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Search results for: GENERALIZED EIGENVALUE PROBLEM, FEM, COMPLEX-VALUED SPARSE MATRIX PENCIL, GPU, MAXWELL’S EQUATIONS.
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublicationIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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THE USE OF FEM FOR DETERMINATION OF RESONANT FREQUENCIES OF CIRCULAR SAW BLADES WITH INDIRECT TEETH IN GULLETS
PublicationUnderstanding the dynamical properties of the circular saw blade is necessary, since, there is a really need for a stable work at working rotational speeds, which are determined by frequencies at which the circular saw blade tends to vibrate. It was observed that the resonant frequency depend on the circular saw blade shape, a collar diameter and on saw’s teeth shape. In the presented work an attention was paid to the effect of...
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An adaptive approach to the problem of collision avoiding at sea
PublicationW referacie przedstawiono koncepcję podejścia adaptacyjnego do unikania kolizji na morzu. Omawiany problem został sklasyfikowany jako problem uczenia się ze wzmocnieniem. Zamieszczono opis podstawowych technik uczenia się ze wzmocnieniem, ich ograniczeń i sposobu w jaki można zapewnić efektywne uczenie się, mimo wspomnianych ograniczeń. Zaprezentowana metoda została zilustrowana przykładowym procesem konstrukcji modelu i algorytmami...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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On delay differential equations with nonlinear boundary conditions
PublicationStosując metodę iteracji monotonicznych podano warunki dostateczne na istnienie kwazirozwiązań lub ekstremalnych rozwiązań rozpatrywanego zagadnienia. Problem jednoznaczności rozwiązania był również przedmiotem badań. Zajmowano się również nierównościami różniczkowymi z opóżnionymi argumentami.
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublicationIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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Existence and uniqueness for neutral equations with state dependent delays
PublicationW pracy w celu wykazania istnienia i jednoznaczności rozwiązania równania została zaprezentowana metoda porównawcza.
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
PublicationGiven a graph G= (V, E), the subdivision of an edge e=uv∈E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions...
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Efficient Fabry-Perot Open Resonator Analysis by the use of a Scattering Matrix Method
PublicationIn this paper a comparative study of the computational efficiency of two modeling methods applied to the analysis of the plano- and double-concave Fabry-Perot open resonators is presented. In both numerical approaches, a scattering matrix method was applied, which allows splitting the analysis of the resonator into several sections, including the one with a spherical mirror, which requires the largest computing resources. Two modeling...
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A Generalized Framework Towards Structural Mechanics of Three-layered Composite Structures
PublicationThree-layered composite structures find a broad application. Increasingly, composites are being used whose layer thicknesses and material properties diverge strongly. In the perspective of structural mechanics, classical approaches to analysis fail at such extraordinary composites. Therefore, emphasis of the present approach is on arbitrary transverse shear rigidities and structural thicknesses of the individual layers. Therewith...
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Application of Pierson-Moskowitz wave spectrum to solution differential equations of multihull vessel
PublicationMotion of a dynamic system can be generated by different external or internal factors. At mathematical modelling external excitation factors of the most significant effect on the system, are selected. Such external factors are usually called excitations. Response of the system to given excitations is mathematically characterized by a definite transformation called operator of a system. For a broad class of dynamic systems the...
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Monotone iterative method for first-order differential equations at resonance
PublicationThis paper concerns the application of the monotone iterative technique for first-order differential equations involving Stieltjes integrals conditions. We discuss such problems at resonance when the measure in the Stieltjes integral is positive and also when this measure changes the sign. Sufficient conditions which guarantee the existence of extremal, unique and quasi-solutions are given. Three examples illustrate the results.
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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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Minimal and maximal solutions of differential equations with a singularmatrix.
PublicationPraca dotyczy zagadnień początkowych dla układów równań różniczkowych z macierzą osobliwą. Równania różniczkowo-algebraiczne są szczególnym przypadkiem takich zagadnień.Stosując metodę iteracji monotonicznych pokazano, że przy pewnych założeniach problem wyjściowy ma ekstremalne rozwiązania w pewnym sektorze.Teoretyczne rozważania zilustrowano przykładem.
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Compressed Projection Bases for Model-Order Reduction of Multiport Microwave Components Using FEM
PublicationThis paper presents a projection basis compression technique for generating compact reduced-order models (ROM) in the FE analysis of microwave devices. In this approach redundancy is removed from the projection basis by means of the proper orthogonal decomposition technique applied to the projected system of linear equations. Compression allows for keeping the size of a reduced-order model as small as possible without compromising...
