DOCSLIB.ORG

Parallelising a Simulator for the Analysis of Electromagnetic Radiation Using MUMPS Library∗

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Parallelising a Simulator for the Analysis of Electromagnetic Radiation Using MUMPS Library∗ Parallelising a simulator for the analysis of electromagnetic radiation using MUMPS library∗ † R. Rico López V. Escuder Cabañas R. Durán Díaz Dep. de Automática Dep. de Automática Dep. de Automática Univ. de Alcalá Univ. de Alcalá Univ. de Alcalá Alcalá de Henares, Spain Alcalá de Henares, Spain Alcalá de Henares, Spain [email protected] [email protected] [email protected] L.E. García-Castillo I. Gómez-Revuelto J.A. Acebrón Dep. de Teoría de la Señal y Dep. de Ingeniería Audiovisual Center for Mathematics and its Comunicaciones y Comunicaciones Applications Univ. Carlos III Univ. Politécnica de Madrid Lisbon, Portugal Madrid, Spain Madrid, Spain [email protected] [email protected] [email protected] ABSTRACT that implements a novel hybrid Finite Element-Boundary The practical experience of parallelising a simulator of gen- Integral, known as Finite Element - Iterative Integral Equa- eral scattering and radiation electromagnetic problems is tion Evaluation (FE-IIEE) method ([11], [12], [10]), based on presented. The simulator stems from an existing sequential the well-known Finite Element Method (FEM). This method simulator in the frequency domain and can be fruitfully used permits an efficient analysis and solution of general problems in applications such as the test of coverage of a wireless net- of radiation and scattering of electromagnetic waves. work, analysis of complex structures, and so on. After the The analysis of the radiation and scattering of electromag- analysis of a test case, two steps were carried out: firstly, netic waves is an important issue that finds applications in a “hand-crafted” code parallelisation was developed within many electromagnetic engineering areas. Currently, compa- the kernel of the simulator. Secondly, the sequential library, nies face the challenge of cutting costs in many areas and in used in the existing simulator, was replaced by the parallel this context, it is very interesting the use of simulators be- MUMPS library in order to solve the associated linear al- fore the actual setting up of several kinds of resources. One gebra problem in parallel. For factorising the matrix with of such resources is, for example, the growing demand of MUMPS, two different ordering methods have been consid- wireless networks in urban areas. In this and other settings, ered. simulators can be advantageously used in order to reduce the time to availability and design cycles of products. Modern radiating structures, which may exhibit complex Keywords configurations with the presence of different materials, call Parallel Computing, MPI, Sparse Direct Solvers, MUMPS for the use of FEM (see, for example, [17]), which is very library flexible and able to handle within the same code, complex geometries, non-canonical surfaces, exotic permeable mate- 1. INTRODUCTION rials, anisotropy, and so on. However, FEM formulation does This paper presents the practical experience and the re- not incorporate the radiation condition. For this reason, sults obtained in the parallelisation of the code of a simulator FEM is hybridised with the use of the Boundary Integral (BI) representation of the exterior field, thus endowing the ∗Jointly funded by Comunidad Aut´onoma de Madrid FEM analysis with a numerically exact radiation boundary and Universidad de Alcal´a under grant number CAM- condition at the mesh truncation boundary. Several hybrid UAH2005/042. Also, supported by the Ministerio de schemes FEM-BI have been proposed (see, for example, [16, Educaci´on y Ciencia, Spain, under project TEC2007- 21, 13]). In contrast with standard FEM-BI approaches, FE- 65214/TCM † IIEE preserves the original sparse and banded structure of Corresponding author. the FEM matrices, allowing the use of efficient FEM solvers. In this work we