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Building an Affordable Linux

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Title: Building an Affordable Linux


1
Building an Affordable Linux Cluster Dedicated to
Large Scale Simulations
by Professor Tate T. H. Tsang Department of
Chemical Materials Engineering University of
Kentucky Lexington, KY 40506 tsang_at_engr.uky.edu
2
  • What is Parallel Supercomputing ?
  • Solving Large Scale Problems on Multiple
    Processors at the same time
  • It Provides High Resolution
    Results or Large Domain Simulations

  • Examples of Parallel Supercomputing
  • Oil and Gas Reservoir Simulation
  • Ground Water Pollution Simulation
  • Air Pollution Simulation
  • Global Warming
  • Numerical Weather Prediction
  • Aircraft and Automobile Design
  • Reactive Flows
  • Computational Fluid Dynamics
  • Simulation of Turbulent Flows
  • Molecular Dynamics
  • Computational Biology and Chemistry
  • Materials Processing

3
  • Essentials of Parallel Supercomputing
  • Problem Formulation Mathematical Modeling --
    putting
  • Physics, Chemistry and Biology together
  • Mesh Generation
  • Domain Decomposition
  • Development of Parallel Algorithms Numerical
    Methods
  • Parallel Programming Load Balancing and the
    use of
  • Message Passing Interface (MPI)
    Communication Library
  • Efficient Parallel Solver for Large, Sparse
    Linear Systems of
  • Equations
  • A x b
  • Scientific Visualization of Simulation Results
  • Analysis of Results

4
  • Why Linux Cluster Supercomputing ?
  • Parallel Supercomputing is based on Cluster
    Computing
  • Technology
  • The Speed of Microprocessors has increased
    Drastically
  • Pentium IV 3 GHz , RDRAM, DDR
  • AMD Athlon XP 2800 DDR
  • The Affordability and Availability of Fast
    Ethernet,
  • Gigabit Network Cards and Switches
  • The Affordability of Disk Storage (120 Gbytes)
  • PCs have the best Price/Performance ratio
  • Message Passing Interface (MPI) Communication
    Libraries
  • are Standardized and Available
  • Linux is an Open Source Operating System. Many
    Software
  • are Free for Linux !

5
  • How Fast are Todays PCs
  • Time-dependent, three-dimensional shear flow
    simulation (3D Navier-Stokes equations) from t
    0 to t 40 (steady-state) with 80 time steps,
    about 200 Newton steps, 62,500 elements and
    442,975 unknowns for each Newton steps
  • Double Precision Calculations
  • A x b
  • Single Processor
    comparison

6
  • Cluster
  • Cruncher (a 16-node AMD 1.2/1.33 GHz, DDR
    Cluster)

7
  • Cluster
  • Speedy_Gonzalez (a 5-node AMD 1.33 GHz, DDR
    Cluster)

8
  • Cluster
  • Speedy_Gonzalez2 (a 4-node Intel P4, 1.7 GHz,
    RDRAM Cluster)

9
  • Setting-up Software for the Linux Cluster
  • Install Redhat 7.1 on every node
  • Users can rlogin to any compute node without
    using password
  • Set up a Network File System (NFS) for the
    Cluster
  • Download MPICH from Argonne National Laboratory
  • Configurate and Compile MPICH on the Server Node
  • Compile your Fortran, C or C programs on the
    Server Node
  • You can set up a 8-node Linux cluster in 4 hours
  • Happy Cluster Computing Liberte, Egalite,
    Fraternite
  • Through the NFS, you can use the Cluster as an
    Archival System

10
  • Unsteady State, Three-dimensional Fluid Flow and
  • Transport Processes

11
  • Least-Squares Finite Element Methods (LSFEM)
  • First-Order Formulations
  • Tang and Tsang, Int. J. Numerical Methods
    Fluids, 21(1995), 413-432.
  • Ding and Tsang, Int. J. Comp. Fluid
    Dynamics, In Press (2001)
  • LSFEM leads to Symmetric Positive Definite
    Linear System of Equations
  • A
    x b
  • Robust Preconditioned Conjugate Gradient Methods
    can be used to obtain
  • Numerical Solution for the above SPD
    Linear System
  • Matrix-free Method (no need to assemble A) can
    be used to greatly reduce
  • Memory Requirement. This allows us to
    simulate very large problems
  • LSFEM has been used Successfully for a variety
    of Laminar and Turbulent
  • Flows
  • Ding and Tsang, Int. J. Numerical Methods
    Fluids, 37(2001), 297-319.

