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用于波动方程模拟的Chebshev谱元法 被引量:1
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作者 林伟军 Geza Seriani 《声学技术》 CSCD 北大核心 2005年第z1期1-2,共2页
  1引言   在瞬态分析,工程地震学,计算声学等领域(如无损检测,油气勘探等),如何利用数值计算的方法更精确地得到弹性波动方程的解一直是国内外研究者的工作重点.随着计算机技术的发展,一些原来影响数值计算方法应用的瓶颈一一被克...   1引言   在瞬态分析,工程地震学,计算声学等领域(如无损检测,油气勘探等),如何利用数值计算的方法更精确地得到弹性波动方程的解一直是国内外研究者的工作重点.随着计算机技术的发展,一些原来影响数值计算方法应用的瓶颈一一被克服,但对于大型的复杂二维问题或三维问题的研究,仍然对原有的数值模拟方法提出了挑战.   …… 展开更多
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Some theoretical aspects of elastic wave modeling with a recently developed spectral element method 被引量:8
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作者 SERIANI Geza 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2007年第2期185-207,共23页
A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based... A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang. 展开更多
关键词 WEAK FORMULA ELASTIC wave MODELING spectral ELEMENT ELEMENT by ELEMENT
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