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Search results for: numerical integration
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Numerical integration of a coupled Korteweg-deVries system
PublicationMetoda numeryczna została wprowadzona do rozwiązania ogólnych układów równańKorteweg´a- de Vries´a. Zastosowana do równania Hirota-Satsuma.
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Multi-core and Multiprocessor Implementation of Numerical Integration in Finite Element Method
PublicationThe paper presents techniques for accelerating a numerical integration process which appears in the Finite Element Method. The acceleration is achieved by taking advantages of multi-core and multiprocessor devices. It is shown that using multi-core implementation with OpenMP and a GPU acceleration using CUDA architecture allows one to achieve the speedups by a factor of 5 and 10 on a CPU and GPUs, respectively.
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Modal modification of structural damping applied to increase the stability and convergence of numerical integration
PublicationThe presented paper refers to numerical tests done on systems fused of multibody and finite-element parts. The appearance of its multibody part gives rise to significant nonlinear components, i.e., second-order nonlinear differential equations express the dynamics. We usually solve these equations by “step-by-step” integration methods. When using the currently available integration algorithms, we approximate these initial systems...
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Is reduced integration just a numerical trick
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Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow
PublicationIn this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study...
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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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Accuracy, Memory and Speed Strategies in GPU-based Finite-Element Matrix-Generation
PublicationThis paper presents strategies on how to optimize GPU-based finite-element matrix-generation that occurs in the finite-element method (FEM) using higher order curvilinear elements. The goal of the optimization is to increase the speed of evaluation and assembly of large finite-element matrices on a single GPU (Graphics Processing Unit) while maintaining the accuracy of numerical integration at the desired level. For this reason,...
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Integration and verification of meteorological observations and NWP model data for the local GNSS tomography
PublicationGNSS meteorology applies the Global Navigation Satellite Systems (GNSS) to derive information about the state of the atmosphere (particularly troposphere). The tomography is one of the methods used in GNSS meteorology. The input data of GNSS tomography are the signal troposphere delays, results of GNSS data processing and additionally meteorological observations and Numerical Weather Prediction (NWP) models data. Different types...
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On the Structure of Time in Computational Semantics of a Variable-Step Solver for Hybrid Behavior Analysis
PublicationHybrid dynamic systems combine continuous and discrete behavior. Often, computational approaches are employed to derive behaviors that approximate the analytic solution. An important part of this is the approximation of differential equation behavior by numerical integration. The accuracy and computational efficiency of the integration usually depend on the complexity of the method and its implicated approximation errors, especially...
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Integration of Multi-Source Geospatial Data from GNSS Receivers, Terrestrial Laser Scanners, and Unmanned Aerial Vehicles
PublicationThe analysis based on geospatial data from different measurement systems now constitutes a complex numerical and practical enterprise. The dynamic development of modern technologies enables rapid and precise acquisition of such data. Nonetheless, the diversity of reference systems is today one of the main challenges for their correct interpretation. The combined use of the processed measurement results and archival data in paper...
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Parallelization of Selected Algorithms on Multi-core CPUs, a Cluster and in a Hybrid CPU+Xeon Phi Environment
PublicationIn the paper we present parallel implementations as well as execution times and speed-ups of three different algorithms run in various environments such as on a workstation with multi-core CPUs and a cluster. The parallel codes, implementing the master-slave model in C+MPI, differ in computation to communication ratios. The considered problems include: a genetic algorithm with various ratios of master processing time to communication...
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Numerical Analysis of Seismic Pounding between Adjacent Buildings Accounting for SSI
PublicationThe structural pounding caused by an earthquake may damage structures and lead to their collapse. This study is focused on the pounding between two adjacent asymmetric structures with different dynamic properties resting on the surface of an elastic half-space. An exploration of the relationship between the effects of the seismic analysis with the impact response to the torsional pounding between adjacent buildings under different...
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Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
PublicationThe paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modified finite element method with triangular elements for space discretization. The accuracy analysis of the applied scheme was performed using a modified equation method for three different...
