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

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software Pub Date : 2024-08-12 DOI:10.1016/j.advengsoft.2024.103753

Jason L. Roberts

引用次数: 0

Abstract

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.

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任意节点的无网格加权系数：使用超二元数高效计算机器精度

本文提出了一种计算高效的算法，用于计算任意多维点分布导数评估所需的加权系数。迭代算法保证了加权系数的 IEEE 754 64 位精度（至少 15 位有效小数位）。通过使用最高三阶的泰勒级数和超二元数来获取泰勒级数所需的导数，实现了收敛加速。该方法作为有限点求解的一部分，应用于三个测试实例：泊松方程、圆柱体周围的蠕动流和三角形环形空间中的热传导。开源的 FORTRAN-90 实现已针对 1 到 3 维的随机点分布进行了优化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Engineering Software 工程技术-计算机：跨学科应用

CiteScore

7.70

自引率

4.20%

发文量

169

审稿时长

37 days

期刊介绍： The objective of this journal is to communicate recent and projected advances in computer-based engineering techniques. The fields covered include mechanical, aerospace, civil and environmental engineering, with an emphasis on research and development leading to practical problem-solving. The scope of the journal includes: • Innovative computational strategies and numerical algorithms for large-scale engineering problems • Analysis and simulation techniques and systems • Model and mesh generation • Control of the accuracy, stability and efficiency of computational process • Exploitation of new computing environments (eg distributed hetergeneous and collaborative computing) • Advanced visualization techniques, virtual environments and prototyping • Applications of AI, knowledge-based systems, computational intelligence, including fuzzy logic, neural networks and evolutionary computations • Application of object-oriented technology to engineering problems • Intelligent human computer interfaces • Design automation, multidisciplinary design and optimization • CAD, CAE and integrated process and product development systems • Quality and reliability.