PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Heuristic algorithm to predict the location of C0 separators for efficient isogeometric analysis simulations with direct solvers

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
907--917
Opis fizyczny
Bibliogr. 33 poz., rys., wykr.
Twórcy
  • Jagiellonian University, Faculty of Physics, Astronomy and Applied Computer Science, 11 Łojasiewicza St., 30-348 Krakow, Poland
autor
  • AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, 30 Mickiewicza Ave., 30-059 Krakow, Poland
autor
  • AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, 30 Mickiewicza Ave., 30-059 Krakow, Poland
  • AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, 30 Mickiewicza Ave., 30-059 Krakow, Poland
Bibliografia
  • [1] T.J.R. Hughes, The Finite Element Method. Linear Statics and Dynamics Finite Element Method Analysis, Dover (2000).
  • [2] O.C. Zienkiewicz, R.Taylor, and J.Z. Ziu, The Finite Element Method: Its Basis and Fundamentals, Elsevier, 7th edition (2013).
  • [3] L. Demkowicz, Computing with hp adaptive finite element method. Part I, CRC Press, Boca Raton, FL. (2006).
  • [4] L. Demkowicz, J. Kurtz, D. Pardo, M. Paszyński, W. Rachowicz, and A. Zdunek, Computing with hp adaptive finite element method. Part II, CRC Press, Boca Raton, FL (2007).
  • [5] I.S. Duff, A.M. Erisman, and J.K. Reid, Direct Methods for Sparse Matrices, Oxford University Press, Inc., New York, NY, (1986).
  • [6] I.S. Duff and J.K. Reid, The multifrontal solution of indefinite sparse symmetric linear, ACM Transations on Mathematical Software, 9(3), 302–325 (1983).
  • [7] I.S. Duff and K. Reid, The multifrontal solution of unsymmetric sets of linear systems, SIAM Journal of Scientific Statistical Computing, 5, 633–641 (1984).
  • [8] M. Paszyński, Fast solvers for mesh-based computations, Taylor & Francis, CRC Press, (2016).
  • [9] P.R. Amestoy and I.S. Duff, Multifrontal parallel distributed symmetric and unsymmetric solvers, Computer Methods in Applied Mechanics and Engineering, 184 501‒520 (2000).
  • [10] P.R. Amestoy, I.S. Duff, J. Koster, and J.Y. L’Excellent, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM Journal of Matrix Analysis and Applications, 1(23) 15–41 (2001).
  • [11] P.R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet, Hybrid scheduling for the parallel solution of linear systems, Computer Methods in Applied Mechanics and Engineering, 2(32), 136–156 (2001).
  • [12] A. George and J.W.-H. Lu, “An automatic nested dissection algorithm for irregular finite element problems”, SIAM Journal of Numerical Analysis 15, 1053–1069 (1978).
  • [13] H. AbouEisha, V.M. Calo, K. Jopek, M. Moshkov, A. Paszńska, M. Paszyński, and M. Skotniczny, Element partition trees for hrefined meshes to optimize direct solver performance. P. 1, Dynamic programming, International Journal of Applied Mathematics and Computer Science, 27(2) (2017) 351–365.
  • [14] J.A. Cottrell, T.J.R. Hughes, and Y. Bazilevs, Isogeometric Analysis: Toward Unification of CAD and FEA JohnWiley and Sons, (2009).
  • [15] L. Dedè, T.J.R. Hughes, S. Lipton, V.M. and Calo, Structural topology optimization with isogeometric analysis in a phase field approach, USNCTAM2010, 16th US National Congree of Theoretical and Applied Mechanics.
  • [16] L. Dedè, M. J. Borden, and T.J.R. Hughes, Isogeometric analysis for topology optimization with a phase field model, ICES REPORT 11‒29, The Institute for Computational Engineering and Sciences, The University of Texas at Austin (2011).
  • [17] R. Duddu, L. Lavier, T.J.R. Hughes, and V.M. Calo, A finite strain Eulerian formulation for compressible and nearly incompressible hyper-elasticity using high-order NURBS elements, International Journal of Numerical Methods in Engineering, 89(6) (2012) 762‒785.
  • [18] M. Łoś, M. Paszyński, A. Kłlusek, and W. Dzwinel, Application of fast isogeometric L2 projection solver for tumor growth simulations, Computer Methods in Applied Mechanics and Engineering, 316 (2017) 1257‒1269.
  • [19] H. Gómez, V.M. Calo, Y. Bazilevs, and T.J.R. Hughes, Isogeometric analysis of the Cahn-Hilliard phase-field model, Computer Methods in Applied Mechanics and Engineering 197 (2008) 4333–4352.
  • [20] H. Gómez, T.J.R. Hughes, X. Nogueira, and V.M. Calo, Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations. Computer Methods in Applied Mechanics and Engineering 199 (2010) 1828‒1840.
  • [21] S. Hossain, S.F.A. Hossainy, Y. Bazilevs, V.M. Calo, and T.J.R. Hughes, Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patientspecific coronary artery walls, Computational Mechanics, doi: 10.1007/s00466‒011‒0633‒2, (2011).
  • [22] M.-C. Hsu, I. Akkerman, and Y. Bazilevs, High-performance computing of wind turbine aerodynamics using isogeometric analysis, Computers and Fluids, 49(1) (2011) 93‒100.
  • [23] Y. Bazilevs, L. Beirao da Veiga, J.A. Cottrell, T.J.R. Hughes, and G. Sangalli, Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes, Mathematical Methods and Models in Applied Sciences, 16 (2006) 1031–1090.
  • [24] Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, and G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Computer Methods in Applied Mechanics and Engineering 197 (2007) 173‒201.
  • [25] Y. Bazilevs, V.M. Calo, Y. Zhang, and T.J.R. Hughes: Isogeometric fluid-structure interaction analysis with applications to arterial blood flow, Computational Mechanics 38 (2006).
  • [26] K. Chang, T.J.R. Hughes, and V.M. Calo, Isogeometric variational multiscale large-eddy simulation of fully-developed turbulent flow over a wavy wall, Computers and Fluids, 68 (2012) 94‒104.
  • [27] D. Garcia, D. Pardo, L. Dalcin, M. Paszyński, N. Collier, and V.M. Calo, The value of continuity: Refined isogeometric analysis and fast direct solvers, Computer Methods in Applied Mechanics and Engineering, 316 (2017) 586‒605.
  • [28] B. Janota and M. Paszyński, Algorithms for construction of Element Partition Trees for Direct Solver executed over h refined grids with B-splines and C0 separators, Procedia Computer Science, 108 (2017) 857‒866.
  • [29] B. Janota and A. Paszyńska, Automatic algorithms for the construction of element partition trees for isogeometric finite element method, accepted to International Conference on Man-Machine Interactions (ICMMI) (2017), Kraków, Poland.
  • [30] L. Piegl, and W. Tiller, The NURBS Book (Second Edition), Springer-Verlag New York, Inc., (1997).
  • [31] S. Fiałko, “A block sparse shared-memory multifrontal finite element solver for problems of structural mechanics”, Computer Assisted Mechanics and Engineering Science 16, 117– 131 (2009).
  • [32] S. Fiałko, “The block subtracture multifrontal method for solution of large finite element equation sets”, Technical Transactions, 1-NP, 8, 175–188 (2009).
  • [33] S. Fiałko, “PARFES: A method for solving finite element linear equations on multi-core computers”, Advanced Engineering Software 40(12), 1256–1265 (2010).
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7b566029-881c-4d20-947f-88e54daaa4b5
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.