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Evaluating the Origin Intensity Factor in the Singular Boundary Method for Three-Dimensional Dirichlet Problems

Part of:Partial differential equations, boundary value problemsFunctional-differential and differential-difference equationsOther generalizationsPartial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  28 November 2017

Linlin Sun,
Wen Chen and
Alexander H.-D. Cheng
Linlin Sun
Affiliation:
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, ChinaDepartment of Computational Science and Statistics, School of Science, Nantong University, Nantong, Jiangsu 226019, ChinaSchool of Engineering, University of Mississippi, University, MS 38677, USA
Wen Chen*
Affiliation:
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China
Alexander H.-D. Cheng
Affiliation:
School of Engineering, University of Mississippi, University, MS 38677, USA
*
*Corresponding author. Email:chenwen@hhu.edu.cn (W. Chen)

Abstract

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In this paper, a new formulation is proposed to evaluate the origin intensity factors (OIFs) in the singular boundary method (SBM) for solving 3D potential problems with Dirichlet boundary condition. The SBM is a strong-form boundary discretization collocation technique and is mathematically simple, easy-to-program, and free of mesh. The crucial step in the implementation of the SBM is to determine the OIFs which isolate the singularities of the fundamental solutions. Traditionally, the inverse interpolation technique (IIT) is adopted to calculate the OIFs on Dirichlet boundary, which is time consuming for large-scale simulation. In recent years, the new methodology has been developed to efficiently calculate the OIFs on Neumann boundary, but the Dirichlet problem remains an open issue. This study employs the subtracting and adding-back technique based on the integration of the fundamental solution over the whole boundary to develop a new formulation of the OIFs on 3D Dirichlet boundary. Several problems with varied domain shapes and boundary conditions are carried out to validate the effectiveness and feasibility of the proposed scheme in comparison with the SBM based on inverse interpolation technique, the method of fundamental solutions, and the boundary element method.

Keywords

Origin intensity factorssingular boundary methodboundary-type meshless methodpotential problemfundamental solution

MSC classification

Secondary:31C20: Discrete potential theory and numerical methods34K28: Numerical approximation of solutions65N80: Fundamental solutions, Green's function methods, etc.65M70: Spectral, collocation and related methods

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017, pp. 1289 - 1311
Copyright
Copyright © Global-Science Press 2017 

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