PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Powiadomienia systemowe
  • Sesja wygasła!
  • Sesja wygasła!
  • Sesja wygasła!
  • Sesja wygasła!
Tytuł artykułu

Comparison of multi-frontal and alternating direction parallel hybrid memory iGRM direct solver for non-stationary simulations

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
Strony
419--439
Opis fizyczny
Bibliogr. 37 poz., rys.
Twórcy
  • AGH University of Science and Technology, Krakow, Department of Computer Science, Poland
  • AGH University of Science and Technology, Krakow, Department of Computer Science, Poland
Bibliografia
  • [1] Amestoy P.R., Duff I.S., L’Excellent J.Y.: Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer Methods in Applied Mechanics and Engineering, vol. 184, pp. 501–520, 2000.
  • [2] Amestoy P.R., Duff I.S., L’Excellent J.Y., Koster J.: A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling. SIAM Journal of Matrix Analysis and Applications, vol. 23(1), pp. 15–41, 2001.
  • [3] Amestoy P.R., Guermouche A., L’Excellent J.Y., Pralet S.: Hybrid scheduling for the parallel solution of linear systems. Parallel Computing, vol. 32, pp. 136–156, 2006.
  • [4] Balay S., Abhyankar S., Adams M.F., Brown J., Brune P., Buschelman K., Dalcin L., Dener A., Eijkhout V., Gropp W.D., Karpeyev D., Kaushik D., Knepley M.G., May D.A., McInnes L.C., Mills R.T., Munson T., Rupp K., Sanan P., Smith B.F., Zampini S., Zhang H., Zhang H.: PETSc Web page, 2019. https://www.mcs.anl.gov/petsc.
  • [5] Balay S., Abhyankar S., Adams M.F., Brown J., Brune P., Buschelman K., Dalcin L., Dener A., Eijkhout V., Gropp W.D., Karpeyev D., Kaushik D., Knepley M.G., May D.A., McInnes L.C., Mills R.T., Munson T., Rupp K., Sanan P., Smith B., Zampini S., Zhang H., Zhang H.: PETSc Users Manual, 2020. https://www.mcs.anl.gov/petsc.
  • [6] Balay S., Gropp W.D., McInnes L.C., Smith B.F.: Efficient Management of Parallelism in Object Oriented Numerical Software Libraries. In: Arge E., Bruaset A.M., Langtangen H.P. (eds.), Modern Software Tools for Scientific Computing, pp. 163–202, Springer Science+Business Media, New York, 1997.
  • [7] Barton M., Calo V.: Optimal quadrature rules for isogeometric analysis. 2015. ArXiv:1511.03882.
  • [8] Bazilevs Y., Calo V.M., Cottrell J.A., Evans J.A., Hughes T.J.R., Lipton S., Scott M.A., Sederberg T.W.: Isogeometric analysis using T-splines, Computer Methods in Applied Mechanics and Engineering, vol. 199, pp. 229–263, 2010.
  • [9] Beirao da Veiga L., Buffa A., Sangalli G., Vazquez R.: Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties, Mathematical Models and Methods in Applied Sciences, vol. 23(11), pp. 1979– 2003, 2013.
  • [10] Benson D.J., Bazilevs Y., Hsu M.C., Hughes T.J.R.: A large-deformation, rotation-free isogeometric shell, Computer Methods in Applied Mechanics and Engineering, vol. 200, pp. 1367–1378, 2011.
  • [11] Bubak M., Kitowski J., Wiatr K. (eds.): eScience on Distributed Computing Infrastructure: Achievements of PLGrid Plus Domain-Specific Services and Tools, vol. 8500, Springer, 2014.
  • [12] Calabro F., Sangalli G., Tani M.: Fast formation of isogeometric Galerkin matrices by weighted quadrature, Computer Methods in Applied Mechanics and Engineering, vol. 316, pp. 606–622, 2017.
  • [13] Calo V.M., Brasher N.F., Bazilevs Y., Hughes T.J.R.: Multiphysics model for blood flow and drug transport with application to patient-specific coronary artery flow, Computational Mechanics, vol. 43, pp. 161–177, 2008.
  • [14] Chang K., Hughes T.J.R., Calo V.M.: Isogeometric Variational Multiscale Large -Eddy Simulation of Fully-Developed Turbulent Flow Over a Wavy Wall, Computers and Fluids, vol. 68, pp. 94–104, 2012.
  • [15] Collier N., Pardo D., Dalcin L., Paszyński M., Calo V.M.: The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers, Computer Methods in Applied Mechanics and Engineering, vol. 213–216, pp. 353–361, 2012.
  • [16] Cottrell J.A., Hughes T.J.R., Bazilevs Y.: Isogeometric Analysis: Toward Integration of CAD and FEA, 2009.