show the experience and results obtained along the process of parallelising an already existing sequen- tial FE-IIEE simulator. To achieve this goal we identified Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are bottlenecks from the point of view of both memory usage not made or distributed for profit or commercial advantage and that copies and computational load, targeting a modified code which bear this notice and the full citation on the first page. To copy otherwise, to is scalable in the range of a modest number of processors. republish, to post on servers or to redistribute to lists, requires prior specific This result overcomes the limitations of the original simula- permission and/or a fee. tor, especially in terms of memory availability, thus allowing VALUETOOLS 2009, October 20-22, 2009 - Pisa, Italy. the analysis of larger problems. Copyright 2009 ICST 978-963-9799-70-7/00/0004 $5.00. Digital Object Identifier: 10.4108/ICST.VALUETOOLS2009.7456 http://dx.doi.org/10.4108/ICST.VALUETOOLS2009.7456 2. COMPUTATIONAL ANALYSIS OF THE xxxxxxxxx d ata input xxxxxxxxx SIMULATION METHOD xxxxxxxxx xxxxxxxxx In this section we analyse the consumption of computa- xxxxxxxxx xxxxxxxxx tional resources by the different building blocks inside ex- xxxxxxxxx xxxxxxxxx isting the code in order to prioritise their parallelisation. xxxxxxxxx fiactorizat on xxxxxxxxx By computational resources we refer to two clearly different xxxxxxxxx xxxxxxxxx xxxxxxxxx aspects: xxxxxxxxx xxxxxxxxx xxxxxxxxx simulator kernel • xxxxxxxxx time in computational cycles; and xxxxxxxxx xxxxxxxxx accumulated time IiE evaluat on xxxxxxxxx • memory consumption. xxxxxxxxx in 6 iterations xxxxxxxxx upgrade of b. c. xxxxxxxxx xxxxxxxxx The first aspect refers to the total time needed for the appli- xxxxxxxxx A·X B xxxxxxxxx = resolution cation to compute the results, whereas the second aspect has xxxxxxxxx xxxxxxxxx an impact over the size limit of the problems to be solved. xxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxx 2.1 Methodology xxxxxxxxx xxxxxxxxx The computational analysis of the existing code of the xxxxxxxxx error xxxxxxxxx xxxxxxxxx simulator was carried out by running a test problem. The xxxxxxxxx xxxxxxxxx test problem was selected keeping in mind that the avail- xxxxxxxxx xxxxxxxxx able computational resources were rather limited. The test xxxxxxxxx xxxxxxxxx peost-procss problem consists in the scattering problem of a plane wave xxxxxxxxx xxxxxxxxx incident on a dielectric cube with losses. The number of xxxxxxxxx xxxxxxxxx mesh elements is 2, 684, and the number of unknowns is xxxxxxxxx xxxxxxxxx 18, 288. xxxxxxxxx The available system was a cluster of eight nodes (known xxxxxxxxx new K0 as blades by the manufacturer, Sun Microsystems) model SunFire B1600. The technical details of each node can be found in Table 1. fpinal clean u Table 1: Configuration of every cluster node xxxx xxxx fiactorizat on Processor: AMD Athlon XP-M 1800+ xxxx xxxx IiE evaluat on Clock: 1.5 Ghz xxxx xxxx peost-procss Cache: 256 KB xxxx Main memory: 1 GB Hard disk: 30 GB Figure 1: Program flow and monitorisation points Network interface: 1 Gbps the simulator kernel consists of the evaluation of a double 2.2 Monitorisation integral, the upgrade of the boundary conditions and the The sequential source code was conveniently probed by solution of a linear sparse system, A · X = B. Both the ini- inserting time and memory-size controlling functions at crit- tial phase and the iterative phase are handled using a sparse ical points. solver, since A is a sparse matrix. The original sequential The probed code was sequentially executed for the test implementation used the HSL linear algebra library package problem using only one cluster node of the SunFire B1600. (formerly known as Harwell Subroutine Library, see [2]) as As a result, it became clear that the program exhibits two building block for simulation. separate computational phases: HSL is a collection of Fortran packages for large scale scientific computation