Block algorithms of a simultaneous difference solution of d’Alembert's and Maxwell's equations

Yablokova, Liudmila; Golovashkin, D. L.

doi:10.18287/2412-6179-2018-42-2-320-327

Cited by 9 publications

(3 citation statements)

References 14 publications

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“…The efficiency of the algorithm compared to the quick sorting we studied earlier in [11]. Block algorithms allow to optimize performance in different areas of computing then heterogeneous and/or distributed hardware is in use [12].…”

Section: Related Workmentioning

confidence: 99%

Using the bag-of-tasks model with centralized storage for distributed sorting of large data array

Vostokin

Bobyleva

2019

Proceedings of the v International Conference Information Technology and Nanotechnology 2019

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The article discusses the application of the bag of tasks programming model for the problem of sorting a large data array. The choice is determined by the generality of its algorithmic structure with various problems from the field of data analysis including correlation analysis, frequency analysis, and data indexation. The sorting algorithm is a blockby-block sorting, followed by the pairwise merging of the blocks. At the end of the sorting, the data in the blocks form an ordered sequence. The order of sorting and merging tasks is set by a static directed acyclic graph. The sorting algorithm is implemented using MPI library in C ++ language with centralized storing of data blocks on the manager process. A feature of the implementation is the transfer of blocks between the master and the worker MPI processes for each task. Experimental study confirmed the hypothesis that the intensive data exchange resulting from the centralized nature of the bag of task model does not lead to a loss of performance. The data processing model makes it possible to weaken the technical requirements for the software and hardware.

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Section: Related Workmentioning

confidence: 99%

Using the bag-of-tasks model with centralized storage for distributed sorting of large data array

Vostokin

Bobyleva

2019

Proceedings of the v International Conference Information Technology and Nanotechnology 2019

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“…The model, numerical method and software complex presented in [22,31,32] and based on the joint difference solution of Maxwell's equations with the use of block algorithm of organization of calculations are chosen as a tool for calculating diffraction on various silicon lenses. Вased on [26,27,30], we assume the refractive index of silicon n=3.42 for the wavelength λ=141 µm, to which we further give all distances.…”

Section: The Study Of the Silicon Fresnel's Lensmentioning

confidence: 99%

Block algorithm for the joint difference solution of the d’Alembert and Maxwell’s equations

Yablokova

Golovashkin²

2018

Collection of Selected Papers of the IV International Conference on Information Technology and Nanotechnology

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A characteristic feature of mathematical modeling at the present stage of development is the consideration of the architecture of the computer system, not only for stage of compiling a computer program, but also during the development of a numerical method and synthesis of the mathematical model. This method significantly broadens the researcher's ability to search for the optimal mapping of the numerical method to the mentioned architecture, in the sense of accelerating computations. In this paper, this idea is illustrating by examples of the basic mathematical model of computational electrodynamics and optics, Maxwell's equations, and the FDTD. This modification allows to reducing the data exchange rate between the operational and cache memory due to the greater number of arithmetic operations per one grid function in solving the d'Alembert equation. On the other hand, freely use the technologies FDTD method and ready-made software implementations for setting the incident wave, imposing the absorbing layers, taking into account the dispersion of the medium.

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“…Tridiagonal matrices have an extremely important role in difference methods of solving problems of mathematical physics [2]. In addition, many linear algebra problems, such as solving equations and finding eigenvalues, are solved through transformations of matrices of general form to tridiagonal ones [3]. These matrices also play an important role in the theory of orthogonal polynomials [4].…”

Section: Introductionmentioning

confidence: 99%

Research of parallel algorithms for solving three-diagonal systems of linear algebraic equations on a graphical computing device using various types of memory

Pogorelskih¹,

Loganova²

2019

Proceedings of the v International Conference Information Technology and Nanotechnology 2019

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In this paper, we research and compare different implementations of cyclic reduction and sweep algorithms on a graphics processing unit (GPU) using different types of device memory. As a result of the work, it was found that the algorithm of the run should be used to solve the set of the tridiagonal linear system. However, the best results are shown by a parallel version of the cyclic reduction algorithm with partial use of shared memory, when solving a single linear system on the GPU.

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Block algorithms of a simultaneous difference solution of d’Alembert's and Maxwell's equations

Cited by 9 publications

References 14 publications

Using the bag-of-tasks model with centralized storage for distributed sorting of large data array

Using the bag-of-tasks model with centralized storage for distributed sorting of large data array

Block algorithm for the joint difference solution of the d’Alembert and Maxwell’s equations

Research of parallel algorithms for solving three-diagonal systems of linear algebraic equations on a graphical computing device using various types of memory

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