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Solving the Problem of Dynamic Adaptability of Artificial Intelligence Systems that Control Dynamic Technical Objects
PublicationThis paper investigates the increase in the response speed and stability of artificial intelligence systems that control dynamic technical objects. The problem of calculating the optimal time of switching an artificial intelligence system between software classes by the criterion of the rigidity degree of the model of a control object is considered. The solution of this problem is proposed for the general case of the control object...
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NUMERICAL SIMULATION OF CRATER CREATING PROCESS IN DYNAMIC REPLACEMENT METHOD BY SMOOTH PARTICLE HYDRODYNAMICS
PublicationA theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method...
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Performance evaluation of unified memory and dynamic parallelism for selected parallel CUDA applications
PublicationThe aim of this paper is to evaluate performance of new CUDA mechanisms—unified memory and dynamic parallelism for real parallel applications compared to standard CUDA API versions. In order to gain insight into performance of these mechanisms, we decided to implement three applications with control and data flow typical of SPMD, geometric SPMD and divide-and-conquer schemes, which were then used for tests and experiments. Specifically,...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublicationWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublicationWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...
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Effective highly accurate time integrators for linear Klein-Gordon equations across the scales
PublicationWe propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...
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O zbieżności rozwiązań w nieliniowym mikropolarnym ośrodku sprężysto-plastycznym - zastosowanie elementów skończonych wyższego rzędu.
PublicationEfekty lokalizacji w nieliniowym geometrycznie sprężysto-plastycznym mikropolarnym ośrodku z osłabieniem materiału. Hipotezy Hubera-Misesa-Hencky’ego i Druckera-Pragera. Rozwiązanie równań sprężysto-plastycznych przy użyciu algorytmu powrotnego. Opis zastosowanych elementów skończonych. Przykłady numeryczne obliczeń w geotechnice.
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Quasi-analytical Near-to-Far Field Transformation Based on Field Matching Method for Scattering Problems
PublicationA new quasi-analytical near-to-far field transformation based on field matching method (field expansion in a base of Hankel functions) is presented. This approach uses finite element method to obtain near field, then the field is expressed in a base of Hankel functions. The evaluated coefficients allow to calculate the field outside the numerical domain, also in a far distance. The main advantage of the proposed technique is avoiding of...
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Finite element matrix generation on a GPU
PublicationThis paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The performance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core...
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Impact of diffusion coefficient averaging on solution accuracy of the 2D nonlinear diffusive wave equation for floodplain inundation
PublicationIn the study, the averaging technique of diffusion coefficients in the two-dimensional nonlinear diffusive wave equation applied to the floodplain inundation is presented. As a method of solution, the splitting technique and the modified finite element method with linear shape functions are used. On the stage of spatial integration, it is often assumed that diffusion coefficient is constant over element and equal to its average...
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Wybrane elementy nieliniowej dynamiki struktur kratowych
PublicationW pracy jest dyskutowany problem nieliniowej dynamiki struktur kratowych. Zastosowano stacjonarny opis Lagrange'a (ang. Total Lagrange), pokazano silne i słabe sformułowanie dla pręta kratowego, jego aplikację do MES. W zakresie całkowania równań ruchu przedstawiono metodę Newmarka i metodę-a dla problemów liniowych i nieliniowych. Załączony przykład numeryczny ilustruje cechy przedstawionych metod.
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Special Issue: “Non-Destructive Testing of Structures”
PublicationThe Special Issue “Non-Destructive Testing of Structures” has been proposed to present recent developments in the field of diagnostics of structural materials and components in civil and mechanical engineering. The papers highlighted in this editorial concern various aspects of non-invasive diagnostics, including such topics as condition assessments of civil and mechanical structures and connections of structural elements, the...
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GPU-Accelerated 3D Mesh Deformation for Optimization Based on the Finite Element Method
PublicationThis paper discusses a strategy for speeding up the mesh deformation process in the design-byoptimization of high-frequency components involving electromagnetic field simulations using the 3D finite element method (FEM). The mesh deformation is assumed to be described by a linear elasticity model of a rigid body; therefore, each time the shape of the device is changed, an auxiliary elasticity finite-element problem must be solved....