that makes extensive use of BLAS • an initial phase, where the matrix is factorised; package (Basic Linear Algebra Subprograms, see [1]). The • an iterative phase, where the code performs a number sequential code uses a Fortran solver: either ME62 or ME42 of iterations inside the simulator kernel before achiev- routines, depending on whether the matrix A is symmet- ing the required accuracy. For the test problem con- ric/hermitian or not. Optionally, those routines may work sidered, obtaining a threshold relative error δ between with direct-access files for the matrix factors so that large −4 subsequent iterations below 10 required a total of problems can be solved using a relatively small in-core mem- six iterations. ory. However, the storage in disk has a limited speed to ac- cess factors and the size of the files can render the situation The previous scheme can be repeated for different frequen- unmanageable as the number of unknowns grows. cies. In our test case, only one frequency, denoted K0 in Thus, the parallelisation is motivated to overcome the lim- Fig. 1, was used. itations of the sequential code, so that larger problems can The results obtained with the previous execution are de- be run in a reasonable time frame and with limited memory picted in Fig. 1, showing the points where the monitorisation resources. Specifically, the results relative to the present im- was inserted. Only those blocks that have a relevant com- plementation shown in this paper have been obtained using putational load are shown. In this Fig. it is apparent that ME62 Fortran solver (complex symmetric case) with in-core Digital Object Identifier: 10.4108/ICST.VALUETOOLS2009.7456 http://dx.doi.org/10.4108/ICST.VALUETOOLS2009.7456 storage. 3. HAND-CRAFTED PARALLELISATION The algorithm used for element ordering (crucial for the The parallelisation was carried out using the message pass- performance of the frontal solver) with HSL is a variant ing interface (MPI, [5]), with the support of the MPICH2 of Sloan’s algorithm [20], implemented in MC63 routine of library (specifically, version 1.0.8) HSL. Indirect element ordering with default MC63 param- The hand-crafted code parallelisation targeted essentially eters is used prior to calling the frontal solver factorisation the heavy computation load given by the convolution-type routines.
Load more

Recommended publications
  • MUMPS Users' Guide
    MUltifrontal Massively Parallel Solver (MUMPS 5.4.1) Users’ guide * August 3, 2021 Abstract This document describes the Fortran 95 and C user interfaces to MUMPS5.4.1, a software package to solve sparse systems of linear equations, with many features. For some classes of problems, the complexity of the factorization and the memory footprint of MUMPS can be reduced thanks to the Block Low-Rank (BLR) feature. We describe in detail the data structures, parameters, calling sequences, and error diagnostics. Basic example programs using MUMPS are also provided. Users are allowed to save to disk MUMPS internal data before or after any of the main steps of MUMPS (analysis, factorization, solve) and then restart. *Information on how to obtain updated copies of MUMPS can be obtained from the Web page http://mumps-solver.org/ 1 Contents 1 Introduction 5 2 Notes for users of other versions of MUMPS 6 2.1 ChangeLog........................................7 2.2 Binary compatibility....................................7 2.3 Upgrading between minor releases............................7 2.4 Upgrading from MUMPS 5.3.5 to MUMPS 5.4.1 ...................8 2.5 Upgrading from MUMPS 5.2.1 to MUMPS 5.3.5 ...................8 2.6 Upgrading from MUMPS 5.1.2 to MUMPS 5.2.1 ...................8 2.7 Upgrading from MUMPS 5.0.2 to MUMPS 5.1.2 ...................9 2.7.1 Changes on installation issues...........................9 2.7.2 Selective 64-bit integer feature..........................9 2.8 Upgrading from MUMPS 4.10.0 to MUMPS 5.0.2 .................. 10 2.8.1 Interface with the Metis and ParMetis orderings................
