Vassil N. Alexandrov

Parallel runs of a large air pollution model on a grid of Sun computers

Large-scale air pollution models can successfully be used in different environmental studies. These models are described mathematically by systems of partial differential equations. Splitting procedures followed by discretization of the spatial derivatives lead to several large systems of ordinary differential equations of order up to 80 millions. These systems have to be handled numerically at up to 250,000 time-steps. Furthermore, many scenarios are often to be run in order to study the dependence of the model results on the variation of some key parameters (as, for example, the emissions). Such huge computational tasks can successfully be treated only if: (i) fast and sufficiently accurate numerical methods are used and (ii) the models can efficiently be run on parallel computers.The mathematical description of a large-scale air pollution model will be discussed in this paper. The principles used in the selection of numerical methods and in the development of parallel codes will be described. Numerical results, which illustrate the ability of running the fine resolution versions of the model on Sun computers, will be given. Applications of the model in the solution of some environmental tasks will be presented.

Towards understanding uncertainty in Cloud computing resource provisioning

In spite of extensive research of uncertainty issues in different fields ranging from computational biology to decision making in economics, a study of uncertainty for cloud computing systems is limited. Most of works examine uncertainty phenomena in users perceptions of the qualities, intentions and actions of cloud providers, privacy, security and availability. But the role of uncertainty in the resource and service provisioning, programming models, etc. have not yet been adequately addressed in the scientific literature. There are numerous types of uncertainties associated with cloud computing, and one should to account for aspects of uncertainty in assessing the efficient service provisioning. In this paper, we tackle the research question: what is the role of uncertainty in cloud computing service and resource provisioning? We review main sources of uncertainty, fundamental approaches for scheduling under uncertainty such as reactive, stochastic, fuzzy, robust, etc. We also discuss potentials of these approaches for scheduling cloud computing activities under uncertainty, and address methods for mitigating job execution time uncertainty in the resource provisioning.

Collaborative grid infrastructure for molecular simulations: The eMinerals minigrid as a prototype integrated compute and data grid

This paper describes a prototype grid infrastructure, called the “eMinerals minigrid”, for molecular simulation scientists. which is based on an integration of shared compute and data resources. We describe the key components, namely the use of Condor pools, Linux/Unix clusters with PBS and IBMs LoadLeveller job handling tools, the use of Globus for security handling, the use of Condor-G tools for wrapping globus job submit commands, Condors DAGman tool for handling workflow, the Storage Resource Broker for handling data, and the CCLRC dataportal and associated tools for both archiving data with metadata and making data available to other workers.

Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors.

Mixed Monte Carlo Parallel Algorithms for Matrix Computation

In this paper we consider mixed (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. In this paper 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. Experimental results with dense and sparse matrices are presented.

Using haptics to improve immersion in virtual environments

Current immersive Virtual Reality (VR) system strategies do not fully support dynamic Human Computer Interaction (HCI) and since there is a growing need for better immersion, due consideration should be given to integrate additional modalities for improved HCI. While feedback in Virtual Environments (VE) is predominantly provided to the user through the visual and auditory channels, additional modalities such as haptics can increase the sense of presence and efficiency in VE simulations. Haptic interfaces can enhance the VE interaction by enabling users to “touch” and “feel” virtual objects that are simulated in the environment. This paper examines the reasons behind its integration based on the limitations of present immersive projection system.

Workflow-Oriented collaborative grid portals

The paper presents how workflow-oriented, single-user Grid portals could be extended to meet the requirements of users with collaborative needs. Through collaborative Grid portals different research and engineering teams would be able to share knowledge and resources. At the same time the workflow concept assures that the shared knowledge and computational capacity is aggregated to achieve the high-level goals of the group. The paper discusses the different issues collaborative support requires from Grid portal environments during the different phases of the workflow-oriented development work. While in the design period the most important task of the portal is to provide consistent and fault tolerant data management, during the workflow execution it must act upon the security framework its back-end Grids are built on.

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.

Monte Carlo Numerical Treatment of Large Linear Algebra Problems

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.

A sparse parallel hybrid monte carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B−1b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.