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Dual reciprocity hybrid boundary node method for nonlinear problems

机译：求解非线性问题的对等互惠混合边界节点方法

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摘要

In this paper, a boundary type meshless method of dual reciprocity hybrid boundary node method (DHBNM) is proposed to solve complicate Poisson type linear and nonlinear problems. Firstly, the solutions are divided into the complementary solutions related to homogeneous equation and the particular solutions solved by nonhomogeneous terms, for the latter, they are approximated by the radial basis function interpolation based on dual reciprocity method, and the complementary solutions are obtained based on simple Poisson's equation by hybrid boundary node method, by which a simple fundamental solution of the Laplacian operator is employed instead of some other complicated ones; then a function of field functions and their derivatives on any point can be easily obtained, employing the concept of the analog equation of Katsikadelis, the field functions and their derivatives can be expressed as the function of unknown series of coefficients, and a series of nonlinear equivalent equations can be established by collocating the original governing equation at discrete points in the interior and on boundary of the domain. As a result, a new meshless method of dual reciprocity hybrid boundary node method is proposed to solve nonlinear Poisson type problems, because of the usage of those techniques, the boundary type meshless properties can be kept for any type of nonlinear equations. Different types of classical nonlinear problems are presented to validate the effectiveness and the accuracy of the present method.
机译：为了解决复杂的泊松型线性和非线性问题，本文提出了一种边界类型无网格双对等混合边界节点方法（DHBNM）。首先，将解分为与齐次方程有关的互补解和由非齐次项求解的特殊解，对于后者，通过基于对偶方法的径向基函数插值对其进行逼近，并基于混合边界节点法的简单泊松方程，用拉普拉斯算子的简单基本解代替其他复杂的解；然后，通过使用Katsikadelis的模拟方程的概念，可以轻松获得任意点上的场函数及其导数的函数，场函数及其导数可以表示为未知系数系列的函数，以及一系列非线性函数。通过将原始控制方程并置在域内部和边界上的离散点上，可以建立等效方程。因此，提出了一种新的双互惠混合边界节点方法无网格方法来解决非线性泊松型问题，由于使用了这些技术，可以对任何类型的非线性方程保持边界型无网格性质。提出了不同类型的经典非线性问题，以验证本方法的有效性和准确性。

著录项

  • 来源
    《Engineering analysis with boundary elements》 |2019年第11期|385-392|共8页
  • 作者

    Yan Fei; Jiang Quan; Bai Guo-Feng; Li Shao-Jun; Li Yun; Qiao Zhi-Bin;

  • 作者单位

    Chinese Acad Sci Inst Rock & Soil Mech State Key Lab Geomech & Geotech Engn Wuhan 430071 Hubei Peoples R China|CAS Ctr Excellence Complex Syst Mech Hefei Anhui Peoples R China|Northeastern Univ Key Lab Minist Educ Safe Min Deep Met Mines Shenyang 110819 Liaoning Peoples R China;

    Chinese Acad Sci Inst Rock & Soil Mech State Key Lab Geomech & Geotech Engn Wuhan 430071 Hubei Peoples R China;

    China Railway 12 Bur Grp Co Ltd Beijing Peoples R China;

    Inst Hydrogeol & Engn Geol Wuhan Hubei Prov Geol Survey Wuhan 430051 Hubei Peoples R 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

    Hybrid boundary node method; Particular solution; Analog equation; Dual reciprocity; Nonlinear problem;

    机译：混合边界节点法;特殊解决方案;模拟方程双重互惠;非线性问题;

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