    [Show full text]
  • Arxiv:2105.11220V1 [Cs.DC] 24 May 2021 the Motion of Particles Is Described by a Set of Convection-Diffusion-Reaction Equations
    Towards Parallel CFD computation for the ADAPT framework Imad Kissamiy∗, Christophe Ceriny, Fayssal Benkhaldoun∗, and Gilles Scarella∗ Universit´ede Paris 13 y LIPN, ∗ LAGA, 99, avenue Jean-Baptiste Cl´ement, 93430 Villetaneuse, France [email protected] Abstract. In order to run Computational Fluid Dynamics (CFD) codes on large scale infrastructures, parallel computing has to be used because of the computational intensive nature of the problems. In this paper we investigate the ADAPT platform where we couple flow Partial Differ- ential Equations and a Poisson equation. This leads to a linear system which we solve using direct methods. The implementation deals with the MUMPS parallel multi-frontal direct solver and mesh partitioning meth- ods using METIS to improve the performance of the framework. We also investigate, in this paper, how the mesh partitioning methods are able to optimize the mesh cell distribution for the ADAPT solver. The ex- perience gained in this paper facilitates the move to the 3D version of ADAPT and the move to a Service Oriented view of ADAPT as future work. Keywords: Unstructured mesh, Mesh partitioning, Parallel direct solver, Multi-frontal method, MUMPS, METIS, Multi-physics, Multi-scale and Multilevel Algorithms. 1 Introduction and context of the work In the last recent decades CFD (Computational Fluid Dynamics) used to play an important role in industrial designs, environmental impact assessments and academic studies. The aim of our work is to fully parallelize an unstructured adaptive code for the simulation of 3D streamer propagation in cold plasmas. As a matter of fact, the initial sequential version of the Streamer code needs up to one month for running typical benchmarks.
    [Show full text]
  • Multifrontal Massively Parallel Solver (MUMPS 4.8.4) Users' Guide
    MUltifrontal Massively Parallel Solver (MUMPS 4.8.4) Users’ guide ∗ December 15, 2008 Abstract This document describes the Fortran 90 and C user interface to MUMPS 4.8.4 We describe in detail the data structures, parameters, calling sequences, and error diagnostics. Example programs using MUMPS are also given. A preliminary out-of-core functionality (with limited support) is included in this version. ∗Information on how to obtain updated copies of MUMPS can be obtained from the Web pages http://mumps.enseeiht.fr/ and http://graal.ens-lyon.fr/MUMPS/ 1 Contents 1 Introduction 4 2 Main functionalities of MUMPS 4.8.4 5 2.1 Inputmatrixstructure . ....... 5 2.2 Preprocessing ................................... .... 5 2.3 Post-processingfacilities . .......... 6 2.4 Solvingthetransposedsystem. ......... 6 2.5 Reduce/condense a problem on an interface (Schur complement and reduced/condensed right-handside) .................................... 7 2.6 Arithmeticversions .... ............. ............. ...... 8 2.7 Theworkinghostprocessor . ....... 8 2.8 Sequentialversion..... ............. ............. ...... 8 2.9 Sharedmemoryversion . ..... 8 2.10 Out-of-corefacility . ........ 8 3 Sequence in which routines are called 8 4 Input and output parameters 11 4.1 Versionnumber ................................... 11 4.2 Control of the three main phases: Analysis, Factorization,Solve ............. 11 4.3 Controlofparallelism . ....... 12 4.4 Matrixtype ...................................... 13 4.5 Centralized assembled matrix input: ICNTL(5)=0 and ICNTL(18)=0 .......... 13 4.6 Element matrix input: ICNTL(5)=1 and ICNTL(18)=0 . ............. 14 4.7 Distributed assembled matrix input: ICNTL(5)=0 and ICNTL(18)=0 .......... 14 4.8 Scaling.........................................6 . 15 4.9 Givenordering:ICNTL(7)=1 . ....... 15 4.10 Schur complement with reduced (or condensed) right-hand side: ICNTL(19) and ICNTL(26) .......................................
    [Show full text]
  • Python Interface Release 5.4.1
    Python Interface Release 5.4.1 Luis Saavedra Jul 22, 2021 Contents 1 Introduction 1 2 Installation 3 3 Preliminary 5 4 Python GetFEM interface7 4.1 Introduction........................................7 4.2 Parallel version.......................................7 4.3 Memory Management...................................8 4.4 Documentation.......................................8 4.5 Python GetFEM organization...............................8 5 Examples 11 5.1 A step-by-step basic example............................... 11 5.2 Another Laplacian with exact solution (source term)................... 14 5.3 Linear and non-linear elasticity.............................. 16 5.4 Avoiding the model framework.............................. 19 5.5 Other examples....................................... 20 6 How-tos 23 6.1 Import gmsh mesh..................................... 23 7 API reference 25 7.1 ContStruct......................................... 25 7.2 CvStruct.......................................... 27 7.3 Eltm............................................ 28 7.4 Fem............................................. 28 7.5 GeoTrans.......................................... 31 7.6 GlobalFunction....................................... 32 7.7 Integ............................................ 33 7.8 LevelSet.......................................... 35 7.9 Mesh............................................ 36 7.10 MeshFem.......................................... 44 7.11 MeshIm........................................... 50 7.12 MeshImData.......................................
