Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries

Tekoing Lim; Gregoire Pichenot; Marc Bonnet

doi:10.3233/978-1-60750-750-5-79

Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries

Tekoing Lim, Gregoire Pichenot, Marc Bonnet

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The motivation of this work is to develop a computational treatment of eddy current simulation applicable to complex 3D geometries. To this end, an approach based on surface integral equations and involving the homogeneous full-space Green's function and dyad is developed. A Galerkin variant of the method of moments, using bilinear basis functions, is employed for discretizing the surface integral equations, leading to a linear system. Solving the linear system using a direct matrix solver is prohibitively expensive in computing time and memory resources. This difficulty is circumvented by using an iterative solver (typically GMRES) together with the Fast Multipole Method (FMM). The response of an eddy current probe is finally expressed with the Auld reciprocity theorem.

Original language	English
Title of host publication	Electromagnetic Nondestructive Evaluation (XIV)
Editors	Tomasz Chady, Stanislaw Gratkowski, Toshiyuki Takagi, Satish S. Udpa
Pages	79-86
Number of pages	8
DOIs	https://doi.org/10.3233/978-1-60750-750-5-79
Publication status	Published - 1 Dec 2011
Externally published	Yes

Publication series

Name	Studies in Applied Electromagnetics and Mechanics
Volume	35
ISSN (Print)	1383-7281
ISSN (Electronic)	1879-8322

Keywords

Fast Multipole Method
Method of Moments
Singularity
Surface Integral Equations

Access to Document

10.3233/978-1-60750-750-5-79

Cite this

Lim, T., Pichenot, G., & Bonnet, M. (2011). Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries. In T. Chady, S. Gratkowski, T. Takagi, & S. S. Udpa (Eds.), Electromagnetic Nondestructive Evaluation (XIV) (pp. 79-86). (Studies in Applied Electromagnetics and Mechanics; Vol. 35). https://doi.org/10.3233/978-1-60750-750-5-79

Lim, Tekoing ; Pichenot, Gregoire ; Bonnet, Marc. / Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries. Electromagnetic Nondestructive Evaluation (XIV). editor / Tomasz Chady ; Stanislaw Gratkowski ; Toshiyuki Takagi ; Satish S. Udpa. 2011. pp. 79-86 (Studies in Applied Electromagnetics and Mechanics).

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title = "Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries",

abstract = "The motivation of this work is to develop a computational treatment of eddy current simulation applicable to complex 3D geometries. To this end, an approach based on surface integral equations and involving the homogeneous full-space Green's function and dyad is developed. A Galerkin variant of the method of moments, using bilinear basis functions, is employed for discretizing the surface integral equations, leading to a linear system. Solving the linear system using a direct matrix solver is prohibitively expensive in computing time and memory resources. This difficulty is circumvented by using an iterative solver (typically GMRES) together with the Fast Multipole Method (FMM). The response of an eddy current probe is finally expressed with the Auld reciprocity theorem.",

keywords = "Fast Multipole Method, Method of Moments, Singularity, Surface Integral Equations",

author = "Tekoing Lim and Gregoire Pichenot and Marc Bonnet",

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Lim, T, Pichenot, G & Bonnet, M 2011, Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries. in T Chady, S Gratkowski, T Takagi & SS Udpa (eds), Electromagnetic Nondestructive Evaluation (XIV). Studies in Applied Electromagnetics and Mechanics, vol. 35, pp. 79-86. https://doi.org/10.3233/978-1-60750-750-5-79

Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries. / Lim, Tekoing; Pichenot, Gregoire; Bonnet, Marc.
Electromagnetic Nondestructive Evaluation (XIV). ed. / Tomasz Chady; Stanislaw Gratkowski; Toshiyuki Takagi; Satish S. Udpa. 2011. p. 79-86 (Studies in Applied Electromagnetics and Mechanics; Vol. 35).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The motivation of this work is to develop a computational treatment of eddy current simulation applicable to complex 3D geometries. To this end, an approach based on surface integral equations and involving the homogeneous full-space Green's function and dyad is developed. A Galerkin variant of the method of moments, using bilinear basis functions, is employed for discretizing the surface integral equations, leading to a linear system. Solving the linear system using a direct matrix solver is prohibitively expensive in computing time and memory resources. This difficulty is circumvented by using an iterative solver (typically GMRES) together with the Fast Multipole Method (FMM). The response of an eddy current probe is finally expressed with the Auld reciprocity theorem.

AB - The motivation of this work is to develop a computational treatment of eddy current simulation applicable to complex 3D geometries. To this end, an approach based on surface integral equations and involving the homogeneous full-space Green's function and dyad is developed. A Galerkin variant of the method of moments, using bilinear basis functions, is employed for discretizing the surface integral equations, leading to a linear system. Solving the linear system using a direct matrix solver is prohibitively expensive in computing time and memory resources. This difficulty is circumvented by using an iterative solver (typically GMRES) together with the Fast Multipole Method (FMM). The response of an eddy current probe is finally expressed with the Auld reciprocity theorem.

KW - Fast Multipole Method

KW - Method of Moments

KW - Singularity

KW - Surface Integral Equations

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BT - Electromagnetic Nondestructive Evaluation (XIV)

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Lim T, Pichenot G, Bonnet M. Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries. In Chady T, Gratkowski S, Takagi T, Udpa SS, editors, Electromagnetic Nondestructive Evaluation (XIV). 2011. p. 79-86. (Studies in Applied Electromagnetics and Mechanics). doi: 10.3233/978-1-60750-750-5-79

Fast multipole method for 3D electromagnetic boundary integral equations. Application to non destructive testing on complex 3D geometries

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