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首页> 外文期刊>Applied Mathematical Modelling >A Spectral Collocation Technique Based On Integrated Chebyshev Polynomials For Biharmonic Problems In Irregular Domains
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A Spectral Collocation Technique Based On Integrated Chebyshev Polynomials For Biharmonic Problems In Irregular Domains

机译：基于积分Chebyshev多项式的不规则域双调和问题的谱配点技术

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In this paper, an integral collocation approach based on Chebyshev polynomials for numerically solving biharmonic equations [N. Mai-Duy, R.I. Tanner, A spectral collocation method based on integrated Chebyshev polynomials for biharmonic boundary-value problems, J. Comput. Appl. Math. 201 (1) (2007) 30-47] is further developed for the case of irregularly shaped domains. The problem domain is embedded in a domain of regular shape, which facilitates the use of tensor product grids. Two relevant important issues, namely the description of the boundary of the domain on a tensor product grid and the imposition of double boundary conditions, are handled effectively by means of integration constants. Several schemes of the integral collocation formulation are proposed, and their performances are numerically investigated through the interpolation of a function and the solution of 1D and 2D biharmonic problems. Results obtained show that they yield spectral accuracy.
机译：本文提出了一种基于Chebyshev多项式的积分配置方法，用于数值求解双调和方程[N. Mai-Duy，R.I. Tanner，基于积分Chebyshev多项式的双谐波边值问题的频谱配置方法，J。Comput。应用数学。 201（1）（2007）30-47]针对形状不规则的域进行了进一步开发。问题域嵌入规则形状的域中，这有助于使用张量积网格。通过积分常数可以有效地处理两个相关的重要问题，即在张量积网格上描述域的边界和施加双边界条件。提出了几种整体配置公式，并通过函数插值和一维和二维双调和问题的求解，对它们的性能进行了数值研究。获得的结果表明，它们产生了光谱精度。

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