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Tytuł artykułu

Minimizing the memory usage with parallel out-of-core multi-frontal direct solver

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Języki publikacji
EN
Abstrakty
EN
This paper presents the out-of-core solver for three-dimensional multiphysics problems. In particular, our study focuses on the three-dimensional simulations of the linear elasticity coupled with acoustics. The out-of-core solver is designed with three principles in mind. First, to store the dense matrices associated with the nodes of the elimination tree with blocks related to nodes of the mesh, where many degrees of freedom may be located in the case of multiphysics computations with high order polynomials. The second principle is to minimize the memory usage. This is obtained by dumping out all local systems from the entire elimination tree to the disk during the elimination stage. The local systems are reutilized later during the backward substitution stage. The third principle is that the communication in the parallel version of the out-of-core solver occurs through the parallel file system. The memory usage of the solver is compared against the state-of-the-art MUMPS solver.
Rocznik
Strony
15--41
Opis fizyczny
Bibliogr. 25 poz., rys., tab., wykr.
Twórcy
  • AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications Department of Computer Scienceal. A. Mickiewicza 30, 30-059 Krakow, Poland
Bibliografia
  • [1] M. Paszyński, D. Pardo, C. Torres-Verdin, L. Demkowicz,V. Calo. A parallel direct solver for the self-adaptive hp finite element method. Journal of Parallel and Distributed Computing, 70(3): 270–281, 2010.
  • [2] M. Paszyński, R. Schaefer. Graph grammar driven partial differential eqautions solver. Concurrency and Com-putations: Practise and Experience, 22(9): 1063–1097, 2010.
  • [3] A. Szymczak, M. Paszyński. Graph grammar based Petri netcontrolled direct sovler algorithm. Computer Science, 11: 65–79, 2010.
  • [4] M. Paszyński, R. Schaefer. Reutilization of partial LU factorizations for self-adaptive hp Finite Element Method solver. Lecture Notes in Computer Science, 5101: 965–974, 2008.
  • [5] M. Paszyński, L. Demkowicz. Parallel, fully automatic,hp-adaptive 3D finite element package. Engineering withComputers, 22: 255–276, 2006.
  • [6] L. Demkowicz, J. Kurtz, D. Pardo, M. Paszyński, W. Rachowicz, A. Zdunek. Computing with hp-Adaptive FiniteElements, Vol. II. Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications. Chapman &Hall/CRC Applied Mathematics & Nonlinear Science, 2007.
  • [7] M. Paszyński, D. Pardo, A. Paszyńska. Parallel multi-frontal solver forp-adaptive finite element modeling ofmulti-physics computational problems. Journal of Computational Science, 1: 48–54, 2010.
  • [8] L. Demkowicz, P. Gatto, J. Kurtz, M. Paszynski, W. Rachowicz, E. Bleszyński, M. Bleszyński, M. Hamilton,C. Champlin, D. Pardo. Modeling of bone conduction of sound in human head using hp finite elements. Part I.Code design and modificaton. Computer Methods in Applied Mechanics and Engineering, 200: 1757–1773, 2011.
  • [9] D. Pardo. Integration of hp-Adaptivity with a Two-Grid Solver. PhD. Dissertation. University of Texas atAustin, 2004.
  • [10] D. Pardo, L. Demkowicz, C. Torres-Verdin, M. Paszyński. A self-adaptive goal-oriented hp finite element methodwith electromagnetic applications. Pt. 2, Electrodynamics. Computer Methods in Applied Mechanics and Engineering, 196: 3585–3597, 2007.
  • [11] P.R. Amestoy, I.S. Duff, J. Koster, J.-Y. L’Excellent. Afully asynchronous multifrontal solver using distributeddynamic scheduling.SIAM Journal of Matrix Analysis and Applications, 23(1): 15–41, 2001.
  • [12] P.R. Amestoy, A. Guermouche, J.-Y. L’Excellent, S. Pralet. Hybrid scheduling for the parallel solution of linearsystems. Parallel Computing, 32(2): 136–156, 2006.
  • [13] Multi-frontal Massively Parallel Sparse direct solver (MUMPS), http://graal.ens-lyon.fr/MUMPS.
  • [14] D. Pardo, M.J. Nam, C. Torres-Verdin, M. Hoversten, I. Garay. Simulation of Marine Controlled Source Electro-magnetic Measurements Using a Parallel Fourierhp-Finite Element Method. Computational Geosciences, 15(1):53–67, 2011
  • [15] N.I.M. Gould, J.A. Scott, Hu Yifan. Numerical Evaluation of Sparse Direct Solvers for the Solution of LargeSparse Symmetric Linear Systems of Equations.ACM Transactions on Mathematical Software (TOMS), 33(2)10:300–331, 2007.
  • [16] S. Fialko. A block sparse shared-memory multifrontal finite element solver for problems of structural mechanics. Computer Assisted Mechanics and Engineering Sciences,16: 117–131, 2009.[17] S. Fialko.A Sparse Shared-Memory Multifrontal Solver in SCAD Software, Proceedings of the International Multiconference on Computer Science and Information Technology. October 22–28, 2009,Wisła, Poland, 3: 277–283, 2008.
  • [18] S. Fialko. The block substructure multifrontal methodfor solution of large finite element equation SETS. Tech-nical Transactions, 1-NP/2009 (8): 175–188, 2009.
  • [19] A. George, J.W.H. Liu.Computer solution of sparse positive definite systems. New Jersey: Prentice-Hall, Inc.Englewood Cliffs, 1981.
  • [20] S. Fialko. The Nested Substructures Method for SolvingLarge Finite-Element Systems as Applied to Thin-Walled Shells with High Ribs. International Applied Mechanics, 39(3): 324–332, 2003.
  • [21] P. Gend, J.T. Oden, R. van de Geijn. A parallel multifrontal algorithm and its implementation. ComputerMethods in Applied Mechanics and Engineering, 149: 289–301, 1997.
  • [22] C. Ashcraft, J.W.H. Liu.Robust Ordering of Sparse Matrices Using Multisection, Technical Report CS 96-01. Department of Computer Science, York University, Ontario,Canada, 1996.
  • [23] I. Babuska, B. Guo. The hp-version of the finite elementmethod, Part I: The basic approximation results.Computational Mechanics, 1: 21–41, 1986.
  • [24] I. Babuska, B. Guo. The hp-version of the finite elementmethod, Part II: General results and applications.Computational. Mechanics, 1: 203–220, 1986.
  • [25] M. Paszyński, D. Pardo, A. Paszyńska. Parallel multi-frontal solver forpadaptive finite element modeling of multi-physics computational problems.Journal of Computational Science, 1: 48–54, 2010.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-62850571-b33c-46e8-91d9-a30200dd2f63
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