An enhanced version of a stochastic SParse Approximate Inverse (SPAI) preconditioner for general matrices is presented in this paper. This method is used in contrast to the standard deterministic preconditioners compu...
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An enhanced version of a stochastic SParse Approximate Inverse (SPAI) preconditioner for general matrices is presented in this paper. This method is used in contrast to the standard deterministic preconditioners computed by the Modified SParse Approximate Inverse Preconditioner (MSPAI). Thus we present a Monte Carlo preconditioner that relies on the use of Markov Chain Monte Carlo (MCMC) methods to compute a rough approximate matrix inverse first, which can further be optimized by an iterative filter process and a parallel refinement, to enhance the accuracy of the inverse and the preconditioner respectively. The advantage of the proposed approach is that finding the sparse Monte Carlo matrix inversion has a computational complexity linear of the size of the matrix, it is inherently parallel and thus can be obtained very efficiently for large matrices and can be used also as an efficient preconditioner while solving systems of linear algebraic equations. The behaviour of the proposed algorithm is studied and its performance measured, evaluated and compared with MSPAI. (C) 2015 Published by Elsevier Ltd.
Graph partitioning is required for solving tasks on graphs that need to be distributed over disks or computers. This problem is well studied, but the majority of the results on this subject are not suitable for proces...
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Graph partitioning is required for solving tasks on graphs that need to be distributed over disks or computers. This problem is well studied, but the majority of the results on this subject are not suitable for processing graphs with billions of nodes on commodity clusters, since they require shared memory or lowlatency messaging. One of the approaches suitable for cluster computing is the balanced label propagation, which is based on the label propagation algorithm. In this work, we show how multi-level optimization can be used to improve quality of the partitioning obtained by means of the balanced label propagation algorithm.
In order to improve the probabilistic load flow calculation efficiency of Monte-Carlo simulation to meet the large-scale power system analysis and calculation time requirements, this paper introduced the coarse-graine...
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This paper studies the electric response of a common lattice tower when it is hit by a lightning stroke. Although some studies have been already done about this subject, the novelty of this one lies in the usage of a ...
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This paper studies the electric response of a common lattice tower when it is hit by a lightning stroke. Although some studies have been already done about this subject, the novelty of this one lies in the usage of a highly accurate electric model of an actual lattice tower. This model allows to calculate the impedance variation with different frequencies by using an adaptation of the well-known method of moments. Moreover, the authors also analyze how the impedance is affected when the grounding parameters and the connection to ground conditions are modified. These results are lately used to explain the electric behavior of the tower under two kinds of lightning impulses and different grounding configurations.
The article focuses on the simulation of low temperature multicomponent plasmas. Discussed is the simulation of the trajectory of the particle as well as the dynamics of cathode electrons. Explored is the message pass...
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The article focuses on the simulation of low temperature multicomponent plasmas. Discussed is the simulation of the trajectory of the particle as well as the dynamics of cathode electrons. Explored is the message passing interface (MPI) in parallel algorithm along with the propagation of cathode electrons.
Wireless sensor networks (WSNs) are energyconstrained, so energy saving is one of the most important issues in typical applications. The clustered WSN topology is considered in this paper. To achieve the balance of en...
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Seismic responses from fractured geological layers are mathematically simulated by applying the grid-characteristic method on unstructured tetrahedral meshes with the use of high-performance computer systems. The meth...
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Seismic responses from fractured geological layers are mathematically simulated by applying the grid-characteristic method on unstructured tetrahedral meshes with the use of high-performance computer systems. The method is intended for computing complicated spatial dynamical processes in complex heterogeneous media and is characterized by exact formulation of contact conditions. As a result, it can be applied to the simulation of seismic exploration problems, including in regions with a large number of inhomogeneities, examples of which are fractured structures. The use of unstructured tetrahedral meshes makes it possible to specify geological cracks of various shapes and spatial orientations. As a result, problems are solved in a formulation maximally close to an actual situation. A cluster of computers is used to improve the accuracy of the computation by optimizing its duration.
We present an algorithm for inversion of symmetric positive definite matrices that combines the practical requirement of an optimal number of arithmetic operations and the theoretical goal of a polylogarithmic critica...
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The polynomial partitioning method of Guth and Katz (arXiv:1011.4105) has numerous applications in discrete and computational geometry. It partitions a given n-point set using the zero set Z(f) of a suitable d-variate...
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The polynomial partitioning method of Guth and Katz (arXiv:1011.4105) has numerous applications in discrete and computational geometry. It partitions a given n-point set using the zero set Z(f) of a suitable d-variate polynomial f. Applications of this result are often complicated by the problem, "What should be done with the points of P lying within Z(f)?" A natural approach is to partition these points with another polynomial and continue further in a similar manner. So far this has been pursued with limited success-several authors managed to construct and apply a second partitioning polynomial, but further progress has been prevented by technical obstacles. We provide a polynomial partitioning method with up to d polynomials in dimension d, which allows for a complete decomposition of the given point set. We apply it to obtain a new algorithm for the semialgebraic range searching problem. Our algorithm has running time bounds similar to a recent algorithm by Agarwal et al. (SIAM J Comput 42:2039-2062, 2013), but it is simpler both conceptually and technically. While this paper has been in preparation, Basu and Sombra, as well as Fox, Pach, Sheffer, Suk, and Zahl, obtained results concerning polynomial partitions which overlap with ours to some extent.
Scalarization approaches are the simplest methods for solving the multiobjective problems. The idea of scalarization is based on decomposition of multiobjective problems into single objective sub-problems. Every one o...
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Scalarization approaches are the simplest methods for solving the multiobjective problems. The idea of scalarization is based on decomposition of multiobjective problems into single objective sub-problems. Every one of these sub-problems can be solved in a parallel manner since they are independent with each other. Hence, as a scalarization approach, systematically modification on the desirability levels of the objective values of multiobjective problems can be employed for solving these problems. In this study, desirability function-based scalarization approach is converted into parallel algorithm and applied into seven benchmark problems. The performance of parallel algorithm with respect to sequential one is evaluated based on execution time on different graphical processing units and central processing units. The results show that even the accuracy of parallel and sequential codes are same, the execution time of parallel algorithm is up to 24.5-times faster than the sequential algorithm (8.25-times faster on average) with respect to the complexity of the problem.
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