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A boundary-only treatment by singular boundary method for two-dimensional inhomogeneous problems

机译：奇异边界法的二维非齐次问题的纯边界处理

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摘要

In this study, an effective singular boundary method (SBM) in conjunction with the recursive multiple reciprocity method (MRM) is developed and validated for inhomogeneous problems. It avoids the inner nodes or domain discretizations to evaluate the particular solution, and preserves the boundary-only property of the SBM. Rather than using only polyharmonic operators in the traditional MRM, a recursive MRM is proposed to annihilate source terms with different partial differential operators recursively. Nevertheless, high-order fundamental solutions are involved in the recursive MRM. The absence of the origin intensity factors of higher order fundamental solutions is a major bottleneck in applying the SBM. In order to remedy this difficulty, the origin intensity factors of higher order fundamental solutions are derived with simple formulas. Numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.
机译：在这项研究中，有效的奇异边界方法（SBM）与递归多重互易方法（MRM）一起开发并验证了非均匀性问题。它避免了内部节点或域离散化来评估特定解决方案，并保留了SBM的仅边界属性。提议在递归MRM中使用递归不同的偏微分算子来消除源项，而不是在传统MRM中仅使用多谐算子。但是，递归MRM中涉及高阶基本解决方案。缺少高阶基本解的原点强度因子是应用SBM的主要瓶颈。为了解决这个困难，可以用简单的公式推导高阶基本解的原点强度因子。数值算例说明了该方法的准确性和有效性。

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