1. Atomic Physics with Supercomputers. Darío M. Mitnik

2. Electron-Ion scattering calculations. Darío M. Mitnik

3. Atomic Physics with Supercomputers. Darío M. Mitnik

4. M. S. Pindzola, F. Robicheaux, J. Colgan, Auburn University, Auburn, AL D. C. Griffin, Rollins College, Winter Park, FL N. R. Badnell Strathclyde University, Glasgow, UK

5. Outline What are we calculating? Why do we need supercomputers for such calculations? How do we use the supercomputers in these calculations?

6. What are we calculating? Rate Coefficients Cross Sections

7. Electron-Impact Excitation kiki N  electron ion kfkf E th bb aa

8. Electron-Impact Excitation aa bb ii ff

9. (N  1) – electron ion kfkf keke Electron-Impact Ionization kiki EIEI N – electron ion aa

10. Electron-Impact Ionization aa ee ii ff

11. Radiative Recombination  N – electron ion EIEI (N+1) – electron ion kiki aa bb

12. Radiative Recombination M ba = bb a+ ia+ i  Photoionization: Radiative Recombination: M ab = 4  2 c 2 /(  2 k i ) |M ba | 2

13. Dielectronic Recombination M ba = bb a+ ia+ i  Photoionization: bb a+ ia+ i  nn nn +  n + i  n /2 +

14. N – electron ion bb EIEI (N+1) – electron ion Dielectronic Recombination kiki nn  aa

15. EIEI 1s 2 2s 1s 2 2s 2 Li-like Be-like 1s 2 2p 1s 2 2pnl 1s 2 2p 3/2 1s 2 2p 3/2 nl

16. Dielectronic Recombination D.M. Mitnik et al, Phys. Rev. A 61, 022705 (2000)

17. Dielectronic Recombination D.M. Mitnik et al, Phys. Rev. A 57, 4365 (1998)

18. Electron-ion Recombination D.M. Mitnik et al, Phys. Rev. A 59, 3592 (1999)

19. Excitation-Autoionization EIEI 1s 2 2s 1s 2 2s 2 Li-like Be-like 1s 2 2p 1s 2 2p 3/2 1s 2 2p 3/2 nl

20. Excitation-Autoionization D.M. Mitnik et al, Phys. Rev. A 53, 3178 (1996)

21. Excitation (resonances) EIEI 1s 2 2s 1s 2 2s 2 Li-like Be-like 1s 2 2p 1s 2 2p 3/2 1s 2 2p 3/2 nl

22. Excitation (resonances) D.M. Mitnik et al, Phys. Rev. A 62, 062711 (2000)

23. Excitation (resonances) D.C. Griffin et al, J. Phys. B 33, 4389 (2000)

24. Why supercomputers in Atomic Physics? only a few atomic physicists are using supercomputers

25. “Collisional breakup in a quantum system of three charged particles” M. S. Pindzola and F. Robicheaux, Phys. Rev. A 54, 2142 (1996). Why supercomputers in Atomic Physics? T. R. Rescigno et al., Science 286, 2474 (1999).

26. Electron-Impact Ionization of Hydrogen even the simplest example: e  + H H  + e  + e  has resisted solution until now

27. Methods Perturbative methods Non-Perturbative methods Distorted Waves Time-independent Time-dependent

28. Time-independent: R-matrix method P. G. Burke and K. A. Berrington 27 key papers reprinted Short Bibliography list: 547 references

29. Time-independent: R-matrix method Internal RegionExternal Region a Target H  = E   ~ sin(kr) + Kcos(kr)

30. Why supercomputers? Size of (N+1)-Hamiltonian : MXMAT = MZCHF x MZNR2 + MZNC2 # scattering channels # of continuum orbitals for given L # (N+1) terms for given SL  158 x 50 + 100 = 8000 ~ 512 Mb

31. Why supercomputers? Thousands of points are needed in order to map the narrow resonances. Energy (eV) Collision Strength D.C. Griffin et al, J. Phys. B 33, 4389 (2000)

32. Time-Dependent method Time-dependent Schrodinger equation:

33. Time-Dependent method Time-dependent close-coupled equation:

34. Why supercomputers? 16 x 250 x 250 = 1000000 250 x 250 = 62500 # coupled channels # partial waves # points in spatial lattice

35. Why supercomputers? Memory Time

36. What is a supercomputer? Distributed-Memory Shared-Memory

37. Glossary functional parallelism parallelization data parallelism

38. Example of data parallelism we have 10000 cards we want to pick up the highest card each comparison takes 1 second

39. Example of data parallelism 1 processor 10000  1 sec Time (sec) Processors 2 processors 5000  1  1 sec 10 processors 1008 sec 100 processors 198 sec 10000 processors 10000 sec

40. Example of a simple program print*, ‘hello world’ stop end call mpi_init call mpi_ rank(iam,nproc) print*, ‘hello world, from process # ’,iam call mpi_finalize stop end

41. Example of a simple program hello world hello world, from process 2 hello world, from process 0 hello world, from process 4 hello world, from process 1 hello world, from process 3

42. The R-matrix I package Inner-Region STG1 : calculates the orbital basis and all radial integrals STG2 : calculates LS-coupling matrix elements. solves the N-electron problem. sets the (N+1)-electron Hamiltonian STG3 : diagonalizes the (N+1)-electron Hamiltonian in the continuum basis

43. The R-matrix I package Outer-Region STGF : solves the external-region coupled equations. STGICF : calculates level-to-level collision strengths by doing an intermediate- coupling frame transformation.

44. Diagonalization Timing

45. Example 191 x 34 + 506 = 7000 62-state calculation: 191 coupled channels 34 continuum-box orbitals 506 (N+1)-electron bound configurations 55-state calculation (Dell 603): 59 h and 41 min 62-state calculation (T3E-900) : 64-processors - 69 min.

46. Parallelization of the external-region codes processor 1 processor 6

47. Time-Dependent method Time evolution of a single-channel: Time-dependent Schrodinger equation:

48. Time-Dependent method Initial condition for the solution:

50. Time-Dependent method

51. Propagated wavefunction:

52. Time-Dependent method Cross Section: Projection of the wavefunction:

53. Parallelization of the time-dependent codes processor 1 processor 6

54. Conclusions Atomic Physics is still alive