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Can we really solve an arch stability problem?
PublicationWe bring attention to the problem of solving nonlinear boundary-value problems for elastic structures such as arches and shells. Here we discuss a classical problem of a shear-deformable arch postbuckling. Considering a postbuckling behaviour of a circular arch we discuss the possibility to find numerically a solution for highly nonlinear regimes. The main attention is paid to the problem of determination of all solutions. The...
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Solution of the dike-break problem using finite volume method and splitting technique
PublicationIn the paper the finite volume method (FVM) is presented for the solution of two-dimensional shallow water equations. These equations are frequently used to simulate the dam-break and dike-break induced flows. The applied numerical algorithm of FVM is based on the wave-propagation algorithm which ensures a stable solution and simultaneously minimizes the numerical errors. The dimensional decomposition according to the coordinate...
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Scanning the special section on technologies of large scale and complex systems
PublicationArtykuł wprowadza do Specjalnej Sekcji pt. Technologies for large scale and complex systems, zamieszczonej w czasopiśmie Annual Reviews in Control, Vol. 32, Issue 1 wydanego w kwietniu 2008. Specjalna sekcja zawiera artykuły będące rozszerzeniem referatów plenarnych wygłoszonych podczas 11th IFAC Symposium on Large Scale Complex Systems, które odbyło się w Gdańsku, Lipiec 2007r.
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Tracking analysis of a generalized adaptive notch filter
PublicationUogólniony adaptacyjny filtr wycinający służy do identyfikacji obiektów zmieniających się w sposób pseudookresowy. W pracy przedstawiono analizę własności śledzących takiego filtru a także omówiono zasady jego strojenia.
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Generalized access control in hierarchical computer network
PublicationThe paper presents the design of the security layer for a distributed system located in the multizone hierarchical computer network. Depending on the zone from which a client’s request comes to the system and the type of the request, it will be either authorized or rejected. There is one common layer for the access to all the business services and interactions between them. Unlike the commonly used RBAC model, this system enforces...
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Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions
PublicationIn this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments α and also in the case when α(t)=t, t∈[0,1]....
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Comments on ''An innovative fast powerful method for tackling electromagnetic eigenvalue problems for multistrip transmission lines''
PublicationPraca stanowi komentarz do publikacji Casanuevy i Garcii dotyczącej techniki szybkiego obliczania charakterystyk dyspersyjnych falowodów z niejednorodnym wypełnieniem. Zwrócono uwagę na niepotrzebną komplikację zagadnienia poprzez zastosowanie techniki rozkładu na wartości szczególne.
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Multi-objective design optimization of antennas for reflection, size, and gain variability using kriging surrogates and generalized domain segmentation
PublicationCost-efficient multi-objective design optimization of antennas is presented. The framework exploits auxiliary data-driven surrogates, a multi-objective evolutionary algorithm for initial Pareto front identification, response correction techniques for design refinement, as well as generalized domain segmentation. The purpose of this last mechanism is to reduce the volume of the design space region that needs to be sampled in order...
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Numerical tests of time-stepping schemes in the context of FEM for 6-field shell dynamics
PublicationThe paper deals with integration of dynamic equations of irregular shells performed with relatively long time steps. Numerical instability appearing often in this kind of analysis motivated the authors to present some studies based on numerical tests referring to convergence problems of finite element analysis as well the applied stability conditions. The analysis is carried out on simulations of shell dynamics with the where the...
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Residue-Pole Methods for Variability Analysis of S-parameters of Microwave Devices with 3D FEM and Mesh Deformation
PublicationThis paper presents a new approach for variability analysis of microwave devices with a high dimension of uncertain parameters. The proposed technique is based on modeling an approximation of system by its poles and residues using several modeling methods, including ordinary kriging, Adaptive Polynomial Chaos (APCE), and Support Vector Machine Regression (SVM). The computational cost is compared with the traditional Monte-Carlo...
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Selection Pressure in the Evolutionary Path Planning Problem
PublicationThis article compares an impact of using various post-selection methods on the selection pressure and the quality of the solution for the problem of planning the path for a moving object using the evolutionary method. The concept of selection pressure and different methods of post-selection are presented. Article analyses behaviour of post-selection for four options of evolutionary algorithms. Based on the results achieved, waveform...
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The searchlight problem for road networks
PublicationWe consider the problem of searching for a mobile intruder hiding in a road network given as the union of two or more lines, or two or more line segments, in the plane. Some of the intersections of the road network are occupied by stationary guards equipped with a number of searchlights, each of which can emit a single ray of light in any direction along the lines (or line segments) it is on. The goal is to detect the intruder,...
