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Wyszukujesz frazę "isogeometric finite element method" wg kryterium: Temat

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    Wyświetlanie 1-5 z 5
    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:
    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:
    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:
    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:
    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
      Wyświetlanie 1-5 z 5

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