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Search results for: GENERALIZED EIGENVALUE PROBLEM, FEM, COMPLEX-VALUED SPARSE MATRIX PENCIL, GPU, MAXWELL’S EQUATIONS.
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn 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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Parallel Background Subtraction in Video Streams Using OpenCL on GPU Platforms
PublicationImplementation of the background subtraction algorithm using OpenCL platform is presented. The algorithm processes live stream of video frames from the surveillance camera in on-line mode. Processing is performed using a host machine and a parallel computing device. The work focuses on optimizing an OpenCL algorithm implementation for GPU devices by taking into account specific features of the GPU architecture, such as memory access,...
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On the generalized model of shell structures with functional cross-sections
PublicationIn the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic,...
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FEM modelling of screw displacement pile interaction with subsoil
PublicationPredicting the-settlement characteristics of piles is an important element in the designing of pile foundations. The most reliable method in evaluating pile-soil interaction is the static load test, preferably performed with instrumentation for measuring shaft and pile base resistances. This, however, is a mostly post-implementation test. In the design phase, prediction methods are needed, in which numerical simulations play an...
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Performance Evaluation of Selected Parallel Object Detection and Tracking Algorithms on an Embedded GPU Platform
PublicationPerformance evaluation of selected complex video processing algorithms, implemented on a parallel, embedded GPU platform Tegra X1, is presented. Three algorithms were chosen for evaluation: a GMM-based object detection algorithm, a particle filter tracking algorithm and an optical flow based algorithm devoted to people counting in a crowd flow. The choice of these algorithms was based on their computational complexity and parallel...
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Tomasz Zubowicz dr inż.
PeopleTomasz Zubowicz has received his M.Sc. Eng. degree in Control Engineering from the Faculty of Electrical and Control Engineering at the Gda{\'n}sk University of Technology (GUT) in $2008$. He received his Ph.D. Eng. (Hons.) in the field of Control Engineering from the same faculty in $2019$. In $2012$ he became a permanent staff member at the Department of Intelligent Control and Decision Support Systems at GUT and a member of...
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GPU based implementation of Temperature-Vegetation Dryness Index for AVHRR3 Satellite Data
PublicationPaper presents an implementation of TVDI (Temperature-Vegetation-Dryness Index) algorithm on GPU (Graphics Processing Unit). Calculation of this index is based on LST (Land Surface Temperature) and NDVI (Normalized Difference Vegetation Index). Discussed results are based on multi-spectral imagery retrieved from AVHRR3 sensors for area of Poland. All phases of TVDI implementation on GPU are modified in respect to CUDA platform....
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Implementation of FDTD-compatible Green's function on heterogeneous CPU-GPU parallel processing system
PublicationThis paper presents an implementation of the FDTD-compatible 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, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates...
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An MOR Algorithm Based on the Immittance Zero and Pole Eigenvectors for Fast FEM Simulations of Two-Port Microwave Structures
PublicationThe aim of this article is to present a novel model-order reduction (MOR) algorithm for fast finite-element frequency-domain simulations of microwave two-port structures. The projection basis used to construct the reduced-order model (ROM) comprises two sets: singular vectors and regular vectors. The first set is composed of the eigenvectors associated with the poles of the finite-element method (FEM) state-space system, while...
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On the Peano Theorem for Some Functional Differential Equations on Time Scale
PublicationThe Peano Theorem for some functional differential equations on time scale is proved. Assumptions are of Caratheodory type. Two counter examples for false Peano theorems in the literature are presented.
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MATRIX BIOLOGY
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Generalized Dold sequences on partially-ordered sets
PublicationDold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...
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Bifurcation in von Karman problem for rectangular, thin, elastic plate resting on elastic foundation of Winkler type
PublicationPraca poświęcona jest utracie stateczności prostokątnej, cienkiej płyty sprężystej spoczywającej na podłożu liniowo sprężystym typu Winklera. Płyta jest ściskana równomiernie rozłożonymi obciążeniami na dwóch równoległych brzegach. Wyznaczono obciążenia krytyczne, formy utraty stateczności płyty oraz początkowe zachowanie pokrytyczne. Analizę prowadzono za pomocą analizy funkcjonalnej przy zachowaniu precyzyjnego matematycznego...
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RENOVATION OF ARCHIVE AUDIO RECORDINGS USING SPARSE AUTOREGRESSIVE MODELING AND BIDIRECTIONAL PROCESSING
PublicationThe paper presents a new approach to elimination of broadband noise and impulsive disturbances from archive audio recordings. The proposed adaptive Kalman-like algorithm, based on a sparse autoregressive model of the audio signal, simultaneously detects noise pulses, interpolates the irrevocably distorted samples and performs signal smoothing. It is shown that bidirectional (forward-backward) processing of the archive signal improves...
