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    Wyświetlanie 1-12 z 12
    Tytuł:
    Applications of alternating direction solver for simulations of time-dependent problems
    Autorzy:
    Łoś, M.
    Paszyński, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/952948.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    finite element method
    isogeometric analysis
    Alternating Direction Solver
    Opis:
    This paper deals with the application of an Alternating Direction Solver (ADS) to a non-stationary linear elasticity problem solved with the isogeometric finite element method (IGA-FEM). Employing a tensor product B-spline basis in isogeometric analysis under some restrictions leads to a system of linear equations with a matrix possessing a tensor product structure. The ADI algorithm is a direct method that exploits this Kronecker product structure to solve the system in O (N), where N is the number of degrees of freedom (basis functions). This is asymptotically faster than state-of-the-art, general-purpose, multi-frontal direct solvers when applied to explicit dynamics. In this paper, we also present a complexity analysis of the ADS incorporating dependence on the B-spline basis of order p.
    Źródło:
    Computer Science; 2017, 18 (2); 117-128
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Comparison of multi-frontal and alternating direction parallel hybrid memory iGRM direct solver for non-stationary simulations
    Autorzy:
    Woźniak, Maciej
    Bukowska, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/1839249.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    isogeometric finite element method
    integration
    shared memory
    parallel
    Opis:
    Three-dimensional isogeometric analysis (IGA-FEM) is a modern method for simulation. The idea is to utilize B-splines or NURBS basis functions for both computational domain descriptions and engineering computations. Refined isogeometric analysis (rIGA) employs a mixture of patches of elements with B-spline basis functions and C 0 separators between them. This enables a reduction in the computational cost of direct solvers. Both IGA and rIGA come with challenging sparse matrix structures that are expensive to generate. In this paper, we show a hybrid parallelization method using hybrid-memory parallel machines. The two-level parallelization includes the partitioning of the computational mesh into sub-domains on the first level (MPI) and loop parallelization on the second level (OpenMP). We show that the hybrid parallelization of the integration reduces the contribution of this phase significantly. We compare the multi-frontal solver and alternating direction solver, including the integration and the factorization phases.
    Źródło:
    Computer Science; 2020, 21 (4); 419-439
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Free vibration and buckling analysis of higher order laminated composite plates using the isogeometric approach
    Autorzy:
    Peković, O.
    Stupar, S.
    Simonović, A.
    Svorcan, J.
    Trivković, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/281145.pdf
    Data publikacji:
    2015
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    isogeometric
    laminated composite plate
    third order shear deformation theory
    Opis:
    This research paper presents a higher order isogeometric laminated composite plate finite element formulation. The isogeometric formulation is based on NURBS (non-uniform rational B-splines) basis functions of varying degree. Plate kinematics is based on the third order shear deformation theory (TSDT) of Reddy in order to avoid shear locking. Free vibration and the buckling response of laminated composite plates are obtained and efficiency of the method is considered. Numerical results with different element order are presented and the obtained results are compared to analytical and conventional numerical results as well as existing isogeometric plate finite elements.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2015, 53, 2; 453-466
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Linear computational cost implicit solver for parabolic problems
    Autorzy:
    Gurgul, Grzegorz
    Łoś, Marcin
    Paszynski, Maciej
    Calo, Victor
    Powiązania:
    https://bibliotekanauki.pl/articles/1839258.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    isogeometric analysis
    implicit dynamics
    linear computational cost
    direct solvers
    Opis:
    In this paper, we use the alternating direction method for isogeometric finite elements to simulate transient problems. Namely, we focus on a parabolic problem and use B-spline basis functions in space and an implicit time-marching method to fully discretize the problem. We introduce intermediate time-steps and separate our differential operator into a summation of the blocks that act along a particular coordinate axis in the intermediate time-steps. We show that the resulting stiffness matrix can be represented as a multiplication of two (in 2D) or three (in 3D) multi-diagonal matrices, each one with B-spline basis functions along the particular axis of the spatial system of coordinates. As a result of these algebraic transformations, we get a system of linear equations that can be factorized in a linear O(N) computational cost at every time-step of the implicit method. We use our method to simulate the heat transfer problem. We demonstrate theoretically and verify numerically that our implicit method is unconditionally stable for heat transfer problems (i.e., parabolic). We conclude our presentation with a discussion on the limitations of the method.
    Źródło:
    Computer Science; 2020, 21 (3); 335-352
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Elastic-plastic analysis of pressure vessels and rotating disks made of functionally graded materials using the isogeometric approach
    Autorzy:
    Kalali, A. T.
    Hassani, B.