    [Show full text]
  • DEPARTMENT of INFORMATICS Configuration of a Linear Solver For
    DEPARTMENT OF INFORMATICS TECHNISCHE UNIVERSITÄT MÜNCHEN Master’s Thesis in Computational Science and Engineering Configuration of a linear solver for linearly implicit time integration and efficient data transfer in parallel thermo-hydraulic computations Ravil Dorozhinskii DEPARTMENT OF INFORMATICS TECHNISCHE UNIVERSITÄT MÜNCHEN Master’s Thesis in Computational Science and Engineering Configuration of a linear solver for linearly implicit time integration and efficient data transfer in parallel thermo-hydraulic computations Konfiguration eines Lösers für linear-implizite Zeitintegration und effizienter Datentransfer in parallelen thermohydraulischen Berechnungen Author: Ravil Dorozhinskii Supervisor: Prof. Dr. Thomas Huckle Advisors: Dr. rer. nat. Tim Steinhoff, Dr. rer. nat. Tobias Neckel Submission Date: 07 March 2019 I confirm that this master’s thesis is my own work and I have documented all sources and material used. Munich, 07 March 2019 Ravil Dorozhinskii Abstract Key words. numerical time integration, direct sparse linear methods, multifrontal methods, MUMPS, BLAS, parallel performance, distributed-memory computations, multi-threading, MPI, OpenMP, non-blocking communication An application of linearly implicit methods for time integration of stiff systems of ODEs results in solving sparse systems of linear equations. An optimal selection and configuration of a parallel linear solver can considerably accelerate the time integration process. A comparison of iterative and direct sparse linear solvers has shown that direct ones are the most suitable for this purpose because of their natural robustness to ill-conditioned linear systems that can occur during numerical time integration. Testing of different direct sparse solvers applied to systems generated by ATHLET software has revealed that MUMPS, an implementation of the multifrontal method, performs better than the others in terms of the overall parallel execution time.
    [Show full text]
  • Combinatorial Problems in Solving Linear Systems Iain
    COMBINATORIAL PROBLEMS IN SOLVING LINEAR SYSTEMS IAIN S. DUFF and BORA UC¸AR Technical Report: No: TR/PA/09/60 CERFACS 42 av. Gaspard Coriolis, 31057 Toulouse, Cedex 1, France. Available at http://www.cerfacs.fr/algor/reports/ Date: August 7, 2009. COMBINATORIAL PROBLEMS IN SOLVING LINEAR SYSTEMS∗ IAIN S. DUFFy z AND BORA UC¸ARx Abstract. Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices therefore form the basis of the interaction of these two seemingly disparate subjects. As the core of many of today's numerical linear algebra computations consists of the solution of sparse linear system by direct or iterative methods, we survey some combinatorial problems, ideas, and algorithms relating to these computations. On the direct methods side, we discuss issues such as matrix ordering; bipartite matching and matrix scaling for better pivoting; task assignment and scheduling for parallel multifrontal solvers. On the iterative method side, we discuss preconditioning techniques including incomplete factorization preconditioners, support graph preconditioners, and algebraic multigrid. In a separate part, we discuss the block triangular form of sparse matrices. Key words. Combinatorial scientific computing, graph theory, combinatorial optimization, sparse matrices, linear system solution 1. Introduction. In this short review paper, we examine the interplay between the solution of sparse linear systems and combinatorics. Most of this strong associa- tion comes from the identification of sparse matrices with graphs so that most algo- rithms dealing with sparse matrices have a close or exact analogue to an algorithm on a graph.
