transmisyjnych z pojedynczym przewodem masy. Oryginalne, nie znane wcześniej wyniki modelowania numerycznego potwierdzone zostały dużą zgodnością z wynikami pomiarów wykonanych dla struktury falowodu koplanarnego z pojedynczym przewodem masy (SGP-CPW.
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IP Core of Coprocessor for Multiple-Precision-Arithmetic Computations
PublicationIn this paper, we present an IP core of coprocessor supporting computations requiring integer multiple-precision arithmetic (MPA). Whilst standard 32/64-bit arithmetic is sufficient to solve many computing problems, there are still applications that require higher numerical precision. Hence, the purpose of the developed coprocessor is to support and offload central processing unit (CPU) in such computations. The developed digital...
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Analytical Expression for the Time-Domain Green's Function of a Discrete Plane Wave Propagating in the 3-D FDTD Grid
PublicationIn this paper, a closed-form expression for the time-domain dyadic Green’s function of a discrete plane wave (DPW) propagating in a 3-D finite-difference time-domain (FDTD) grid is derived. In order to verify our findings, the time-domain implementation of the DPW-injection technique is developed with the use of the derived expression for 3-D total-field/scattered-field (TFSF) FDTD simulations. This implementation requires computations...
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Open-Source Coprocessor for Integer Multiple Precision Arithmetic
PublicationThis paper presents an open-source digital circuit of the coprocessor for an integer multiple-precision 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,...
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Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis
PublicationIn this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function...
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FPGA implementation of the multiplication operation in multiple-precision arithmetic
PublicationAlthough standard 32/64-bit arithmetic is sufficient to solve most of the scientific-computing problems, there are still problems that require higher numerical precision. Multiple-precision arithmetic (MPA) libraries are software tools for emulation of computations in a user-defined precision. However, availability of a reconfigurable cards based on field-programmable gate arrays (FPGAs) in computing systems allows one to implement...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublicationIn 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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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublicationThe 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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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublicationIn 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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Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
PublicationClassical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies causality in the time domain....
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Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative
PublicationIn 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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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 total-field/scattered-field 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...
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Magnetic switching of Kerker scattering in spherical microresonators
PublicationMagneto-optical materials have become a key tool in functional nanophotonics, mainly due to their ability to offer active tuning between two different operational states in subwavelength structures. In the long-wavelength limit, such states may be considered as the directional forward- and back-scattering operations, due to the interplay between magnetic and electric dipolar modes, which act as equivalent Huygens sources. In this...
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A New Expression for the 3-D Dyadic FDTD-Compatible Green's Function Based on Multidimensional Z-Transform
PublicationIn this letter, a new analytic expression for the time-domain discrete Green's function (DGF) is derived for the 3-D finite-difference time-domain (FDTD) grid. The derivation employs the multidimensional Z-transform 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 multiple-precision...
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublicationIn 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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Hybrid Technique Combining the FDTD Method and Its Convolution Formulation Based on the Discrete Green's Function
PublicationIn this letter, a technique combining the finite-difference time-domain (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...
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Implementation of FDTD-Compatible Green's Function on Graphics Processing Unit
PublicationIn this letter, implementation of the finite-difference time domain (FDTD)-compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closed-form 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...
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Fast implementation of FDTD-compatible green's function on multicore processor
PublicationIn this letter, numerically efficient implementation of the finite-difference time domain (FDTD)-compatible Green's function on a multicore processor is presented. Recently, closed-form 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...
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Nonreciprocal cavities and the time-bandwidth limit: comment
PublicationIn their paper in Optica 6, 104 (2019), Mann et al. claim that linear, time-invariant nonreciprocal structures cannot overcome the time-bandwidth limit and do not exhibit an advantage over their reciprocal counterparts, specifically with regard to their time-bandwidth performance. In this Comment, we argue that these conclusions are unfounded. On the basis of both rigorous full-wave simulations and insightful physical justifications,...
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Topological, nonreciprocal, and multiresonant slow light beyond the time-bandwidth limit
PublicationTopologically protected transport has recently emerged as an effective means to address a recurring problem hampering the field of slow light for the past two decades: its keen sensitivity to disorders and structural imperfections. With it, there has been renewed interest in efforts to overcome the delay-time-bandwidth limitation usually characterizing slow-light devices, on occasion thought to be a fundamental limit. What exactly...
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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Electromagnetic Problems Requiring High-Precision Computations
PublicationAn overview of the applications of multiple-precision arithmetic in CEM was presented in this paper for the first time. Although double-precision floating-point arithmetic is sufficient for most scientific computations, there is an expanding body of electromagnetic problems requiring multiple-precision arithmetic. Software libraries facilitating these computations were described, and investigations requiring multiple-precision...
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Electromagnetic-based derivation of fractional-order circuit theory
PublicationIn 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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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn 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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