کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
518910 867624 2012 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimal variable shape parameter for multiquadric based RBF-FD method
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Optimal variable shape parameter for multiquadric based RBF-FD method
چکیده انگلیسی

In this follow up paper to our previous study in Bayona et al. (2011) [2], we present a new technique to compute the solution of PDEs with the multiquadric based RBF finite difference method (RBF-FD) using an optimal node dependent variable value of the shape parameter. This optimal value is chosen so that, to leading order, the local approximation error of the RBF-FD formulas is zero. In our previous paper (Bayona et al., 2011) [2] we considered the case of an optimal (constant) value of the shape parameter for all the nodes. Our new results show that, if one allows the shape parameter to be different at each grid point of the domain, one may obtain very significant accuracy improvements with a simple and inexpensive numerical technique. We analyze the same examples studied in Bayona et al. (2011) [2], both with structured and unstructured grids, and compare our new results with those obtained previously. We also find that, if there are a significant number of nodes for which no optimal value of the shape parameter exists, then the improvement in accuracy deteriorates significantly. In those cases, we use generalized multiquadrics as RBFs and choose the exponent of the multiquadric at each node to assure the existence of an optimal variable shape parameter.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 231, Issue 6, 20 March 2012, Pages 2466–2481
نویسندگان
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