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High performance parallel algorithm for solving elliptic equations with non-separable variables
TL;DR: A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented and it is shown that the algorithm proposed is highly efficient for a large number of processors.
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Abstract: A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented. The resultant matrix is symmetric positive definite, thus the preconditioning conjugate gradient or the chebyshev method can be applied. A differential analog to the Laplace operator is used as preconditioner. For inversion of the Laplace operator we implement a parallel version of the separation variable method, which includes the sequential FFT algorithm and the parallel solver for tridiagonal matrix equations (dichotomy algorithm). On an example of solving acoustic equations by the integral Laguerre transformation method, we show that the algorithm proposed is highly efficient for a large number of processors.
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Citations
A fast parallel algorithm for solving block-tridiagonal systems of linear equations including the domain decomposition method
TL;DR: This study develops a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides and proposes a parallel realization of the domain decomposition method (the Schur complement method).
A fast parallel algorithm for solving block-tridiagonal systems of linear equations including the domain decomposition method
Andrew V. Terekhov
- 01 Jun 2013
TL;DR: In this paper, a parallel algorithm for solving block-tridiagonal systems of equations is presented, which is an effective and simple set of procedures for solving engineering tasks on a supercomputer.
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Демонстрация взаимосвязанных явлений на примерах из статики и динамики жидкости
Б. М. Валиев,В. Д. Егоренков +1 more
- 01 Jan 2005
TL;DR: A number of experiments on statics and dynamics of liquids showing the physical phenomena in their mutual relation are described, used in secondary schools as well as universities.
1
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