Emanouil I. Atanassov

Development of Grid e-Infrastructure in South-Eastern Europe

Over the period of six years and three phases, the SEE-GRID programme has established a strong regional human network in the area of distributed scientific computing and has set up a powerful regional Grid infrastructure. It attracted a number of user communities and applications from diverse fields from countries throughout the South-Eastern Europe. From the infrastructure point view, the first project phase has established a pilot Grid infrastructure with more than 20 resource centers in 11 countries. During the subsequent two phases of the project, the infrastructure has grown to currently 55 resource centers with more than 6,600 CPUs and 750 TBs of disk storage, distributed in 16 participating countries. Inclusion of new resource centers to the existing infrastructure, as well as a support to new user communities, has demanded setup of regionally distributed core services, development of new monitoring and operational tools, and close collaboration of all partner institution in managing such a complex infrastructure. In this paper we give an overview of the development and current status of SEE-GRID regional infrastructure and describe its transition to the NGI-based Grid model in EGI, with the strong SEE regional collaboration.

Generating and Testing the Modified Halton Sequences

The Halton sequences are one of the most popular low-discrepancy sequences, used for calculating multi-dimensional integrals or in quasi-Monte Carlo simulations. Various techniques for their randomization exist. One of the authors proved that for one such modification an estimate of the discrepancy with a very small constant before the leading term can be proved. In this paper we describe an efficient algorithm for generating these sequences on computers and show timing results, demonstrating the efficiency of the algorithm. We also compare the integration error of these sequences with that of the classical Halton sequences on families of functions widely used for such benchmarking purposes. The results demonstrate that the modified Halton sequences can be used successfully in quasi-Monte Carlo methods.

A new optimal Monte Carlo method for calculating integrals of smooth functions

An optimal Monte Carlo method for numerical integration of multidimensional integrals is proposed and studied. It is know that the best possible order of the mean square error of a Monte Carlo integration method over the class of the k times differentiate functions of d variables is Ο (Ν~*~?}. In this paper we present two algorithms implementing the method under consideration. Estimates for the computational complexity are obtained. Numerical tests showing the efficiency of the algorithms are also given.

Tuning the generation of sobol sequence with owen scrambling

Sobol sequence is the most widely used low discrepancy sequence for numerical solving of multiple integrals and other quasi-Monte Carlo computations Owen first proposed scrambling of this sequence through permutation in a manner that maintained its low discrepancy Scrambling is necessary not only for error analysis but for parallel implementations Good scrambling is especially important for GRID applications However, scrambling is often difficult to implement and time consuming In this paper we propose fast generation of Sobol sequence with Owen scrambling, tuned to specific hardware Numerical and timing results, demonstrating the advantages of our approach are presented and discussed.

Parallel hybrid monte carlo algorithms for matrix computations

In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D – C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D−1C, of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Further we run the algorithms on a mini-Grid and investigate their efficiency depending on the granularity. Corresponding experimental results are presented.

Parallel Quasi-Monte Carlo Methods for Linear Algebra Problems

In this paper we propose an improved quasi-Monte Carlo method for solving Linear Algebra problems. We show that by using low-discrepancy sequences both the convergence and the CPU time of the algorithm are improved. Two parallelization schemes using the Message Passing Interface with static and dynamic load balancing are proposed. The dynamic scheme is useful for computing in the GRID environment.

Quasi-Monte Carlo integration on the grid for sensitivity studies

In this paper we present error and performance analysis of quasi-Monte Carlo algorithms for solving multidimensional integrals (up to 100 dimensions) on the grid using MPI. We take into account the fact that the Grid is a potentially heterogeneous computing environment, where the user does not know the specifics of the target architecture. Therefore parallel algorithms should be able to adapt to this heterogeneity, providing automated load-balancing. Monte Carlo algorithms can be tailored to such environments, provided parallel pseudorandom number generators are available. The use of quasi-Monte Carlo algorithms poses more difficulties. In both cases the efficient implementation of the algorithms depends on the functionality of the corresponding packages for generating pseudorandom or quasirandom numbers. We propose efficient parallel implementation of the Sobol sequence for a grid environment and we demonstrate numerical experiments on a heterogeneous grid. To achieve high parallel efficiency we use a newly developed special grid service called Job Track Service which provides efficient management of available computing resources through reservations.

Ultra-fast Semiconductor Carrier Transport Simulation on the Grid

We consider the problem of computer simulation of ultra-fast semiconductor carrier transport. The mathematical description of this problem includes quantum kinetic equations whose approximate solving is a computationally very intensive problem. In order to reduce the computational cost we use recently developed Monte Carlo methods as a numerical approach. We study intra-collision field effect, i.e. effective change of phonon energy, which depends on the field direction and the evolution time. In order to obtain results for different evolution times in a reasonable time-frame, we implement simulation on the computational grid. We split the task into thousands of subtasks (jobs) which are sent to different grid sites to be executed. In this paper we present new results for inhomogeneous case in the presence of electric field, and we describe our grid implementation scheme.

Femtosecond evolution of spatially inhomogeneous carrier excitations part II: stochastic approach and grid implementation

We present a stochastic approach for solving the quantum-kinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.

Monte carlo grid application for electron transport

In this paper we present a Grid application developed for electron transport problems called SALUTE (Stochastic ALgorithms for Ultra-fast Transport in sEmiconductors). We consider a physical model of a femtosecond relaxation of optically excited electrons which interact with phonons in an one-band semicondoctor. The electron-phonon interaction is switched on after a laser pulse creates an initial electron distribution. The Barker-Ferry equation is utilized as a quantum-kinetic model of the process under consideration. Two cases of this process are investigated – with and without an applied electric field. The electric field causes shift in the replicas, population of the semiclassically forbidden regions and influences the broadening and retardation of the electron distribution. The paper describes Grid implementation of these CPU-intensive algorithms. Using this application innovative results for different materials can be obtained. Here we present the first version of SALUTE which is used to obtain innovative results for GaAs materials. The results from a number of tests on MPI-enabled Grid are shown and disscussed.