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High Performance Computing Methods

High Performance Computing Methods. Content and informations. Ralf Gruber, EPFL-STI-LIN ralf.gruber@epfl.ch. HPC methods. AT: What you hear today, must not be valid tomorrow. These days, you must be flexible at any time. RG: Theory is good, examples better, even if they are

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High Performance Computing Methods

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  1. High Performance Computing Methods Content and informations Ralf Gruber, EPFL-STI-LIN ralf.gruber@epfl.ch HPC Methods

  2. HPC methods AT: What you hear today, must not be valid tomorrow. These days, you must be flexible at any time. RG: Theory is good, examples better, even if they are only valid at the time they are executed. “HPC methods” = “Numerical experimentations” 4 credits HPC Methods

  3. Content Part 1: Computer architectures and optimisation Part 2: Approximation methods Part 3: Efficient computing Exercises HPC Methods

  4. Part 1: Computer architectures and optimisation 1.1. Evolution of supercomputing 1.1.1. Introduction to HPC 1.1.2. Historical aspects: Hardware 1.1.3. Historical aspects: Software and algorthmics 1.1.4. Bibliography 1.2. Single processor architecture and optimisation 1.2.1. Memory and processor architectures 1.2.2. Data representation and pipelining 1.2.3. System software issues 1.2.4. Application related single processor parameters 1.2.5. Application optimisation on a single processor 1.3. Parallel computer architectures 1.3.1. SMP and NUMA architectures 1.3.2. Communication network technologies 1.3.3. Cluster architectures 1.3.4. Parameterisation of parallel applications 1.3.5. Grid computing HPC Methods

  5. Part 2: Approximation methods 2.1. Stable numerical approach 2.1.1. grad-div equations: Primal form 2.1.2. Bilinear elements leading to spectral pollution 2.1.3. Ecological solution for a Cartesian grid 2.1.4. Problems with triangular meshes 2.1.5. Spectral pollution for a non-Cartesian grid 2.1.6. Non-polluting finite hybrid element method 2.1.7. Dual formulation approach 2.1.8. Isoparametric transformation 2.1.9. Bibliography 2.2. Improve precision by an h-p approach 2.2.1. Standard h-p finite elements 2.2.2. Hybrid h-p Method 2.3. Improve precision by mesh adaptation 2.3.1. The redistribution (r) method 2.3.2. 1D Example: Optimal boundary layer 2.3.3. 2D Example: The Gyrotron HPC Methods

  6. Part 3: Efficient computing 3.1. Programme environment for rapid prototyping 3.1.1. Domain decomposition 3.1.2. Memcom 3.1.3. Astrid 3.1.4. Baspl++ 3.1.5. Gyrotron example 3.1.6. 3D example: S 3.1.7. Electrofilter 3.2. Mathematical libraries 3.2.1. Introduction on direct and iterative solvers 3.2.2. BLAS, LAPACK, ScaLAPACK, ARPACK 3.2.3. MUMPS: Direct matrix solver 3.2.4. PETSc: Iterative matrix solver 3.2.5. FFTW, PRNG 3.2.6. matlab 3.2.7. Visualisation 3.3. Parallel computing 3.3.1. Direct matrix solver 3.3.2. Iterative matrix solver and MPI implementation HPC Methods

  7. Exercises E1: Exercises proposed during course E2: Practical work . by attendees . proposed by RG HPC Methods

  8. Proposals for practical work (together with specialists) Parallel Poisson finite element solver 1. For existing 2D solver, realise interface to Petsc 2. For existing 2D solver, realise interface to Mumps 3. For existing 2D solver, realise a preconditioner Graddiv eigenvalue solvers using h-p method 4. Convergence study for primal and dual forms with quadrangles and Cartesian gird 5. Influence of a non-Cartesian grid 6. Triangular elements 7. Replace Lapack eigenvalue solver by a more efficient one (Arpack) Personal programme 8. Optimise existing programme 9. Parallelise an existant serial programme 10. Replace a solver by a more efficient one Plasma physics programme 11. Optimize VMEC 12. Optimize TERPSICHORE HPC Methods

  9. Exam Practical work : 60% 15’ presentation and questions Questions on the course: 40% 15’ HPC Methods

  10. Dates/Places Course: Thursday 16:15-18:00 27.10./3.11.05 CM106 Friday 10:15-12:00 28.10.05-27.1.06 ME B31 Exercises: Thursday 16:15-18:00 10.11.-9.2.06 CM103 Friday 10:15-12:00 3.2./10.2.06 ? HPC Methods

  11. Team Course: Ralf.Gruber@epfl.ch (35906) Exercises: Vincent Keller (33856) Ralf Gruber Trach-Minh Tran MPICH, Math. libraries, Linux, plasma physics Ali Tolou (33565) Pleiades, Linux HPC Methods

  12. Global GRID? SOS workshops in HPC Commodity Computing Sandia NL 5-9.9.05 at EPFL: Oak Ridge NL CoreGRID Summer School Switzerland EU GRID? ielnx EPFL GRID Cray-1 Cray-2 Cray-T3D Swiss-T1 Pleiades Swiss GRID vector parallel vector customised MPP commodity clusters GRIDS environment applications integration industry relevance Astrid EPFL PATP EPFL Cray JPL, PSC LLNL, LANL Forall GRID: ISS EPFL ETHZ, CSCS SCS AG Compaq SNL/ORNL Swiss-Tx CoreGRID GeneProt Architecture de serveurs: Le passé à l’EPFL Computer architectures buy HPC year 02 86 90 94 98 06 10 Application-related R&D HPC Methods

