Basis Light-Front Quantization: a non-perturbative approach for quantum field theory Xingbo Zhao...
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Basis Light-Front Quantization: a non-perturbative approach for quantum field theory Xingbo Zhao With Anton Ilderton, Heli Honkanen, Pieter Maris, James
Basis Light-Front Quantization: a non-perturbative approach for
quantum field theory Xingbo Zhao With Anton Ilderton, Heli
Honkanen, Pieter Maris, James P. Vary, Stan J. Brodsky Department
of Physics and Astronomy Iowa State University Ames, USA CScADS,
Snowbird, Utah, July 23-26, 2012
Slide 2
Basis Light-Front Quantization (BLFQ) approach A
nonperturbative numerical approach to quantum field theory Evaluate
the structure and interaction of elementary particles such as
electrons and nucleons, from first principle Alternative approach
to Lattice Gauge Theory History Tam-Dancoff Method [1950s] DLCQ
[1985] BLFQ [2010] Group member James Vary (advisor), Pieter Maris
(professor), Xingbo Zhao (postdoc), Paul Wiecki (student), Yang Li
(student) Funded by DoE A) Project Overview
Slide 3
B) Science Lesson Two codes presented here: electron and laser
electron: calculates the structure of electron based on quantum
electrodynamics (QED) nonperturbatively 1.Construct the Hamiltonian
matrix in optimized basis (large sparse matrix; large:
intrinsically infinite d.o.f for quantum field, sparse: the basis
respect symmetry of the Hamiltonian) 2.Diagonalize the Hamiltonian
matrix (time-independent Schrodinger Eq.) 3.Obtain the eigenvalues
(electron mass) and eigenstates (electron wavefunctions) for ground
state (physical electron) and several low-lying excited states
(excited electrons) 4.Evaluate other observables (anomalous
magnetic moment, parton distribution function) from electron
wavefunction (vector-matrix-vector multiplication) laser:
calculates the radiation from electron placed in strong background
laser field 1.Obtain electron wavefunction (column vector) from
electron code 2.Construct the operator (matrix) for the background
laser field 3.Multiply the laser matrix with the wavefunction
consecutively and obtain the quantum state at all time steps
(time-dependent Schrodinger eq.)
Slide 4
C+D) Parallel Programming Model +Code Environment Electron:
Eigenvalue/state problem for large sparse matrix Only a few
lowest-lying states are required (P)ARPACK used for (parallel)
serial diagonalization Fortran 90 at linux and Mac OS MPI as sole
parallelization Blas and lapack are required by ARPACK Numerical
recipe library used for solving nonlinear algebraic equation for
renormalization Laser: Large sparse matrix-vector multiplication
problem Fortran 95 and Mathematica Parallelization (Fortran) is
planned Matrix-vector multiplication by Fortran 95 built-in
matmul
Slide 5
E) I/O Patterns and Strategy Input I/O and output I/O patterns
Electron: Master process reads-in single input file, and writes
single output file for the entire code; both input and output files
are text files Laser: Not yet parallelized; optimization on output
desired Approximate sizes of inputs and outputs (before, during,
and after computation) Electron: input: ~ KB, output: ~ KB Laser:
input: ~ GB or above, output: ~ GB or above Checkpoint / Restart
capabilities: Electron: Results are a list of data from different
input parameters, each datum is written to file once available
Laser: Write the history of electron evolution while it is being
generating
Slide 6
F) Visualization and Analysis How do you explore the data
generated? Electron A separate Fortran code reads in the output
files of different runs, combines them and generates a single data
file, which is subsequently sent to Grace to make plots Laser
Mathematica (manipulate[]) is used to make animation for time
evolution of electron quantum state Future plans for your viz and
analysis Laser Visualize evolution of electron state in momentum
space (essentially basis transform matrix-vector
multiplication)
Slide 7
G) Performance What do you believe is your current bottleneck
to better performance? Electron: Communication between MPI
processes in the diagonalization process for Hamiltonian matrix
Laser: Parallelization needs to be done; scaling should be ok since
matrix-vector multiplication involves little communication between
MPI processes Future plans for improving performance Electron:
analyze the diagonalization process using perf. tools and improve
the algorithm for parallelization if necessary Laser: Implement
parallelization
Slide 8
H) Tools Debugging Mostly embedded write() statements to print
intermediate results; Other tools Mathematica is often used to
cross-check results in small basis space cases Current status and
future plans for improved tool integration and support No
experience on tool integration and support, want to learn here
Slide 9
Scaling for electron: Top Pains need to understand the message
passing mechanism/process better to detect / overcome bottlenecks,
hope perf. tools could help slow debug turnaround time esp. when
large core number requested I) Scalability Walltime only 223s ! 24
cores
Slide 10
J) Roadmap Better understanding on parallelization based on
MPI/OpenMP Bottlenecks on current hardware and ways around Usage of
perf tools to find out bottlenecks Electron Improve the
parallelizing algorithm for the diagonalization part (reducing
communication?) Openmp/MPI Hybrid (PARPACK compatibility?) Laser
Implement parallelization using MPI/OpenMP GPU? (mainly sparse
matrix-vector multiplication)