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N-point estimators of the Instantaneous Complex Frequency
PublicationIn this paper estimators of the instantaneous complex frequency (ICF) are presented and discussed. The differential approach for the estimation of the ICF is used, therefore the estimators are based on maximally flat N-point FIR filters: differential and delay. The investigation of the filter performance includes static characteristics of ICF estimation and the error of the ICF estimation in the discrete frequency domain.W pracy...
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Non-Destructive Testing of the Longest Span Soil-Steel Bridge in Europe—Field Measurements and FEM Calculations
PublicationThe article describes interdisciplinary and comprehensive non-destructive diagnostic tests of final bridge inspection and acceptance proposed for a soil-steel bridge made of corrugated sheets, being the European span length record holder (25.74 m). As an effect of an original concept a detailed and precise information about the structure short-term response was collected. Periodic diagnostics of bridge deformations was done one...
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Fast EM-Driven Parameter Tuning of Microwave Circuits with Sparse Sensitivity Updates via Principal Directions
PublicationNumerical optimization has become more important than ever in the design of microwave components and systems, primarily as a consequence of increasing performance demands and growing complexity of the circuits. As the parameter tuning is more and more often executed using full-wave electromagnetic (EM) models, the CPU cost of the overall process tends to be excessive even for local optimization. Some ways of alleviating these issues...
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Efficient Complex Root Finding Algorithm for Microwave and Optical Propagation Problems
PublicationArticle relates to the use of innovative root finding algorithm (on a complex plane) to study propagation properties of microwave and optical waveguides. Problems of this type occur not only in the analysis of lossy structures, but also in the study of complex and leaky modes (radiation phenomena). The proposed algorithm is simple to implement and can be applied for functions with singularities and branch cuts in the complex plane...
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On Von Karman Equations and the Buckling of a Thin Circular Elastic Plate
PublicationWe shall be concerned with the buckling of a thin circular elastic plate simply supported along a boundary, subjected to a radial compressive load uniformly distributed along its boundary. One of the main engineering concerns is to reduce deformations of plate structures. It is well known that von Karman equations provide an established model that describes nonlinear deformations of elastic plates. Our approach to study plate deformations...
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Gas sampling system for matrix of semiconductor gas sensors
PublicationSemiconductor gas sensors are popular commercial sensors applied in numerous gas detection systems. They are reliable, small, rugged and inexpensive. However, there are a few problem limiting the wider use of such sensors. Semiconductor gas sensor usually exhibits a low selectivity, low repeatability, drift of response, strong temperature and moisture influence on sensor properties. Sample flow rate is one of the parameters that...
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Application of genetic algorithms in graph searching problem
PublicationGraph searching is a common approach to solving a problem of capturing a hostile intruder by a group of mobile agents. We assume that this task is performed in environment which we are able to model as a graph G. The question asked is how many agents are needed to capture an arbitrary fast, invisible and smart intruder. This number is called the (edge) search number of G. The strategy which must be performed by agents is called...
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Determination of Odor Air Quality Index (OAQII) Using Gas Sensor Matrix
PublicationThis article presents a new way to determine odor nuisance based on the proposed odor air quality index (OAQII), using an instrumental method. This indicator relates the most important odor features, such as intensity, hedonic tone and odor concentration. The research was conducted at the compost screening yard of the municipal treatment plant in Central Poland, on which a self-constructed gas sensor array was placed. It consisted...
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Distributed NVRAM Cache – Optimization and Evaluation with Power of Adjacency Matrix
PublicationIn this paper we build on our previously proposed MPI I/O NVRAM distributed cache for high performance computing. In each cluster node it incorporates NVRAMs which are used as an intermediate cache layer between an application and a file for fast read/write operations supported through wrappers of MPI I/O functions. In this paper we propose optimizations of the solution including handling of write requests with a synchronous mode,...
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Improved magnitude estimation of complex numbers using alpha max and beta min algorithm
PublicationThe paper presents an improved algorithm for calculating the magnitude of complex numbers. This problem, which is a special case of square rooting, occurs for example, in FFT processors and complex FIR filters. The proposed method of magnitude calculation makes use of the modified alpha max and beta min algorithm. The improved version of the algorithm allows to control the maximum magnitude approximation error by using an adequate...