    Hadidi-Moud, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/949114.pdf
    Data publikacji:
    2016
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    isogeometric analysis
    NURBS
    functionally graded material
    modified rule of mixtures
    Opis:
    An NURBS-based isogeometric analysis for elastic-plastic stress in a cylindrical pressure vessel is presented. The vessel is made of a ceramic/metal functionally graded material, i.e. a particle-reinforced composite. It is assumed that the material plastic deformation follows an isotropic strain-hardening rule based on the von Mises yield criterion. The mechanical properties of the graded material are modelled by the modified rule of mixtures. Selected finite element results are also presented to establish the supporting evidence for validation of the isogeometric analysis. Similar analyses are performed and solutions for spherical pressure vessel and rotating disk made of FGMs are also provided.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2016, 54, 1; 113-125
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Grammar based multi-frontal solver for isogeometric analysis in 1d
    Autorzy:
    Kuźnik, K.
    Paszyński, M
    Calo, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/305531.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    graph grammar
    direct solver
    isogeometric finite element method
    NVIDIA CUDA GPU
    Opis:
    In this paper, we present a multi-frontal direct solver for one-dimensional iso-geometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and eliminations as a set of basic undividable tasks called graph grammar productions. Having the solver algorithm expressed as GG productions, we can find the partial order of execution and create a dependency graph, allowing for scheduling of tasks into shared memory parallel machine. We focus on the implementation of the solver with NVIDIA CUDA on the graphic processing unit (GPU). The solver has been tested for linear, quadratic, cubic, and higher-order B-splines, resulting in logarithmic scalability.
    Źródło:
    Computer Science; 2013, 14 (4); 589-613
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    One-dimensional fully automatic h-adaptive isogeometric finite element method package
    Autorzy:
    Lipski, P.
    Paszyński, M
    Powiązania:
    https://bibliotekanauki.pl/articles/305563.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    finite element method
    isogeometric analysis
    parallel computing
    h-adaptivity
    B-splines
    Opis:
    his paper deals with an adaptive finite element method originally developed by Prof. Leszek Demkowicz for hierarchical basis functions. In this paper, we investigate the extension of the adaptive algorithm for isogeometric analysis performed with B-spline basis functions. We restrict ourselves to h-adaptivity, since the polynomial order of approximation must be fixed in the isogeometric case. The classical variant of the adaptive FEM algorithm, as delivered by the group of Prof. Demkowicz, is based on a two-grid paradigm, with coarse and fine grids (the latter utilized as a reference solution). The problem is solved independently over a coarse mesh and a fine mesh. The fine-mesh solution is then utilized as a reference to estimate the relative error of the coarse-mesh solution and to decide which elements to refine. Prof. Demkowicz uses hierarchical basis functions, which (though locally providing Cp−1 continuity) ensure only C0 on the interfaces between elements. The CUDA C library described in this paper switches the basis to B-spline functions and proposes a one-dimensional isogeometric version of the h-adaptive FEM algorithm to achieve global Cp−1 continuity of the solution.
    Źródło:
    Computer Science; 2016, 17 (4); 439-459
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Crack analysis in bimaterial interfaces using T-spline based XIGA
    Autorzy:
    Habib, S. H.
    Belaidi, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/279517.pdf
    Data publikacji:
    2017
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    extended isogeometric analysis
    T-splines
    bimaterial interface cracks
    enrichment functions
    local refinement
    Opis:
    Analysis-suitable T-splines are used for the modeling and analyzing of cracks in bimaterial interfaces within the framework of an extended isogeometric analysis (XIGA). The crack tip enrichment functions of bimaterial interface cracks are implemented to reproduce singular fields, and the signed distance functions are used to treat the crack face and the interface in the models. A compatible local refinement algorithm is applied to refine location of the crack and the interface, which helps one to avoid produce excessive propagation of control points. The mixed mode stress intensity factors (SIFs) which are evaluated by the interaction integral (M-integral) are used as analysis parameters. Numerical simulations are performed to analyze the problem and to examine the efficiency of the proposed method. The obtained results are compared with other available results.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2017, 55, 1; 55-68
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Isogeometric Fast Multipole Boundary Element Method Based on Burton-Miller Formulation for 3D Acoustic Problems
    Autorzy:
    Chen, Leilei
    Zhao, Wenchang
    Liu, Cheng
    Chen, Haibo
    Marburg, Steffen
    Powiązania:
    https://bibliotekanauki.pl/articles/177486.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    isogeometric analysis
    boundary element method
    Burton-Miller method
    acoustic scattering
    fast multipole method
    Opis:
    An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The singular integrals existing in Burton-Miller formulation are evaluated directly and accurately using Hadamard’s finite part integration. Fast multipole method is applied to accelerate the solution of the system of equations. It is demonstrated that the isogeometric boundary element method based on NURBS performs better than the conventional approach based on Lagrange basis functions in terms of accuracy, and the use of the fast multipole method both retains the accuracy for isogeometric boundary element method and reduces the computational cost.
