Meshless weighting coefficients for arbitrary nodes: The efficient computation to machine precision using hyper-dual numbers

被引:1
作者
Roberts, Jason L. [1 ]
机构
[1] Australian Antarctic Div, 203 Channel Highway, Kingston, Tas 7050, Australia
关键词
Meshfree methods; Finite point; Numerical derivative; Radial basis function; Hyper-dual numbers; RADIAL BASIS FUNCTION; DIFFERENTIAL QUADRATURE; STABLE COMPUTATION; APPROXIMATIONS; INTERPOLATION; EQUATIONS; MATRICES; FLOW;
D O I
10.1016/j.advengsoft.2024.103753
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
A computationally efficient algorithm to calculate the weighting coefficients required to evaluate derivatives for arbitrary multi-dimensional distributions of points is presented. The iterative algorithm guarantees IEEE 754 64-bit precision (at least 15 significant decimal digits) for the weighting coefficients. Convergence acceleration is achieved through the use of a Taylor series of up to third order, and hyper-dual numbers to obtain the derivatives required for the Taylor series. The method is applied as part of a finite point solution for three test examples, a Poisson equation, creeping flow around a cylinder, and heat conduction in a triangular annulus. The open source FORTRAN-90 implementation has been optimised for random distributions of points in 1 to 3 dimensions.
引用
收藏
页数:13
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