atomic physics with supercomputers. darío m. mitnik
TRANSCRIPT
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1Winter Workshop on Computational Atomic Physics
04/21/23
Atomic Physics with Supercomputers
Darío M. . Mitnik
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2Winter Workshop on Computational Atomic Physics
04/21/23
Electron-Ion scatteringcalculations
Darío M. . Mitnik
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3Winter Workshop on Computational Atomic Physics
04/21/23
Atomic Physics with Supercomputers
Darío M. . Mitnik
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4Winter Workshop on Computational Atomic Physics
04/21/23
M. S. Pindzola, F. Robicheaux, J. Colgan,Auburn University, Auburn, AL
D. C. Griffin,Rollins College, Winter Park, FL
N. R. BadnellStrathclyde University, Glasgow, UK
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Outline
What are we calculating?
Why do we need supercomputers for such calculations?
How do we use the supercomputers in these calculations?
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What are we calculating?
Rate Coefficients
Cross Sections
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Electron-Impact Excitation
ki
Nelectron ion
kf
Eth
b
a
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Electron-Impact Excitation
<ai| V | bf>
a
b
i
f
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(N1) – electron ionkf
ke
Electron-Impact Ionization
ki
EI
N – electron ion
a
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Electron-Impact Ionization
<ai| V | ef>
a
e
i
f
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Radiative Recombination
N – electron ion
EI
(N+1) – electron ion
ki
a
b
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Radiative Recombination
Mba= <b| D | ai >
b
a+ i
Photoionization:
Radiative Recombination:
Mab = 42c2/(2ki) |Mba|2
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Dielectronic Recombination
Mba= <b| D | ai >
b
a+ i
Photoionization:
b
a+ i
n n
+
<b| V | n > <n| D | ai >
n + i n/2+
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N – electron ion
bEI
(N+1) – electron ion
Dielectronic Recombination
ki
n
a
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Dielectronic Recombination
EI
1s22s
1s22s2
Li-like
Be-like
1s22p
1s2 2
pnl
1s22p3/2
1s2 2
p 3/2n
l
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Dielectronic Recombination
D.M. Mitnik et al, Phys. Rev. A 61, 022705 (2000)
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Dielectronic Recombination
D.M. Mitnik et al, Phys. Rev. A 57, 4365 (1998)
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Electron-ion Recombination
D.M. Mitnik et al, Phys. Rev. A 59, 3592 (1999)
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Excitation-Autoionization
EI
1s22s
1s22s2
Li-like
Be-like
1s22p
1s22p3/2
1s2 2
p 3/2n
l
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Excitation-Autoionization
D.M. Mitnik et al, Phys. Rev. A 53, 3178 (1996)
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Excitation (resonances)
EI
1s22s
1s22s2
Li-like
Be-like
1s22p
1s22p3/2
1s2 2
p 3/2n
l
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Excitation (resonances)
D.M. Mitnik et al, Phys. Rev. A 62, 062711 (2000)
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Excitation (resonances)
D.C. Griffin et al, J. Phys. B 33, 4389 (2000)
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Why supercomputersin Atomic Physics?
only a few atomic physicists are using supercomputers
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“Collisional breakup in a quantum system of three charged particles”
M. S. Pindzola and F. Robicheaux, Phys. Rev. A 54, 2142 (1996).
Why supercomputersin Atomic Physics?
T. R. Rescigno et al., Science 286, 2474 (1999).
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Electron-Impact Ionization of Hydrogen
even the simplest example: e + H H + e + e
has resisted solution until now
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Methods
Perturbative methods
Non-Perturbative methods
Distorted Waves
Time-independent
Time-dependent
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Time-independent: R-matrix method
P. G. Burke and K. A. Berrington
27 key papers reprinted
Short Bibliography list:
547 references
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Time-independent: R-matrix method
Internal Region External Regiona
Target
H = E
~ sin(kr) + Kcos(kr)
1
( )a
R a ar
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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
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Why supercomputers?
• Thousands of points are needed in order to map the narrow resonances.
Energy (eV)
Col
lisio
n S
tren
gth
D.C. Griffin et al, J. Phys. B 33, 4389 (2000)
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Time-Dependent method
Time-dependent Schrodinger equation:
1 21 2 1 2
( , , )( , ) ( , , )
r r ti H r r r r t
t
������������������������������������������������������������������������������������
1 2
2 21 2 1 2
1 2
1 1 1 1( , , ) ( , )
2 2r rH r r t V r rr r
��������������������������������������������������������
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Time-Dependent method
Time-dependent close-coupled equation:
1 2
2 21 1 1 1
1 2 2 2 2 21 2 1 1 1 2
1 1 ( 1) ( 1) 1 1( , )
2 2 2 2l l
l l l lT r r
r r r r r r
1 2
1 2 1 2
1 21 2 1 2
( , , )( , ) ( , , )
LSl l LS
l l l l
P r r ti T r r P r r t
t
1 2 1 2 1 2
1 2
' ' 1 2 ' ' 1 2' '
( , ) ( , , )L LSl l l l l l
l l
U r r P r r t
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Why supercomputers?
16 x 250 x 250 = 1000000
1 2 1 2( , , )LSl lP r r t
250 x 250 = 62500
# coupled channels
# partial waves# points in
spatial lattice
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Why supercomputers?
Memory
Time
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What is a supercomputer?
Distributed-Memory
Shared-Memory
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Glossary
functional parallelism
parallelization
data parallelism
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Example of data parallelism
• we have 10000 cards• we want to pick up the highest card• each comparison takes 1 second
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Example of data parallelism
1 processor10000 1 sec
Tim
e (s
ec)
Processors
2 processors5000 11 sec
10 processors1008 sec 100 processors
198 sec
10000 processors10000 sec
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Example of a simple program
print*, ‘hello world’stopend
call mpi_initcall mpi_ rank(iam,nproc)print*, ‘hello world, from process # ’,iamcall mpi_finalizestopend
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Example of a simple program
hello world
hello world, from process 2hello world, from process 0 hello world, from process 4 hello world, from process 1 hello world, from process 3
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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
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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.
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Diagonalization Timing
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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.
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Parallelization of the external-region codes
processor 1
processor 6
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Time-Dependent method
Time evolution of a single-channel:
1 2 1 2 1 2( ) exp ( )LS LS LS
l l l l l lP t t i tH P t
Time-dependent Schrodinger equation:
1 2
1 2 1 2
1 21 2 1 2
( , , )( , ) ( , , )
LSl l LS LS
l l l l
P r r ti H r r P r r t
t
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Time-Dependent methodInitial condition for the solution:
1 2 1 1 2 1 2 1
1( , , 0) ( ) ( ) ( ) ( )
2 i is k s kP r r t P r G r P r G r
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Initial condition for the solution:
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Time-Dependent method
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Propagated wavefunction:
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Time-Dependent method
Cross Section:
2
22 1 2 1
4LS LSnlm nlm
LS
L S Ak
Projection of the wavefunction:
1 2, ' ' ' 1 ' ' ' 2( , , ( ) ( ))LSnlm n l m nlm n l m
LS r r rtA r
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Parallelization of the time-dependent codes
processor 1
processor 6
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Conclusions
Atomic Physics is still alive
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