    [Show full text]
  • A Bibliography of Publications of Iain S. Duff
    A Bibliography of Publications of Iain S. Duff Iain S. Duff Rutherford Appleton Laboratory Chilton, Oxon UK Tel: +44-235-445803 FAX: +44-235-446626 E-mail: [email protected] (Internet) 19 March 2021 Version 2.61 Abstract [Duf91b]. 1991 [Ano91, FF93]. 1993 [Duf94a, GW94]. 1994 [MC95]. 1995 This bibliography records publications of Iain [Duf96a, PB96]. 1996 [DGDG97a]. 1997 S. Duff. [Duf98b]. 1999 [Duf00a]. 1st [DFT95, HPP88]. Title word cross-reference 2 [ADD89a, ADD92, DD87a, DD88, DD89, DD90a, DD90b, DD91, Duf88b, DV98a]. 200/VF [DD88, DD89]. 2000 − A 1 [ADLR15]. LU [DD92a, DD90b, DD91]. [ACM00, vdVDE+02]. 2001 QR [ADP94]. LDLT [ADGP07, DHL20]. [Ano01, Duf02a]. 2002 [vdVDE+03]. 2003 LU [DD94a, DD97b]. O(n1=2τ) [DW88]. P 4 [Duf04b]. 2008 [BBD+11, TCJ+10]. 2010 [DAGR87, ADGR90]. P 5 [TBC+11]. 2e [AG80]. 2nd [DAGR87, ADGR90]. QR [ADP96]. [AG80, BBD+11, DR85a]. 1 [DR82a, Duf82b, Duf82c, Duf84g]. 10P 3 [DDP94]. 3090 [ADD89a, ADD92, DD88, DD89]. 11th [ADD89a, ADD92, DD88, DD89, DD90a]. [Duf81i]. 14th [Ame94]. 15th [GW94]. 1978 3090-200 [DD88, DD89]. 3090-200/VF [DS79]. 1979 [GL80]. 1981 [DD88, DD89]. 31-September [ABD+99]. [Hen82, TH82, Wat82]. 1982 [PR83]. 1983 [ESY84, Kow84]. 1984 [DR85a]. 1986 5th [ABD+99, SMMG01, WDPW04]. [IP87, PA88]. 1987 [Duf88c]. 1988 [CRQR89, Duf89f, ES89]. 1989 70th [DW91]. [Ano89, DG89, DMSV90, EJP90]. 1990 1 2 8 [Duf87d, Duf89e, Duf90a]. 80 ALLIANT [DD90a, ADD89a, ADD92, [ADD89a, ADD92, DD90a, DD90b, DD91]. DD90b, DD91, Duf87d, Duf89e, Duf90a]. 818 [DV02a]. 837 [ADD04]. AMD [ADD04]. Analysis [ADLL00, ADLL01c, ADLL01d, ADGS10, ’90 [Sup90, Jap90]. 92-VAPP [BCRT92]. Duf72, Duf81i, Duf86a, Duf88c, Duf89f, ’94 [Ame94, DW94].
    [Show full text]
  • An Interview with IAIN S. DUFF Conducted by Thomas Haigh on 30
    An interview with IAIN S. DUFF Conducted by Thomas Haigh On 30 & 31st August, 2005 In East Hagbourne and Chilton, United Kingdom Interview conducted by the Society for Industrial and Applied Mathematics, as part of grant # DE-FG02-01ER25547 awarded by the US Department of Energy. Transcript and original tapes donated to the Computer History Museum by the Society for Industrial and Applied Mathematics © Computer History Museum Mountain View, California ABSTRACT Iain S. Duff explores the whole of his career to date. Duff grew up in Glasgow, attending The High School before earning a first class degree in Mathematics and Natural Philosophy from the University of Glasgow in 1969. He discusses the mathematical curriculum there, and recounts his early computing experiences as a summer fellow with IBM. Duff won a Carnegie Fellowship for postgraduate work at Oxford, culminating in a D.Phil. conferred in 1972. At Oxford he worked with the numerical analysis group and wrote his thesis on the analysis of sparse systems under the direction of Leslie Fox. While working toward his degree, Duff was already collaborating with Alan Curtis, Michael Powell, and John Reid at the nearby AERE Harwell nuclear power research center. His interest in sparse matrices was cemented by a 1971 visit to IBM’s Yorktown Heights laboratory for a conference, where he first met colleagues such as Alan George, Ralph Willoughby and Fred Gustavson. In 1972, Duff went to the United States on a Harkness postdoctoral fellowship, spending time at SUNY Stony Brook with Reggie Tewarson and Stanford, where he got to know Gene Golub.
