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Singular boundary method for steady-state heat conduction in three dimensional general anisotropic media

机译:三维通用各向异性介质中稳态导热的奇异边界法

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摘要

The singular boundary method (SBM) is a recent strong-form meshless boundary collocation method. Like the method of fundamental solutions (MFS), the SBM uses the fundamental solution of the governing differential equation of interest as the basis function and is mathematically simple, truly meshless, accurate, and easy-to-program. Unlike the MFS, the SBM, however, uses the concept of the origin intensity factor to isolate the singularity of the fundamental solutions and overcomes the fictitious boundary issue which has long perplexed the MFS. This study makes the first attempt to apply the SBM to steady-state heat conduction in three-dimensional (3D) anisotropic materials. Five benchmark numerical examples demonstrate that the SBM is accurate, convergent, stable, and computationally efficient in solving this kind of problems.
机译:奇异边界法(SBM)是近来的一种强形式无网格边界配置法。像基本解法(MFS)一样,SBM使用目标控制微分方程的基本解作为基函数,并且数学上简单,真正无网格,准确且易于编程。但是,与MFS不同,SBM使用起点强度因子的概念来隔离基本解的奇异性,并克服了长期困扰MFS的虚拟边界问题。这项研究首次尝试将SBM应用于三维(3D)各向异性材料的稳态热传导。五个基准数值示例表明,SBM在解决此类问题方面是准确,收敛,稳定且计算效率高的。

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