computation and inversion of the dielectric matrix
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Computation and inversion of the dielectric matrix Derek Vigil-Fowler UC-Berkeley and LBNL BW Symposium 05/12/15 Email - vigil@berkeley.edu Materials Science for Energy, Technology Materials Science for Energy, Technology Dielectric response

  1. Computation and inversion of the dielectric matrix Derek Vigil-Fowler UC-Berkeley and LBNL BW Symposium 05/12/15 Email - vigil@berkeley.edu

  2. Materials Science for Energy, Technology

  3. Materials Science for Energy, Technology

  4. Dielectric response :

  5. Dielectric response : E&M

  6. Dielectric response : E&M

  7. Dielectric response : quantum mechanics

  8. Dielectric response : quantum mechanics

  9. Dielectric response : quantum mechanics

  10. Pictorially

  11. Pictorially

  12. How to do one big matrix multiplication + inversion?

  13. How to do one big matrix multiplication + inversion? Parallelism!

  14. How to do one big matrix multiplication + inversion? BLAS + ScaLAPACK + MPI/OpenMP

  15. Distributed matrix multiplication

  16. Distributed matrix multiplication

  17. Problem with scheme : many frequencies done serially • Lots of communication and array assignments • All processors work on 1 frequency – But ScaLAPACK doesn’t scale past ~ few hundred processors! – Smaller problems : can’t utilize ScaLAPACK enough → Wasted processors

  18. Solution : do many frequencies in parallel!

  19. Solution : do many frequencies in parallel!

  20. Solution : do many frequencies in parallel!

  21. Results

  22. Results Bulk Si with 288 proc CO with 144 proc nfreq_par 1 2 8 1 2 8 Matmul 13.12 8.934 4.395 9.31 6.89 2.13 total Matmul 10.75 7.08 3.23 1.27 1.01 0.66 prep Matmul 2.17 1.75 1.135 1.85 1.60 0.90 dgemm Matmul 0.2 0.104 0.027 6.18 4.27 0.57 comm Invert 0.744 0.26 0.064 5.28 2.60 0.93 total

  23. Conclusions • Parallelizing over frequencies reduced communication, array assignment, and saturates ScalaPACK : faster run- time. • Also, for big problems will allow scaling to higher processors counts for the frequency-dependent inverse dielectric matrix, a quantity of wide interest

  24. Acknowledgments • Blue Waters Graduate Fellowship • Jack Deslippe – NERSC • Felipe Homrich da Jornada – UC-Berkeley This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.

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