An Interpolating Boundary Element-Free Method for 2D Helmholtz Equations
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摘要: 针对二维Helmholtz方程的内外边值问题,提出了插值型边界无单元法(interpolating boundary element-free method).在间接位势理论的基础上,利用Laplace方程基本解的特性,建立了求解Helmholtz方程Neumann边值内外问题的正则化形式,有效消除了强奇异积分的计算.其次通过引入全局距离展开成局部距离的幂级数, 详细推导了距离函数的导数和法向导数差值的极限表达式.最后给出了4个插值型边界无单元法的数值算例, 表明了该方法可取得较高的可行性和有效性.Abstract: An interpolating boundary element-free method was presented for solving interior and exterior boundary value problems of 2D Helmholtz equations. According to the indirect potential theory and the characteristics of the fundamental solution of Laplace’s equation, a regularized boundary integration equation formulation was established to avoid the computation of the strongly singular integration. Besides, through expansion of the global distance into power series in the form of the local distance, the limit expressions of the distance derivative and the difference between 2 normal derivatives were deduced in detail. Finally, 4 numerical examples were given to show the feasibility and efficiency of the proposed method.
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