The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems

Mandar K. Chati; Subrata Mukherjee; Glaucio H. Paulino

doi:10.1016/S0955-7997(01)00040-6

The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems

Mandar K. Chati, Subrata Mukherjee, Glaucio H. Paulino

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

The Boundary Node Method (BNM) represents a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the latter. The result is a 'meshfree' method that decouples the mesh and the interpolation procedures. The BNM has been applied to solve 2-D and 3-D problems in potential theory and linear elasticity. The Hypersingular Boundary Element Method (HBEM) has diverse important applications in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formulation. The present work presents a coupling of Hypersingular Boundary Integral Equations (HBIEs) with MLS approximants, to produce a new meshfree method - the Hypersingular Boundary Node Method (HBNM). Numerical results from this new method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper.

Original language	English (US)
Pages (from-to)	639-653
Number of pages	15
Journal	Engineering Analysis with Boundary Elements
Volume	25
Issue number	8
DOIs	https://doi.org/10.1016/S0955-7997(01)00040-6
State	Published - Sep 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
General Engineering
Computational Mathematics
Applied Mathematics

Keywords

Boundary element method
Boundary mode method
Hypersingular integrals
Linear elasticity
Potential theory

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10.1016/S0955-7997(01)00040-6

Cite this

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title = "The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems",

abstract = "The Boundary Node Method (BNM) represents a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the latter. The result is a 'meshfree' method that decouples the mesh and the interpolation procedures. The BNM has been applied to solve 2-D and 3-D problems in potential theory and linear elasticity. The Hypersingular Boundary Element Method (HBEM) has diverse important applications in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formulation. The present work presents a coupling of Hypersingular Boundary Integral Equations (HBIEs) with MLS approximants, to produce a new meshfree method - the Hypersingular Boundary Node Method (HBNM). Numerical results from this new method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper.",

keywords = "Boundary element method, Boundary mode method, Hypersingular integrals, Linear elasticity, Potential theory",

author = "Chati, {Mandar K.} and Subrata Mukherjee and Paulino, {Glaucio H.}",

note = "Funding Information: The Cornell group (Chati and Mukherjee) acknowledges support by the University Research Programs (URP) grant from Ford Motor Company to Cornell University. Professor Paulino acknowledges support from the National Science Foundation under Grant CMS-9713008. The computing for this research was carried out using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, the National Center for Research Resources at the National Institutes of Health, the National Science Foundation, the Defense Department Modernization program, the United States Department of Agriculture, and corporate partners. The efforts of Prachi Chati for carefully proof reading the manuscript are acknowledged. ",

year = "2001",

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doi = "10.1016/S0955-7997(01)00040-6",

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N1 - Funding Information: The Cornell group (Chati and Mukherjee) acknowledges support by the University Research Programs (URP) grant from Ford Motor Company to Cornell University. Professor Paulino acknowledges support from the National Science Foundation under Grant CMS-9713008. The computing for this research was carried out using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, the National Center for Research Resources at the National Institutes of Health, the National Science Foundation, the Defense Department Modernization program, the United States Department of Agriculture, and corporate partners. The efforts of Prachi Chati for carefully proof reading the manuscript are acknowledged.

PY - 2001/9

Y1 - 2001/9

N2 - The Boundary Node Method (BNM) represents a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the latter. The result is a 'meshfree' method that decouples the mesh and the interpolation procedures. The BNM has been applied to solve 2-D and 3-D problems in potential theory and linear elasticity. The Hypersingular Boundary Element Method (HBEM) has diverse important applications in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formulation. The present work presents a coupling of Hypersingular Boundary Integral Equations (HBIEs) with MLS approximants, to produce a new meshfree method - the Hypersingular Boundary Node Method (HBNM). Numerical results from this new method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper.

AB - The Boundary Node Method (BNM) represents a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the latter. The result is a 'meshfree' method that decouples the mesh and the interpolation procedures. The BNM has been applied to solve 2-D and 3-D problems in potential theory and linear elasticity. The Hypersingular Boundary Element Method (HBEM) has diverse important applications in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formulation. The present work presents a coupling of Hypersingular Boundary Integral Equations (HBIEs) with MLS approximants, to produce a new meshfree method - the Hypersingular Boundary Node Method (HBNM). Numerical results from this new method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper.

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KW - Boundary mode method

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The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems

Abstract

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