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Elastoplastic law of Cosserat type in shell theory with drilling rotation
PublicationWithin the framework of six-parameter non-linear shell theory, with strain measures of the Cosserat type, we develop small-strain J2-type elastoplastic constitutive relations. The relations are obtained from the Cosserat plane stress relations assumed in each shell layer, by through-the-thickness integration employing the first-order shear theory. The formulation allows for unlimited translations and rotations. The constitutive...
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Modal Adjustment of Rayleigh Based Structural Damping and Coordinate-Partitioning Algorithm Dedicated to Frictionless Contact Constraints between Multibody System and Structure Modelled with Finite Elements
PublicationThe paper presents a dedicated numerical algorithm. The algorithm is advantageous during investigations of the dynamics of a hybrid multibody / finite-elements system. We focus our attention on interactions resulting from mechanical contact. Pointwise contact connects a vertex of the multibody structure and a surface of the elastic reference body. Instead of a positive value of the relative penetration factor, constraint equations...
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Transition curve with smoothed curvature at its ends for railway roads
PublicationIn the paper, in view of a railway ballasted track, a new concept of transition curve of linear form of curvature along its length and smoothed extreme regions is presented. For this purpose use has been made of an original, universal method for identifying transition curves by means of differential equations. Some general curvature equations for three regions investigated have been determined to be followed by appropriate parametric...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublicationIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Inverse Flood Routing Using Simplified Flow Equations
PublicationThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublicationThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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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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THIRD-ORDER EXPONENTIAL INTEGRATOR FOR LINEAR KLEIN–GORDON EQUATIONS WITH TIME AND SPACE-DEPENDANT MASS
PublicationAllowing for space- and time-dependance of mass in Klein–Gordon equations re- solves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations....
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THIRD-ORDER EXPONENTIAL INTEGRATOR FOR LINEAR KLEIN–GORDON EQUATIONS WITH TIME AND SPACE-DEPENDANT MASS
PublicationAllowing for space- and time-dependance of mass in Klein–Gordon equations re- solves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations....
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Krzywa przejściowa z wygładzoną krzywizną dla dróg kolejowych
PublicationW pracy przedstawiono koncepcję nowej postaci krzywej przejściowej, o liniowym przebiegu krzywizny na długości i wygładzonymi rejonami skrajnymi. Może ona stanowić alternatywę dla tzw. gładkich krzywych przejściowych, o nieliniowym przebiegu krzywizny na całej długości. Została tutaj wykorzystana uniwersalna metoda identyfikacji krzywych przejściowych za pomocą równań różniczkowych. Wyznaczono ogólne równania krzywizny oraz odpowiednie...
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Analyzing energy/performance trade-offs with power capping for parallel applications on modern multi and many core processors
PublicationIn the paper we present extensive results from analyzing energy/performance trade-offs with power capping observed on four different modern CPUs, for three different parallel applications such as 2D heat distribution, numerical integration and Fast Fourier Transform. The CPU tested represent both multi-core type CPUs such as Intel⃝R Xeon⃝R E5, desktop and mobile i7 as well as many-core Intel⃝R Xeon PhiTM x200 but also server, desktop...
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Integrated Application of GPR and Ultrasonic Testing in the Diagnostics of a Historical Floor
PublicationThe paper presents the results of integrated ground penetrating radar (GPR) and ultrasonic testing (UT) measurements conducted on a historical floor in St. Nicholas’ Church, Gdańsk, Poland. The described inspection was the first stage of the technical state assessment of the building. The aim of the study was the detection of underfloor air gaps, which were observed in a few trial pits. The condition of the ground under the floor...
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Piezoelectric Transducer for Mechanical Assessment of Soft Tissues. Concept, Implementation and Analysis
PublicationThe main goal of this work was following: preparation of a new concept, implementation and analysis of the piezoelectric resonant sensor/actuator for measuring the aging process of human skin. The research work has been carried out in the framework of cooperation between the INP-ENSEEIHT-LAPLACE, Toulouse, France, and at the Gdansk University of Technology, Faculty of Electrical and Control Engineering, Research Group of...