    Źródło:
    Archives of Acoustics; 2019, 44, 3; 475-492
    0137-5075
    Pojawia się w:
    Archives of Acoustics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Heuristic algorithm to predict the location of C0 separators for efficient isogeometric analysis simulations with direct solvers
    Autorzy:
    Paszyńska, A.
    Jopek, K.
    Woźniak, M.
    Paszyński, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/201497.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    refined isogeometric analysis
    finite element method
    multi-frontal direct solver
    heuristic algorithms
    analiza izogeometryczna
    metoda elementów skończonych
    algorytmy heurystyczne
    Opis:
    We focus on two and three-dimensional isogeometric finite element method computations with tensor product Ck B-spline basis functions. We consider the computational cost of the multi-frontal direct solver algorithm executed over such tensor product grids. We present an algorithm for estimation of the number of floating-point operations per mesh node resulting from the execution of the multi-frontal solver algorithm with the ordering obtained from the element partition trees. Next, we propose an algorithm that introduces C0 separators between patches of elements of a given size based on the stimated number of flops per node. We show that the computational cost of the multi-frontal solver algorithm executed over the computational grids with C0 separators introduced is around one or two orders of magnitude lower, while the approximability of the functional space is improved. We show O(NlogN) computational complexity of the heuristic algorithm proposing the introduction of the C0 separators between the patches of elements, reducing the computational cost of the multi-frontal solver algorithm.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 6; 907-917
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of isogeometric approach to dynamics of curved beam
    Autorzy:
    Łasecka-Plura, Magdalena
    Białasik, Jan
    Kuczma, Mieczysław
    Tabrizikahou, Alireza
    Powiązania:
    https://bibliotekanauki.pl/articles/24201980.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Poznańska. Instytut Mechaniki Stosowanej
    Tematy:
    isogeometric analysis
    free-form curved beam
    Timoshenko beam theory
    vibration analysis
    analiza izogeometryczna
    belka zakrzywiona
    teoria Timoshenki
    analiza drgań
    Opis:
    In the paper dynamics of a free-form Timoshenko curved beam is investigated. The considered problem is solved using isogeometric analysis. Non-uniform rational B-spline (NURBS) basis functions are applied to describe both geometry and displacement field of the considered beam. The Timoshenko beam theory is used to derive the element stiffness and mass matrices. The application of the presented method is shown in numerical examples. The correctness of the presented approach is proved by comparing the obtained results to those available in the literature and calculated by the finite element method. Analysis of convergence is presented for different orders of NURBS basis functions.
    Źródło:
    Vibrations in Physical Systems; 2023, 34, 1; art. no. 2023117
    0860-6897
    Pojawia się w:
    Vibrations in Physical Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Three-dimensional simulations of the airborne COVID-19 pathogens using the advection-diffusion model and alternating-directions implicit solver
    Autorzy:
    Łoś, Marcin
    Woźniak, Maciej
    Muga, Ignacio
    Paszynski, Maciej
    Powiązania:
    https://bibliotekanauki.pl/articles/2086863.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    COVID-19
    pathogen spread
    isogeometric analysis
    implicit dynamics
    advection-diffusion
    parallel alternating directions solver
    rozprzestrzenianie się patogenu
    analiza izogeometryczna
    dynamika ukryta
    adwekcja-dyfuzja
    rozwiązywanie równoległych zmiennych kierunków
    Opis:
    In times of the COVID-19, reliable tools to simulate the airborne pathogens causing the infection are extremely important to enable the testing of various preventive methods. Advection-diffusion simulations can model the propagation of pathogens in the air. We can represent the concentration of pathogens in the air by “contamination” propagating from the source, by the mechanisms of advection (representing air movement) and diffusion (representing the spontaneous propagation of pathogen particles in the air). The three-dimensional time-dependent advection-diffusion equation is difficult to simulate due to the high computational cost and instabilities of the numerical methods. In this paper, we present alternating directions implicit isogeometric analysis simulations of the three-dimensional advection-diffusion equations. We introduce three intermediate time steps, where in the differential operator, we separate the derivatives concerning particular spatial directions. We provide a mathematical analysis of the numerical stability of the method. We show well-posedness of each time step formulation, under the assumption of a particular time step size. We utilize the tensor products of one-dimensional B-spline basis functions over the three-dimensional cube shape domain for the spatial discretization. The alternating direction solver is implemented in C++ and parallelized using the GALOIS framework for multi-core processors. We run the simulations within 120 minutes on a laptop equipped with i7 6700 Q processor 2.6 GHz (8 cores with HT) and 16 GB of RAM.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 4; e137125, 1--8
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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