2011
DOI: 10.1016/j.jcp.2010.11.046
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High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm

Abstract: a b s t r a c tA high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES(k) method for modeling elastic waves. A preconditioning operato… Show more

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Cited by 19 publications
(14 citation statements)
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“…For the PML boundary conditions, the following parameters were selected: L PML = 30h z , c p = 4400m/s, ν = 2, χ = 10 −6 . The issues concerning the spectral algorithm based on the Laguerre transform were studied in [13,14], therefore we will dwell on performance and efficiency of the parallel algorithm.…”
Section: Numerical Experimentsmentioning
confidence: 99%
See 1 more Smart Citation
“…For the PML boundary conditions, the following parameters were selected: L PML = 30h z , c p = 4400m/s, ν = 2, χ = 10 −6 . The issues concerning the spectral algorithm based on the Laguerre transform were studied in [13,14], therefore we will dwell on performance and efficiency of the parallel algorithm.…”
Section: Numerical Experimentsmentioning
confidence: 99%
“…It was shown that for Toeplitz tridiagonal matrices, SLAEs can be effectively solved both with one and several right-hand sides. In [13,14], the Dichotomy Algorithm was applied to implement a spectral-difference method of calculation of acoustic and elastic wave fields. This made it possible to effectively use from 2 up to 8192 processors per one calculation and to obtain a highly accurate numerical solution of the dynamic problem of elasticity theory.…”
Section: Introductionmentioning
confidence: 99%
“…Метод позволяет проводить «безартефактные» расчеты на сверхдальние расстояния на профилях большой протяженности. В методе используются аналитические преобразования по пространственной и временной переменной и численно вычисляются значений рядов аналитических функций [Fatyanov, 1990;Fatyanov, Terekhov, 2011]. Важной особенностью метода является получение точного аналитического решения для больших размеров расчетной области, что имеет принципиальное значение для получения сейсмограмм для скоростных моделей земной коры протяженностью несколько сотен километров.…”
Section: математическое моделирование полных волновых полей для скороunclassified
“…The Laguerre integral transform has been used in various fields of mathematical simulation to solve acoustics and elasticity equations [1,2,3,4], Maxwell and heat conduction equations [5,6], and spectroscopy problems [7]. The Laguerre transform has proved to be a very efficient tool in constructing a stable algorithm of wave field continuation when solving inverse problems of seismic prospecting [8,9] and many others.…”
Section: Introductionmentioning
confidence: 99%
“…Consider Laguerre functions [18], which are defined as l n (t) = e −t/2 L n (t), t ≥ 0 (1) where L n (t) is the Laguerre polynomial of degree n, which is defined by the Rodrigues formula…”
Section: Introductionmentioning
confidence: 99%