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Integration and Visualization of the Results of Hydrodynamic Models in the Maritime Network-Centric GIS of Gulf of Gdansk
PublicationEnsuring of security in the coastal area makes on a seaside countries research in the field of infrastructure spatial information of environmental data. The paper presents the results of work on the construction of this infrastructure by integrating electronic navigational chart with ortophotomaps of coastal areas as well as numerical data from weather and hydrodynamic models. Paper focuses on a problems associated with creating...
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Explicit Size-Reduction of Circularly Polarized Antennas through Constrained Optimization with Penalty Factor Adjustment
PublicationModern communication systems of high data capacity incorporate circular polarization (CP) as the preferred antenna radiation field configuration. In many applications, integration of the system circuitry with antennas imposes size limitations on CP radiators, which makes their development process a challenging endeavor. This can be mitigated by means of simulation-driven design, specifically, constrained numerical optimization....
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ATTEMPTS OF THERMAL IMAGING CAMERA USAGE IN ESTIMATIONS OF THE CONVECTIVE HEAT LOSS FROM A VERTICAL PLATE
PublicationIn this paper a new method for determining heat transfer coefficients using a gradient method has been developed. To verify accuracy of the proposed method vertical isothermal heating plate with natural convection mechanism has been examined. This configuration was deliberately chosen, because of the fact that such case is historically the earliest and most thoroughly studied and its rich scientific documentation - the most reliable....
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Assessment of OpenMP Master–Slave Implementations for Selected Irregular Parallel Applications
PublicationThe paper investigates various implementations of a master–slave paradigm using the popular OpenMP API and relative performance of the former using modern multi-core workstation CPUs. It is assumed that a master partitions available input into a batch of predefined number of data chunks which are then processed in parallel by a set of slaves and the procedure is repeated until all input data has been processed. The paper experimentally...
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Numerical Methods
e-Learning CoursesNumerical Methods: for Electronics and Telecommunications students, Master's level, semester 1 Instructor: Michał Rewieński, Piotr Sypek Course description: This course provides an introduction to computational techniques for the simulation and modeling of a broad range of engineering and physical systems. Concepts and methods discussed are widely illustrated by various applications including modeling of integrated circuits,...
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublicationThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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DEPO: A dynamic energy‐performance optimizer tool for automatic power capping for energy efficient high‐performance computing
PublicationIn the article we propose an automatic power capping software tool DEPO that allows one to perform runtime optimization of performance and energy related metrics. For an assumed application model with an initialization phase followed by a running phase with uniform compute and memory intensity, the tool performs automatic tuning engaging one of the two exploration algorithms—linear search (LS) and golden section search (GSS), finds...
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Pantographic metamaterials: an example of mathematically driven design and of its technological challenges
PublicationIn this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those...
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Synergistic effects of a swirl generator and MXene/ water nanofluids used in a heat exchanger pipe of a negative CO2 emission gas power plant
Publicationfocus on optimizing heat exchangers contributes to improved temperature control mechanisms, ensuring the sustainable operation of innovative power plants working towards negative CO2 emissions. In the realm of oxy-combustion within Negative CO2 Emission Power Plants (nCO2PP), the temperature of combustion products surpasses 3000 (K). Addressing this challenge, the imperative arises to reduce these elevated temperatures to a manageable...
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Design centering of compact microwave components using response features and trust regions
PublicationFabrication tolerances, as well as uncertainties of other kinds, e.g., concerning material parameters or operating conditions, are detrimental to the performance of microwave circuits. Mitigating their impact requires accounting for possible parameter deviations already at the design stage. This involves optimization of appropriately defined statistical figures of merit such as yield. Alt-hough important, robust (or tolerance-aware)...
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Integration of natural and artificial intelligence in production systems
PublicationIntegration processes play an increasingly important role in modern economy, and seriously co-decide about the effectiveness of the company. Integration phase occurs in the system life cycle by preceding the final stages of its implementation and activation. In turn, used in software engineering (SE) iteration-evolutionary models, such as spiral model make that the integration activities can occur in varying degrees in all phases...