12
  • Domain Decomposition based Least-Squares Finite
    Element Method
  • for Parallel Computations (DD/PLSFEM)
  • Non-Overlapping Domain Decomposition
  • Each Processor uses LSFEM to Simulate Fluid Flow
    in each Subdomian
  • Ding and Tsang, Int. J. Num. Method
    Fluids (Submitted, 2001)

13
  • Message Passing Interface (MPI) Communication
    Library
  • Standardized MPI-2, MPICH and LAM Communication
    Libraries are
  • now Available for Different Computers
  • These Libraries Make Parallel Codes Portable
    across Different Computing
  • Platforms
  • Examples
  • MPI_Init Initialize MPI
  • MPI_Comm_size Find out how many Processors
  • MPI_Comm_rank Find out which process I am
  • MPI_Send Send a message
  • MPI_Recv Receive a message
  • MPI_Finalize Terminate MPI

14
  • Application 3-D Rayleigh-Benard Convection
  • Ra 8000 50,400 elements 613,965 unknowns
  • Tang and Tsang, Computer Methods in Applied
    Mechanics Engineering,
  • 140 (1997) 201-219.

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18
  • Application Lid-driven Cavity Flow (LDCF)
  • Re 1000 500,000 elements 3,500,000 unknowns
  • Ding and Tsang, International Journal of
    Computational Fluid Dynamics, In Press (2001)

19
Tang and Tsang (1995)
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22
  • Application LDCF on Cruncher (16 processors)
  • Re 400 0 lt t lt 40 62,500 elements 442,975
    unknowns
  • about 200 Newtons steps
  • Re 400 0 lt t lt 40 131,072 elements 975,975
    unknowns
  • about 200 Newtons steps

23
  • Application LDCF, Comparison between Pentium
    IV 1.7 GHz
  • and AMD 1.33
    GHz, DDR
  • Re 400 0 lt t lt 40 131,072 elements 975,975
    unknowns
  • about 200 Newtons steps
  • The Intel system is 2.3 times as costly as the
    AMD system

24
  • Application Backward Facing Step Flow on
    Cruncher
  • Re 400 50 lt t lt 60 1,280,000 elements
    9,231,327 unknowns
  • about 45 Newtons steps. It takes 5371
    sec. on 10 processors

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  • Large Eddy Simulation of Turbulent Flows

28
  • Subgrid Scale Modeling
  • Smagorinsky Model
  • Dynamic Subgrid Scale Model (Germano Lilly, 1991)

29
  • Application Transitional LDCF, use LES
  • Re 3,200 216,000 elements 2,269,810 unknowns

30
  • Application Turbulent Channel Flow

31
  • Application Turbulent Channel Flows on
    Cruncher
  • Re 3,240 0 lt t lt 12 65,536 elements 707,850
    unknowns
  • Large Eddy Simulation (LSFEM), Dynamic
    Subgrid-Scale Model
  • This simulation takes about 1,454 sec. on 8
    Processors
  • Application Turbulent Channel Flows on
    Cruncher
  • Re 3,240 2,097,152 elements 21,466,890
    unknowns
  • This simulation takes about 4 hr. on 16 Processors

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  • Application Turbulent Channel Flow
  • Comparison between AMD 1.33 GHz, DDR (Cruncher)
  • and HP NCX Supercomputer on the
    Univ. of Kentucky
  • Large Eddy Simulation

35
  • Application Turbulent Thermal Convection
  • Ra 2,500,000 76,800 elements 1,153,166
    unknowns
  • Large Eddy Simulation (LSFEM), Dynamic
    Subgrid-Scale Model

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39
  • Future Linux Cluster Supercomputers
  • Intel Itanium2 (64 bits) Processors
  • AMD Clawhammer, Opteron (64 bits) Processors
  • Linux Operating Systems (64 bits)
  • SMP Motherboards (Dual or Multiple Processors)
  • Large Disk Storage
  • Cost-effective Gigabit Network Cards and Switches
  • 10 Gigabit Network under development
  • Parallel File Systems
  • Firewall Systems
  • Sophisticated Network Design to Maximize
    Bandwidth
  • and Minimize Latency
  • Most Companies have their own Cluster
    Supercomputers
  • High Demand of People with Skills in System
    Administration,
  • Mathematical Modeling and Parallel
    Programming
  • When you enter into the world of Linux, you enter
    into

40
The New NCSA Supercomputer
41
  • Acknowledgment
  • U. S. Environmental Protection Agency (1994-2001)
  • Dr. L. Q. Tang for his pioneering research in
    LSFEM
  • Dr. X. Ding for developing and parallelizing the
    LSFEM
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