Advanced Mathematical Methods for Scientists and Engineers

[서평]「Component Software」 - Beyond Object-Oriented Programming -

A brief survey on numerical methods for solving singularly perturbed problems

Postgraduate Students: Vladimír Arnot, Daniel Čapek, Rudolf Čejka, Dao Minh, Tomá Dulík, Martin Hrubý, Radek Kočí, Petr Kotásek, Marek Křejpský, Bohuslav Křena, Vladislav Kubíček, Vladimír Marek, Petr Matouek, Ale Mičín, Jiří Očenáek, Tomá Ondráček, Petr Peňás, Jaroslav Ráb, Richard Růička, Luká Sekanina, Ivan Schwarz, Azedien Sllame, Petr Smolík, Jiří Staroba, Josef Strnadel, Luká Szemla, Pavel Tinovský, Michal Tomů, Milan Urbáek, Michal Vojkůvka, Petr Vurm, Frantiek Zbořil

Department of Computer Science and Engineering

Cloud computing is extensively used in a variety of applications and domains, however task and resource scheduling remains an area that requires improvement. Put simply, in a heterogeneous computing system, task scheduling algorithms, which allow the transfer of incoming tasks to machines, are needed to satisfy high performance data mapping requirements. The appropriate mapping between resources and tasks reduces makespan and maximises resource utilisation. In this contribution, we present a novel scheduling algorithm using Directed Acyclic Graph (DAG) based on the Prediction of Tasks Computation Time algorithm (PTCT) to estimate the preeminent scheduling algorithm for prominent cloud data. In addition, the proposed algorithm provides a significant improvement with respect to the makespan and reduces the computation and complexity via employing Principle Components Analysis (PCA) and reducing the Expected Time to Compute (ETC) matrix. Simulation results confirm the superior performance of the algorithm for heterogeneous systems in terms of efficiency, speedup and schedule length ratio, when compared to the state-of-the-art Min-Min, Max-Min, QoS-Guide and MiM-MaM scheduling algorithms.

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A Task Scheduling Algorithm With Improved Makespan Based on Prediction of Tasks Computation Time algorithm for Cloud Computing

Singularly perturbed self-adjoint boundary-value problems are considered in this article. A difference scheme based on quintic spline is proposed. This scheme is applied to the subproblems obtained from the given problem by dividing the whole domain into nonoverlapping subdomains. The proposed scheme is of fourth-order convergent and more suitable for parallel computers. Stability and convergence of the method are discussed. Numerical examples are provided to show the efficiency and accuracy.

A computational method for self-adjoint singular perturbation problems using quintic spline

Spline based computational technique for linear singularly perturbed boundary value problems

In this article, we consider singularly perturbed reaction-diffusion Robin boundary-value problems. To solve these problems we construct a numerical method which involves both the cubic spline and classical finite difference schemes. The proposed scheme is applied on a piece-wise uniform Shishkin mesh. Truncation error is obtained, and the stability of the method is analyzed. Also, parameter-uniform errors estimates are derived. Three test problems are experimented.

Second-order Numerical Scheme for Singularly Perturbed Reaction-Diffusion Robin Problems

The primary concern in area of computational grid is security and resources. Most of the existing grids address this problem by authenticating the users, hosts and their interactions in an appropriate manner. A secured system is compulsory for the efficient utilization of grid services. The high degree of strangeness has been identified as the problem factors in the secured selection of grid. Without the assurance of a higher degree of trust relationship, competent resource selection and utilization cannot be achieved. In this paper we proposed an approach which is providing reliability and reputation aware security for resource selection in grid environment. In this approach, the self-protection capability and reputation weightage is utilized to obtain the Reliability Factor (RF) value. Therefore jobs are allocated to the resources that posses higher RF values. Extensive experimental evaluation shows that as higher trust and reliable nodes are selected the chances of failure decreased drastically.

Reliable Resource Selection in Grid Environment

Job scheduling is an influential component of Grid computing. Grid consists of large number of heterogeneous resources for solving large scale problems in the area of engineering and research discipline. So a proper job scheduling mechanism is essential for the efficient and reliable working of Grid because if a job is submitted to an inappropriate resource then it will increase the completion time of the job as well as decrease the overall performance of Grid, e.g. if a communicational intensive job is submitted to low bandwidth resource, then it will result in more communication time and thereby delaying the overall execution. Major goals of scheduling is to achieve better throughput while matching applications with the available number of resources. In this paper a modified QoS guided job scheduling algorithm is proposed. We divide the resources in the four different classes High QoS in term of processing speed, Low QoS in term of processing speed, High QoS in term of bandwidth, Low QoS in term of bandwidth. After choosing appropriate class based upon the job parameters, min-min heuristic schedules the job onto the best available resource of that class. The algorithm is tested in a simulated Grid environment. The output of algorithm shows that the new modified QoS guided Min-Min heuristic give much better result as compare with the traditional one.

http://ieeexplore.ieee.org/iel7/6902671/6915061/06915092.pdf

Rajesh K. Bawa

Papers

A computational method for self-adjoint singular perturbation problems using quintic spline

Spline based computational technique for linear singularly perturbed boundary value problems

Second-order Numerical Scheme for Singularly Perturbed Reaction-Diffusion Robin Problems

Reliable Resource Selection in Grid Environment

Modified min-min heuristic for job scheduling based on QoS in Grid environment