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Functional differential equations
PublicationSformułowano dość ogólne warunki dostateczne na to, aby odpowiednio zdefiniowane ciągi monotoniczne były zbieżne do jedynego, w pewnym segmencie, rozwiązania zagadnienia początkowego dla funkcyjnych równań różniczkowych. Omawiane równanie jest ogólne, a np. zwyczajne równania różniczkowe czy równania różniczkowo-całkowe są jego szczególnymi przypadkami.
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Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive a closed-form expression for the magnetizability of an arbitrary discrete state of the relativistic one-electron atom with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric...
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A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
PublicationThe orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices is evaluated in a closed form. It is found to be proportional to a sum of two terms, both depending on the second upper indices and containing the Dirac delta distribution.
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FEM approach to modeling of an irregular trabecular structure
PublicationThe aim of the study is elaboration of a method for creating irregular scaffolds that can be used to model the behaviour of trabecular bone placed in the proximal epiphysis of the femur. The scope of the study encompasses creating six numerical models of irregular scaffolds (two solid irregular scaffolds, two shell irregular scaffolds and two shell irregular scaffolds with fortification) and performing numerical analysis of the...
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Study of displacements of a bridge abutment using FEM
PublicationSteel sheet piles are often used to support excavations for bridge foundations. When they are left in place in the permanent works, they have the potential to increase foundation bearing capacity and reduce displacements; but their presence is not usually taken into account in foundation design. In this article, the results of finite element analysis of a typical abutment foundation, with and without cover of sheet piles, are presented...
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A two-scale (FEM-DEM) approach for concrete
PublicationArtykuł omawia dwu-skalowe podejście do betonu przy wykorzystaniu modelu Mes i DEM. Metodę elementów skończonych zastosowano na poziomie makro. Na poziomie mikro zastosowano metodę elementów dyskretnych. Macierz sztywności wyznaczono na podstawie tensora naprężeń wyznaczonego w skali mikro. Wyniki numeryczne dwusalowe porównano z wynikami dyskretnymi dla całego obszaru.
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General solution of quantum mechanical equations of motion with time-dependent Hamiltonians: A Lie algebraic approach
PublicationThe unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). In these cases we give explicit formulae for obtaining general solutions from special ones. We show that the constructions...
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An extended basis inexact shift–invert Lanczos for the efficient solution of large-scale generalized eigenproblems
PublicationThis paper proposes a technique, based on the Inexact Shift–Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented...
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Measurement of complex refractive index of human blood by low-coherence interferometry
PublicationIn this article, the usefulness of the optical technique for measurements of blood complex refractive index has been examined. Measurement of optical properties of human blood is difficult to perform because of its nonuniform nature. However, results of my investigation have shown the usefulness of low-coherencei nterferometry for measurement complex refractive index of human blood. Furthermore, mathematical analysis of spectrum...
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Runtime Visualization of Application Progress and Monitoring of a GPU-enabled Parallel Environment
PublicationThe paper presents design, implementation and real life uses of a visualization subsystem for a distributed framework for parallelization of workflow-based computations among clusters with nodes that feature both CPUs and GPUs. Firstly, the proposed system presents a graphical view of the infrastructure with clusters, nodes and compute devices along with parameters and runtime graphs of load, memory available, fan speeds etc. Secondly,...
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TensorHive: Management of Exclusive GPU Access for Distributed Machine Learning Workloads
PublicationTensorHive is a tool for organizing work of research and engineering teams that use servers with GPUs for machine learning workloads. In a comprehensive web interface, it supports reservation of GPUs for exclusive usage, hardware monitoring, as well as configuring, executing and queuing distributed computational jobs. Focusing on easy installation and simple configuration, the tool automatically detects the available computing...
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Analytical solution of non-stationary heat conduction problem for two sliding layers with time-dependent friction conditions
PublicationIn this article we conduct an overview of various types of thermal contact conditions at the sliding interface. We formulate a problem of non-stationary heat conduction in two sliding layers with generalized thermal contact conditions allowing for dependence of the heat-generation coefficient and contact heat transfer coefficient on time. We then derive an analytical solution of the problem by constructing a special coordinate...
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Characterizing the Scalability of Graph Convolutional Networks on Intel® PIUMA
PublicationLarge-scale Graph Convolutional Network (GCN) inference on traditional CPU/GPU systems is challenging due to a large memory footprint, sparse computational patterns, and irregular memory accesses with poor locality. Intel’s Programmable Integrated Unffied Memory Architecture (PIUMA) is designed to address these challenges for graph analytics. In this paper, a detailed characterization of GCNs is presented using the Open-Graph Benchmark...