  13. Parallel computer architectures accessible by EPFL HPC Methods

  14. Parallel computer architectures accessible by EPFL HPC Methods

  15. Pleiades HPC Methods

  16. Switch FE 24x24 … … 22 P4 1.8GHz/1GB 10 P4 3/2.8 GHz/2GB EPNET Fe1 Fe2 … NC NC NC NC NC NC PC PC 132 P4 2.8 GHz/2GB Pleiades 1 LIN offices Itanium 1.3 GHz/2GB P1 P2 128.178.87.0 192.168.0.0 SWITCH ProCurve 5300 (76.8Gb/s, 144 ports FE, 8 ports GBE) HPC Methods

  17. EPNET NC NC NC NC Pleiades 2 128.178.87.0 GbE … 192.168.0.0 SWITCH Black Diamond 8810 (432 Gb/s, 144 GbE ports) 120 Xeon (64bits) 2.8 GHz/4GB HPC Methods

  18. Processors of Pleiades 1 cluster (November 2003) 132 Pentium 4 (32 bit) 2.8 GHz processors -> 5.6 Gflop/s peak 2 GB dual access DDR memory (max. 6.4 GB/s) 80 GB disk (7200 turns per minute) Motherboard based on chipset Intel 875P 0.5 (#1-#100)/1(#101-#132) MB secondary cache Low cost (CHF 1’600 per processor) NFS for I/O Linux: SuSE 10.0 ifc and icc compilers from Intel gcc MKL mathematical library HPC Methods

  19. Processors of Pleiades 2 cluster (November 2005) 120 Xeon (64 bit) 2.8 GHz servers -> 5.6 Gflop/s peak 4 GB dual access DDR memory (max. 6.4 GB/s) 40 GB disk (7200 turns per minute) Motherboard based on Intel E7520 1 MB secondary cache NFS for user files, PVFS with 8 I/O nodes for scratch files Low voltage processors (140 W per server) Linux: SuSE 10.0 ifort and icc compilers from Intel gcc MKL mathematical library HPC Methods

  20. Software on Pleiades SuSE linux 10.0 SystemImager OpenPBS resource management /Maui scheduling with fairshare NFS, PVFS MPICH, PVM, (MPI-FCI) ifc/icc/gcc compilers MKL (Blas/Lapack): basic mathematical library HPC Methods

  21. Software on Pleiades petsc, aztec: parallel iterative matrix solvers ScalaPack, mumps: direct parallel matrix solvers arpack, Parpack: eigenvalue solver, serial and parallel nag: general numerical library, serial GSL: GNU scientific library fftw: serial and parallel Fast Fourier Transforms ("the best in the west") sprng: serial and parallel random number generator OpenDX: visualisation system, serial paraview: parallel visualisation system HPC Methods

  22. Software on Pleiades memcom/astrid/baspl++: program environment based on domain decomposition matlab: technical computing environment Fluent cfx/cfxturbogrid icemcfd gamess others HPC Methods

  23. Access to cluster Pleiades Ali Tolou will open accounts. Please put your name on the circulating sheet. Test if .bashrc includes the links to Memcom/Baspl++/Astrid, Matlab, paraview, and ifort compiler: module add smr module add matlab module add paraview module switch intel_comp/7.1 intel_comp/9.0 HPC Methods

  24. How to get exercises To get exercises on your account: scp -p -r ~rgruber/Cours5_6/* . You will get: daphne: The Gyrotron simulation programmedivrot: Eigenvalue computation of the 2D grad(div) and curl(curl) operators DOOR: A test example of parsolh2pm: The eigenvalue code using a H2pMmanuals: Manuals of MUMPS, Astrid, petsc, Aztecparsol: Parallel 2D Poisson solverplayground: Benchmark codes, exercises, and resultsS: A test case of the 3D ASTRID solverStokes: The 2D Stokes eigenvalue solver with div(v)=0 basis functionsterpsichore: The 3D ideal MHD stability programmeVMEC: The 3D MHD equilibrium programmeThere is a README in each directory. HPC Methods

  25. Contributions W.A. Cooper (benchmarks VMEC/TERPSICHORE) M. Deville (some tables) J. Dongarra (Top500) S. Merazzi (MEMCOM/BASPL++/ASTRID) A. Tolou (Pleiades’ system manager, LINUX) T.-M. Tran (MPI, math. libraries, benchmarks, Pleiades) HPC Methods

  26. Announcement of complementary courses Trach-Minh Tran , CRPP MPI, Introduction à la programmation parallèle Février 2006 Inscription: Josiane.Scalfo@epfl.ch, DIT Some doctoral schools give 2 credits HPC Methods

  27. Announcement of a "General Course" Laurent Villard , CRPP and André Jaun, KTH Numerical methods for PDE On-line course with exercises 6 credits HPC Methods

  28. Questions ? HPC Methods

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