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Symmetric singular boundary method for potential problems with mixed boundary conditions

机译：混合边界条件下潜在问题的对称奇异边界法

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摘要

The paper presents a symmetric formulation of the singular boundary method (SBM) for potential problems, whose resultant interpolation matrix is symmetric irrespective of boundary conditions. The SBM is a recent strong-form boundary discretization numerical technique, which is meshless, integration-free, and easy-to-implement. In stark contrast to the method of fundamental solution that requires the fictitious boundary outside physical domain to avoid the singularity of fundamental solution, the SBM can place source points, which coincide with collocation points, on the real physical boundary via the concept of origin intensity factor. The proposed symmetric formulation preserves all the merits of the SBM. The novel idea behind this study is that the unknown solution is represented by both the single and double layer potentials compared with the single layer potential in the original SBM. Numerical solution of three-dimensional potential and two-dimensional fluid flow and heat transfer problems demonstrates the utility and validity of the present SBM symmetric formulation.
机译：本文提出了一种针对潜在问题的奇异边界法（SBM）的对称公式，其所得插值矩阵是对称的，与边界条件无关。 SBM是近来的一种强形式边界离散化数值技术，它是无网格，无积分且易于实现的。与要求物理域外的虚拟边界避免基本解的奇异性的基本解方法形成鲜明对比的是，SBM可以通过起源强度因子的概念将与搭配点重合的源点放置在实际物理边界上。提出的对称公式保留了SBM的所有优点。这项研究背后的新颖思想是，与原始SBM中的单层电势相比，未知解决方案由单层电势和双层电势表示。三维势和二维流体流动和传热问题的数值解证明了本发明的SBM对称公式的实用性和有效性。

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