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Inline Microwave Filters With N+1 Transmission Zeros Generated by Frequency-Variant Couplings: Coupling-Matrix-Based Synthesis and Design
PublicationA general coupling-matrix-based synthesis methodology for inline Nth-order microwave bandpass filters (BPFs) with frequency-variant reactive-type couplings that generate N+1 transmission zeros (TZs) is presented in this brief. The proposed approach exploits the formulation of the synthesis problem as three inverse nonlinear eigenvalue problems (INEVPs) so that the coupling matrix is built from their sets of eigenvalues. For this...
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Performance and Energy Aware Training of a Deep Neural Network in a Multi-GPU Environment with Power Capping
PublicationIn this paper we demonstrate that it is possible to obtain considerable improvement of performance and energy aware metrics for training of deep neural networks using a modern parallel multi-GPU system, by enforcing selected, non-default power caps on the GPUs. We measure the power and energy consumption of the whole node using a professional, certified hardware power meter. For a high performance workstation with 8 GPUs, we were...
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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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Modelling methods in design (CAD, FEM)
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Signal Reconstruction from Sparse Measurements Using Compressive Sensing Technique
PublicationThe paper presents the possibility of applying a new class ofmathematical methods, known as Compressive Sensing (CS) for recovering thesignal from a small set of measured samples. CS allows the faithful recon-struction of the original signal back from fewer random measurements bymaking use of some non-linear reconstruction techniques. Since of all thesefeatures, CSfinds its applications especially in the areas where, sensing is...
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Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body
PublicationGeneralized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or...
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Experimentally feasible semi-device-independent certification of four-outcome positive-operator-valued measurements
PublicationRecently the quantum information science community devoted a lot of attention to the theoretical and practical aspects of generalized measurements, the formalism of all possible quantum operations leading to acquisition of classical information. On the other hand, due to imperfections present in quantum devices, and limited thrust to them, a trend of formulating quantum information tasks in a semi-device-independent manner emerged....
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CFD and FEM model of an underwater vehicle propeller
PublicationDuring the project execution of design and optimization the Remotely Operated Vehicle (ROV) research on its propulsion has been carried out. The entire project was supported by CFD and FEM calculations, which taking into account the characteristics of underwater vehicle. One of the tasks was to optimize the semi-open duct for horizontal propellers, which provided propulsion and controllability in horizontal plane. In order to...
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Journal of Problem Solving
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Open Research DataThe 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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Sparse vector autoregressive modeling of audio signals and its application to the elimination of impulsive disturbances
PublicationArchive audio files are often corrupted by impulsive disturbances, such as clicks, pops and record scratches. This paper presents a new method for elimination of impulsive disturbances from stereo audio signals. The proposed approach is based on a sparse vector autoregressive signal model, made up of two components: one taking care of short-term signal correlations, and the other one taking care of long-term correlations. The method...
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Multipath Complex Root Tracing
PublicationThe problem of multipath root tracing is being addressed in this communication. The self-adaptive complex root tracing algorithm, which was previously utilized for the investigation of various propagation and radiation problems, is analyzed here for the cases when the traced characteristic bifurcates. A procedure of multiroute detection is proposed and demonstrated on the coaxially loaded cylindrical waveguide example.
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Application of the numerical-analytic method for systems of differential equations with parameter
PublicationThe numerical-analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation. We also obtain several existence results for problems with deviations of an argument
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Marek Czachor prof. dr hab.
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Generation of the vorticity Mode by Sound in a Relaxing Maxwell Fluid
PublicationPraca dotyczy nowej teorii akustyki nieliniowej badającej związki modu akustycznego z modem wirowym w płynach z relaksacją maxwellowską. Wyprowadzone zostało równanie ewolucyjne dla modu wirowego wywołanego dźwiękiem, które można stosować zarówno do dźwięków okresowych, jak i aperiodycznych. Przedstawiono przykłady generacji modu wirowego w płynie maxwellowskim z relaksacją wywołanego okresową i aperiodyczną falą dźwiękową.
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Selections and approximations of convex-valued equivariant mappings
PublicationUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.
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Global Complex Roots and Poles Finding Algorithm in C × R Domain
PublicationAn algorithm to find the roots and poles of a complex function depending on two arguments (one complex and one real) is proposed. Such problems are common in many fields of science for instance in electromagnetism, acoustics, stability analyses, spectroscopy, optics, and elementary particle physics. The proposed technique belongs to the class of global algorithms, gives a full picture of solutions in a fixed region ⊂ C × R and...
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FEM simulation of laminate failure in the three point bending
PublicationThe paper presents a FEM simulation of failure of laminate subjected to the three point bending. The numeri-cal model is based on the equivalent single layer approach with 6-paramater non-linear shell theory kinematics. It is implemented in the non-commercial FEM code. The failure initiation is detected with the use of Tsai-Wu criterion. After the failure onset the progressive failure process is modelled through the appropriate...
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The FEM analysis of pressure installation elements after simulated accidental overheating
PublicationThe paper presents innovative analysis focused on the safety aspects of existing pressure installation operation after overheating accidents. Results presented here can be applied in decision-making process concerning further operation of existing pressure installation after cooling system failure. In this paper the results of FEM analysis performed for a straight pipe and 90 degrees elbow, made of super duplex stainless steel,...