  • [17] Dalcin L., Collier N., Vignal P., Cortes A.M.A., Calo V.M.: PetIGA: A framework for high-performance isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol. 308, pp. 151–181, 2016.
  • [18] Dede L., Borden M.J., Hughes T.J.R.: Isogeometric Analysis for Topology Optimization with a Phase Field Model, Archives of Computational Methods in Engineering, vol. 19, pp. 427–465, 2012.
  • [19] Duddu R., Lavier L.L., Hughes T.J.R., Calo V.M.: A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using highorder B-spline finite elements, International Journal of Numerical Methods in Engineering, vol. 89, pp. 762–785, 2012.
  • [20] Garcia D., Pardo D., Dalcin L., Paszyński M., Collier N., Calo V.M.: The Value of Continuity: Refined Isogeometric Analysis and Fast Direct Solvers, Computer Methods in Applied Mechanics and Engineering, vol. 316, pp. 586–605, 2017, https://doi.org/10.1016/j.cma.2016.08.017.
  • [21] Gomez H., Hughes T.J.R., Nogueira X., Calo V.M.: Isogeometric analysis of the isothermal Navier–Stokes–Korteweg equations, Computer Methods in Applied Mechanics and Engineering, vol. 199, pp. 1828–1840, 2010.
  • [22] Hossain S.S., Hossainy S.F.A., Bazilevs Y., Calo V.M., Hughes T.J.R.: Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls, Computational Mechanics, vol. 49, 2012. https://doi.org/10.1007/s00466-011-0633-2.
  • [23] Hsu M.-C., Akkerman I., Bazilevs Y.: High-performance computing of wind turbine aerodynamics using isogeometric analysis, Computers and Fluids, vol. 49, pp. 93–100, 2011.
  • [24] Łoś M., Mu˜noz-Matute J., Muga I., Paszyński M.: Isogeometric Residual Minimization Method (iGRM) for Stokes and Time-Dependent Stokes Problems. ArXiv:2001.00178 [math.NA].
  • [25] Łoś M., Mu˜noz-Matute J., Muga I., Paszyński M.: Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection-diffusion problems, Computers & Mathematics with Applications, vol. 79, pp. 213–229, 2020.
  • [26] Łoś M., Woźniak M., Paszyński M., Lenharth A., Hassaan M.A., Pingali K.: IGA-ADS: Isogeometric analysis FEM using ADS solver, Computer Physics Communications, vol. 217, pp. 99–116, 2017.
  • [27] Paszyński M.: On the Parallelization of Self-Adaptive hp-Finite Element Methods Part I. Composite Programmable Graph Grammar Model, Fundamenta Informaticae, vol. 93(4), pp. 411–434, 2009.
  • [28] Paszyński M.: Fast Solvers for Mesh-Based Computations, CRC Press, Taylor & Francis, 2016.
  • [29] Paszyński M., Paszyńska A.: Graph Transformations for Modeling Parallel hp-Adaptive Finite Element Method. Lecture Notes in Computer Science, vol. 4967, pp. 1313–1322, 2008.
  • [30] Paszyński M., Siwik L., Woźniak M.: Concurrency of three-dimensional refined isogeometric analysis. Parallel Computing, vol. 80, pp. 1–22, 2018.
  • [31] Piegl L., Tiller W.: The NURBS Book (Second Edition). Springer-Verlag New York, Inc., 1997.
  • [32] Prometheus. http://www.cyfronet.krakow.pl/computers/15226,artykul,promet heus.html.
  • [33] Siwik L., Woźniak M., Trujillo V., Pardo D., Calo V.M., Paszyński M.: Parallel Refined Isogeometric Analysis in 3D, IEEE Transactions on Parallel and Distributed Systems, vol. 30, pp. 1134–1142, 2019.
  • [34] Terpstra D., Jagode H., You H., Dongarra J.: Collecting Performance Data with PAPI-C. In: M¨uller M., Resch M., Schulz A., Nagel W. (eds.), Tools for High Performance Computing 2009, Springer, Berlin–Heidelberg, pp. 57–173, 2010.
  • [35] Woźniak M., Kuźnik K., Paszyński M., Calo V.M., Pardo D.: Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers, Computers & Mathematics with Applications, vol. 67, pp. 1864–1883, 2014.
  • [36] Woźniak M., Loś M., Paszyński M., Dalcin L., Calo V.M.: Parallel Fast Isogeometric Solvers for Explicit Dynamic, Computing and Informatics, vol. 36(2), pp. 423–448, 2017.
  • [37] Woźniak M., Paszyński M., Pardo D., Dalcin L., Calo V.M.: Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines, Computers Methods in Applied Mechanics and Engineering, vol. 284, pp. 971–987, 2015.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-16c35297-b2f0-4ddb-998b-aa4055d5b652
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.