A Meshless Regularized Integral Equation Method for Laplace Equation in Arbitrary Interior or Exterior Plane Domains
A Meshless Regularized Integral Equation Method for Laplace Equation in Arbitrary Interior or Exterior Plane Domains
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DOI：
10.3970/icces.2007.003.057
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发表时间：
2007-05
影响因子：
2.4
通讯作者：
Chein-Shan Liu
中科院分区：
文献类型：
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作者：
Chein-Shan Liu
提出了一种求解二维拉普拉斯方程内外Dirichlet问题的新方法，即无网格正则化积分方程法（MRIEM），该方法由傅立叶级数展开、第二类Fredholm积分方程和人工圆上未知边界条件的解析正则化解三部分组成。结果表明，该方法对于边界形状非常复杂、边界噪声较大的问题也具有较强的求解能力。
Summary A new method is developed to solve the interior and exterior Dirichlet problems for the two-dimensional Laplace equation, namely the meshless regularized integral equation method (MRIEM), which consists of three parts: Fourier series expansion, the second kind Fredholm integral equation and an analytically regularized solution of the unknown boundary condition on an artificial circle. We find that the new method is powerful even for the problem with very complex boundary shape and with boundary noise.