1. INFSO-RI-508833 Enabling Grids for E-sciencE www.eu-egee.org SALUTE – Grid application for problems in quantum transport E. Atanassov, T. Gurov, A. Karaivanova, M. Nedjalkov Institute for Parallel Processing Bulgarian Academy of Sciences

2. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 2 Outline Introduction (What is SALUTE) Problem description Monte Carlo methods Grid implementation and results Conclusion and future work

3. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 3 SALUTE SALUTE (Stochastic ALgorithms for Ultra-fast Transport in sEmiconductors) is a Grid application developed for solving computationally intensive problems in quantum transport. It consists of a bunch of Monte Carlo algorithms for solving quantum kinetic equations which describe the considered model. The quantum kinetic model: a femtosecond relaxation process of optically excited carriers in one-band semiconductors or quantum wires. The electron-phonon interaction is switched on after a laser pulse creates an initial electron distribution. Two cases are considered – with and without applied electric field. Using SALUTE innovative results for different materials can be obtained. Here we present the first version of SALUTE (the results are for GaAs).

4. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 4

5. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 5 The integral Equation

6. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 6 The Monte Carlo approach N independent RANDOM WALKS :

7. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 7 Monte Carlo Methods Monte Carlo Methods (MCM) provide numerical solutions to a variety of problems: –Multidimensional integrals and integral equations; –Boundary value problems in complicated domains; –Stochastic differential equations; –Eigenvalue problems, etc. through statistical sampling. They form the computational foundation for many fields including transport theory, quantum physics, computational chemistry, financial mathematics, etc. Time consuming but inherently parallel

8. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 8 Monte Carlo Methods (cont.) J is a quantity to be estimated via a MCM (in our application: different functionals of the solution of an integral equation) θ is a random variable with E[θ]=J θ N is the estimator with N samples σ(θ)N -1/2 is the statistical error Reducing the error:  Variance reduction (antithetic variates, control variates, stratification, importance sampling)  Using more powerful random numbers (quasirandom numbers instead of pseudorandom)

9. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 9 Parallel Monte Carlo Parallelism is an alternative way to accelerate the convergence of a Monte Carlo computation If n processors execute n independent copies of a MC computation, the accumulated result will have a variance n time smaller than that of a single copy A computational grid has attractively tremendous large amount of computational power  Effectively exploring the power of distributed MC application requires that the underlying random number streams in each subtask are independent in a statistical sense  Running quasi-MC in parallel is more challenging because division into subtasks is a non-trivial problem

10. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 10 Numerical tests (parameters) Scalable Parallel Random Number Generator library: independent and non-overlapping r.n. sequences (SPRNG) http://sprng.cs.fsu.edu ; GaAs material parametes; T=0 K, with and without electric field. The initial condition – product of two Gaussian distributions of the energy and space (inhomogeneous case); one Gaussian distribution of the energy (homogeneous case) Results: –Wigner function, energy distribution, electron density (inhomogeneous case); –Energy distribution and intra-collisional field effect (homogeneous case).

11. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 11 Example execution times

12. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 12 Grid implementation –MPI and single-processor versions developed –MPI version run at MPI enabled sites with:  Pbs jobmanager (with shared home directories)  lcgpbs batch system (without shared home directories). –Single processor version run in two modes:  input fixed at job submission time  input downloaded via https protocol from node running secure web service.

13. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 13 SEE sites Sites running SALUTE BG01-IPP GR-01-AUTH GR-02-UoM GR-04-FORTH-ICS HG-01-GRNET HG-04-FORTH RO-01-ICI Jobs successfully executed: > 1000

14. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 14 Collision broadening and memory effects The electron energy distribution |k|.f(0,|k|,t) version |k|^2 for a long evolution time. The relaxation leads to a time-dependent broadening of the replicas.

15. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 15 Quantum scattering- accelerating field Solutions |k|.f(0,0,k_z,t) versus |kxk|, at positive direction of the z-axis. The electric field is 0, 6 kV/cm, and 12 kV/cm. The replicas are shifted to the right by the increasing electric field. Field direction ---->>

16. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 16 Wigner Function 800 x 260 points t=175 fs

17. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 17 Energy relaxation process: collisional broadening Accumulation From 10 fs up 250 fs

18. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 18 Comparison of MPI vs single processor version Positive sides: MPI provides results faster (within the day) Single CPU version allows sites without MPI support to be utilized Single CPU version allows a lot of jobs to be submitted and executed Negative sides: MPI support on production service has some inefficiencies and problems A mysql database backend has to be used in the single CPU version for recording information about succesful/unsuccesful jobs, job inputs and outputs.

19. Enabling Grids for E-sciencE INFSO-RI-508833 EGEE User Forum, CERN, Geneva, 1-3 March 2006 19 Conclusion and Future Work The first version of SALUTE integrates MC algorithms for evaluating ultrafast relaxation processes in one band semiconductors and quantum wire. Successful tests of the application were performed at several South East European ROC EGEE sites using the Resource Broker at BG01-IPP. The test results of the MPI version show excellent parallel efficiency. SALUTE solves computationally intensive problems. By using the Grid environment provided by the EGEE project, we were able to obtain accurate results within a reasonable timeframe. We are working on improving the algorithms and the job submission procedures in order to obtain results for larger evolution times. SALUTE can provide results for other types of semiconductors like Si or for composite materials.