    [Show full text]
  • High Performance Computing of Three-Dimensional Finite Element Codes on a 64-Bit Machine
    Journal of Applied Fluid Mechanics, Vol. 5, No. 2, pp. 123-132, 2012. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645. High Performance Computing of Three-Dimensional Finite Element Codes on a 64-bit Machine M.P. Raju1† and S.K. Khaitan2 1 Department of Mechanical Engg., Case Western Reserve University, Cleveland, OH, 44106, USA 2 Department of Electrical Engg., Iowa State University, Ames, IA, 50014, USA †Corresponding Author Email: [email protected] (Received March 8, 2009; accepted March 28, 2009) ABSTRACT Three dimensional Navier-Stokes finite element formulations require huge computational power in terms of memory and CPU time. Recent developments in sparse direct solvers have significantly reduced the memory and computational time of direct solution methods. The objective of this study is twofold. First is to evaluate the performance of various state-of-the-art sequential sparse direct solvers in the context of finite element formulation of fluid flow problems. Second is to examine the merit in upgrading from 32 bit machine to a 64 bit machine with larger RAM capacity in terms of its capacity to solve larger problems. The choice of a direct solver is dependent on its computational time and its in-core memory requirements. Here four different solvers, UMFPACK, MUMPS, HSL_MA78 and PARDISO are compared. The performances of these solvers with respect to the computational time and memory requirements on a 64-bit windows server machine with 16GB RAM is evaluated. Keywords: Multifrontal, UMFPACK, MUMPS, HSL MA78, PARDISO, 64-bit. 1. INTRODUCTION iterative methods like SIMPLE algorithm used in finite volume formulations.
    [Show full text]
  • Short User Documentation Release 4.0
    Short User Documentation Release 4.0 Yves Renard, Julien Pommier March 22, 2010 CONTENTS 1 Introduction 1 2 How to install 3 2.1 Requirements...............................................3 2.2 Download sources............................................3 2.3 Compilling................................................4 3 Linear algebra procedures 7 4 Parallelization of GetFEM++ 9 5 Catch errors 11 6 Build a mesh 13 6.1 Add an element to a mesh........................................ 13 6.2 Remove an element from a mesh.................................... 15 6.3 Simple structured meshes........................................ 15 6.4 Mesh regions............................................... 16 6.5 Methods of the getfem::mesh object................................ 16 6.6 Using dal::bit_vector ....................................... 18 6.7 Face numbering............................................. 19 6.8 Save and load meshes.......................................... 19 7 Build a finite element method on a mesh 23 7.1 First level: manipulating fems on each elements............................ 24 7.2 Examples................................................. 25 7.3 Second level: the optional “vectorization”................................ 25 7.4 Third level: the optional linear transformation (or reduction)...................... 26 7.5 Obtaining generic mesh_fem‘s...................................... 27 7.6 The partial_mesh_fem object...................................... 27 8 Selecting integration methods 29 8.1 Methods of the mesh_im object....................................
    [Show full text]
  • Amesos 2.0 Reference Guide
    SANDIA REPORT SAND2004-4820 Unlimited Release Printed September 2004 Amesos 2.0 Reference Guide Marzio Sala Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94-AL85000. Approved for public release; further dissemination unlimited. Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or re- sponsibility for the accuracy, completeness, or usefulness of any information, appara- tus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Govern- ment, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from U.S.
    [Show full text]
  • Amesos 2.0 Reference Guide
    SANDIA REPORT SAND2004-XXXX Unlimited Release Printed October 2004 Amesos 2.0 Reference Guide Marzio Sala Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94-AL85000. Approved for public release; further dissemination unlimited. Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or re- sponsibility for the accuracy, completeness, or usefulness of any information, appara- tus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Govern- ment, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from U.S.
    [Show full text]