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A Highly Accurate Regular Domain Collocation Method for Solving Potential Problems in the Irregular Doubly Connected Domains

机译：解决不规则双连通域中潜在问题的高精度规则域配置方法

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摘要

Embedding the irregular doubly connected domain into an annular regular region, the unknown functions can be approximated by the barycentric Lagrange interpolation in the regular region. A highly accurate regular domain collocation method is proposed for solving potential problems on the irregular doubly connected domain in polar coordinate system. The formulations of regular domain collocation method are constructed by using barycentric Lagrange interpolation collocation method on the regular domain in polar coordinate system. The boundary conditions are discretized by barycentric Lagrange interpolation within the regular domain. An additional method is used to impose the boundary conditions. The least square method can be used to solve the overconstrained equations. The function values of points in the irregular doubly connected domain can be calculated by barycentric Lagrange interpolation within the regular domain. Some numerical examples demonstrate the effectiveness and accuracy of the presented method.
机译：将不规则双重连接域嵌入到环形规则区域中，未知函数可以通过规则区域中的重心Lagrange插值来近似。为了解决极坐标系统中不规则双连通域上的潜在问题，提出了一种高精度的规则域配置方法。通过在极坐标系中的正则域上使用重心拉格朗日插值并置法来构造正则域并置法的公式。边界条件通过常规域内的重心拉格朗日插值离散化。使用其他方法来施加边界条件。最小二乘法可以用来求解过约束方程。可以通过在规则域内的重心拉格朗日插值来计算不规则双连通域中的点的函数值。一些数值例子证明了该方法的有效性和准确性。

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  • 来源
    《Mathematical Problems in Engineering》 |2014年第8期|397327.1-397327.9|共9页
  • 作者

    Zhao-Qing Wang; Shuchen Li; Yang Ping; Jian Jiang; Teng-Fei Ma;

  • 作者单位

    Institute of Engineering Mechanics, Shandong Jianzhu University, Jinan 250101, China;

    Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China;

    Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China;

    Institute of Engineering Mechanics, Shandong Jianzhu University, Jinan 250101, China;

    Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China;

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