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Investigation of Parallel Data Processing Using Hybrid High Performance CPU + GPU Systems and CUDA Streams
PublicationThe paper investigates parallel data processing in a hybrid CPU+GPU(s) system using multiple CUDA streams for overlapping communication and computations. This is crucial for efficient processing of data, in particular incoming data stream processing that would naturally be forwarded using multiple CUDA streams to GPUs. Performance is evaluated for various compute time to host-device communication time ratios, numbers of CUDA streams,...
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Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations
PublicationIn this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems.
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Expedited Gradient-Based Design Closure of Antennas Using Variable-Resolution Simulations and Sparse Sensitivity Updates
PublicationNumerical optimization has been playing an increasingly important role in the design of contemporary antenna systems. Due to the shortage of design-ready theoretical models, optimization is mainly based on electromagnetic (EM) analysis, which tends to be costly. Numerous techniques have evolved to abate this cost, including surrogate-assisted frameworks for global optimization, or sparse sensitivity updates for speeding up local...
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Generalized adaptive comb filters/smoothers and their application to the identification of quasi-periodically varying systems and signals
PublicationThe problem of both causal and noncausal identification of linear stochastic systems with quasiharmonically varying parameters is considered. The quasi-harmonic description allows one to model nonsinusoidal quasi-periodic parameter changes. The proposed identification algorithms are called generalized adaptive comb filters/smoothers because in the special signal case they reduce down to adaptive comb algorithms used to enhance...
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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.
PublicationDeparting 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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A Stabilized Complex LOBPCG Eigensolver for the Analysis of Moderately Lossy EM Structures
PublicationThis letter proposes a stabilized locally optimal block preconditioned conjugate gradient method for computing selected eigenvalues for complex symmetric generalized non-Hermitian eigenproblems. Effectiveness of the presented approach is demonstrated for a moderately lossy dual-mode dielectric resonator, modeled using finite-element method with higher order elements
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A simple way of increasing estimation accuracy of generalized adaptive notch filters
PublicationGeneralized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. It is shown that frequency biases, which arisein generalized adaptive notch filtering algorithms, can be significantly reduced by incorporating in the adaptive loop an appropriately chosen decision delay. The resulting performance...
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An facile Fortran-95 algorithm to simulate complex instabilities in three-dimensional hyperbolic systems
Open Research DataIt is well know that the simulation of fractional systems is a difficult task from all points of view. In particular, the computer implementation of numerical algorithms to simulate fractional systems of partial differential equations in three dimensions is a hard task which has no been solved satisfactorily. Here, we provide a Fortran-95 code to solve...
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Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublicationWe develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6-parameter shell theory. The Cosserat plane stress equations are integrated through-the- thickness under assumption of the Reissner-Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar...
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Electromagnetic Simulation with 3D FEM for Design Automation in 5G Era
PublicationElectromagnetic simulation and electronic design automation (EDA) play an important role in the design of 5G antennas and radio chips. The simulation challenges include electromagnetic effects and long simulation time and this paper focuses on simulation software based on finite-element method (FEM). The state-of-the-art EDA software using novel computational techniques based on FEM can not only accelerate numerical analysis, but...
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Data Compression in Ultrasonic Network Communication via Sparse Signal Processing
PublicationThis document presents the approach of using compressed sensing in signal encoding and information transferring within a guided wave sensor network, comprised of specially designed frequency steerable acoustic transducers (FSATs). Wave propagation in a damaged plate was simulated using commercial FEM-based software COMSOL. Guided waves were excited by means of FSATs, characterized by the special shape of its electrodes, and modeled...
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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Complex Steel Structures 2022
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Density functional approaches to the many-body problem
e-Learning Courses -
Adaptive identification of sparse underwater acoustic channels with a mix of static and time-varying parameters
PublicationWe consider identification of sparse linear systems with a mix of static and time-varying parameters. Such systems are typical in underwater acoustics (UWA), for instance, in applications requiring identi- fication of the acoustic channel, such as UWA communications, navigation and continuous-wave sonar. The recently proposed fast local basis function (fLBF) algorithm provides high performance when identi- fying time-varying systems....
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Variational principles for bound states of Schrödinger and Dirac equations allowing the use of discontinuous trial functions
PublicationWe present systematic constructions of variational principles for energies of bound states of the Schroedinger and Dirac equations. The principles allow the use of discontinuous trial functions. The method employed is based on a generalized Lagrange procedure. Relationships between our variational principles and those available in the literature are established.
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A multithreaded CUDA and OpenMP based power‐aware programming framework for multi‐node GPU systems
PublicationIn the paper, we have proposed a framework that allows programming a parallel application for a multi-node system, with one or more GPUs per node, using an OpenMP+extended CUDA API. OpenMP is used for launching threads responsible for management of particular GPUs and extended CUDA calls allow to manage CUDA objects, data and launch kernels. The framework hides inter-node MPI communication from the programmer who can benefit from...