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A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem

机译：二维双调和狄利克雷问题的域类型边界积分方程法

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摘要

This paper reports a new boundary-integral-equation method (BIEM) for numerically solving biharmonic problems with Dirichlet boundary conditions. For the solution of these problems in convex polygons, it was found that the accuracy of the conventional BIEM is significantly reduced, and spurious oscillatory behaviour is often observed in the boundary solutions especially for areas near corners (Mai-Duy N, Tanner RI. An effective high order interpolation scheme in BIEM for biharmonic boundary value problems. Eng Anal Bound Elem 2005;29:210-23). In this study, a new treatment for these difficulties is proposed. The unknown functions in boundary integrals are approximated using a domain-type interpolation scheme rather than traditional boundary-type interpolation schemes. Two test problems are considered to validate the formulation and to demonstrate the attractiveness of the proposed method.
机译：本文报道了一种新的边界积分方程法（BIEM），用于数值求解Dirichlet边界条件下的双调和问题。为了解决凸多边形中的这些问题，发现常规BIEM的精度大大降低，并且在边界解中经常观察到伪振荡行为，特别是对于拐角附近的区域（Mai-Duy N，Tanner RI。 BIEM中针对双调和边值问题的有效高阶插值方案（Eng Anal Bound Elem 2005; 29：210-23）。在这项研究中，针对这些困难提出了一种新的治疗方法。使用域类型插值方案而不是传统的边界类型插值方案来近似边界积分中的未知函数。考虑两个测试问题以验证配方并证明所提出方法的吸引力。

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