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A new implementation of DRM with dual interpolation boundary face method for Poisson equation

机译：双插值边界面法的新实现泊松方程

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摘要

We present a new numerical algorithm combining the dual reciprocity method with the dual interpolation boundary face method for solving the two-dimensional Poisson equations. In this new combined approach, the boundary physical variables and particular solutions are approximated by dual interpolation elements which include source and virtual points. Additionally, this algorithm is implemented by employing the augmented thin plate spline interpolation function to approximate non-homogeneous term and the Hermite-type moving-least-square approximation to approximate physical variables for virtual nodes. Compared with the traditional dual reciprocity boundary element method, this combined method possesses higher accuracy and efficiency and is better suited for structures with small feature sizes. Several numerical examples are given to illustrate the superiority of the proposed method for solving Poisson equations.
机译：我们提出了一种新的数值算法，将双互补方法与双插值边界面法组合，用于求解二维泊松方程。在这种新的组合方法中，边界物理变量和特定解决方案近似于包括源和虚拟点的双插值元素。另外，通过采用增强薄板样条插值函数来实现该算法以近似非同质项和Hermite型移动 - 最小二乘近似来实现，以近似虚拟节点的物理变量。与传统的双互补边界元素法相比，这种组合方法具有更高的准确性和效率，更适合具有小特征尺寸的结构。给出了几个数值例子来说明求解泊松方程的所提出方法的优越性。

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  • 来源
    《Engineering analysis with boundary elements》 |2020年第12期|21-30|共10页
  • 作者

    Rui He; Jianming Zhang; Suliman; Le Yang; Weicheng Lin;

  • 作者单位

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 China;

    School of Mathematics and Statistics Central South University Changsha 410083 China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Dual reciprocity method; Radial basis functions; Dual interpolation boundary face method; Hermite-type approximation; Poisson equation;

    机译：双互惠方法;径向基函数;双插值边界面法;Hermite型近似;泊松方程式;

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