Nuclear structure and reactions Nicolas Michel University of Tennessee

Project Overview Unification of nuclear structure and reactions Developing new nuclear models able to describe the whole nuclear chart with realistic interactions Team: Witek Nazarewicz Thomas Papenbrock, Gaute Hagen, Jason Holt, George Papadimitriou, Jimmy Rotureau, Rodolfo Id Betan, Nicolas Schunck, Markus Kortelainen, Erik Olsen, Jordan Mc Donnell Projects sponsored by INCITE and NICS

Science Lesson Light nuclei: Configuration interation methods, Hamiltonian representation Degrees of freedom: nucleons Nuclear interaction: realistic or effective Very large matrix to diagonalize, matrix calculated on the fly Approximations: nuclear interaction and model space Complexity increases rapidly with number of nucleons Heavy nuclei: Energy density functional methods (Kohn-Sham theory) Degrees of freedom: particle and pairing densities Self-consistent one-body problem (Hartree-Fock-Bogoliubov) Systematic calculations possible Calculations of all even-even nuclei of the nuclear chart Connections: Realistic interactions to build energy density functionals Energy density functionals to contrain effective interactions

Parallel Programming Model MPI as parallelization tool Languages: Fortran 90, C++ Libraries: Blas, Lapack (Fortran 90), none (C++) Debugger, performance: gdb, gprof Platforms: Jaguar (Oak Ridge National Laboratory) Kraken (University of Tennessee) Several methods already parallelized: energy density functionals with unoptimized bases: one input file, several output files (one per nucleus) configuration interactions with renormalization group methods, one input file, a few output files Methods to parallelize in the future: energy density functionals with optimized bases configuration interactions with Davidson method fit of nuclear effective interactions with many nuclei

Computational Methods Algorithms for Hamiltonian matrix diagonalization Davidson method: Vectors must be stored on memory and disk, matrices not so sparse (maximal dimension around 10 7 ) Matrix times vector operations on the fly only, usually very robust, truncation of model space possible Restart: vectors of nuclear states stored on disk (pivot for Davidson method) Future parallelization: several vector components per node for matrix times vector Density matrix renormalization group method: Dimensions unimportant, no truncation of model space, no restart Very costly in memory and time (even parallelized), convergence problems can occur Parallelization method: independent matrix elements calculations distributed over nodes Fit of effective nuclear interactions: Metropolis Monte-Carlo, conjugate gradient method, restart trivial from optimized parameters Algorithm for energy density functionals: Modified Broyden method, trivial parallelization (several independent nuclei per node) Restart: nuclear densities stored on disk

Visualization and Analysis Data obtained from matrix diagonalization: xmgrace, gri, … Tools to obtain automatically figures from data stored on files Example : figure depicting spectrum of energies Energy density functionals: gnuplot to plot mass charts, … Web application to grant access to nuclear data Point-and-click on one nucleus to obtain binding energy, deformation, cross sections of reactions... Need for such a website

Roadmap Develop a parallel code for Davidson method and fit of effective interactions Better comprehension of nuclei at the limit of stability Scalability, memory, I/O: Several files of several Gbs to copy to each core many times Master to read files and distribute all data with MPI ? All files copied on all cores once and read independently afterwards ? New parallel codes within energy density functional being written Restrictions existing in the previous code removed Nuclei with odd number of particles, parity-breaking states