The Method of Fundamental Solutions for the 3D Laplace Inverse Geometric Problem on an Annular Domain

Mojtaba Sajjadmanesh; Hassen Aydi; Eskandar Ameer; Choonkil Park

doi:10.3390/fractalfract6020066

The Method of Fundamental Solutions for the 3D Laplace Inverse Geometric Problem on an Annular Domain

Mojtaba Sajjadmanesh
, Hassen Aydi^*
, Eskandar Ameer
, Choonkil Park

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy data in a least-square sense and minimisation of the objective function. This approach can also be considered with noisy boundary Cauchy data. The simplicity and efficiency of this method is illustrated in several numerical examples.

Original language	English
Article number	66
Journal	Fractal and Fractional
Volume	6
Issue number	2
DOIs	https://doi.org/10.3390/fractalfract6020066
Publication status	Published - Feb 2022
Externally published	Yes

Keywords

Inverse geometric problem
Laplace equation
Least-square problem
Method of fundamental solution

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10.3390/fractalfract6020066

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abstract = "In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy data in a least-square sense and minimisation of the objective function. This approach can also be considered with noisy boundary Cauchy data. The simplicity and efficiency of this method is illustrated in several numerical examples.",

keywords = "Inverse geometric problem, Laplace equation, Least-square problem, Method of fundamental solution",

author = "Mojtaba Sajjadmanesh and Hassen Aydi and Eskandar Ameer and Choonkil Park",

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AU - Park, Choonkil

PY - 2022/2

Y1 - 2022/2

N2 - In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy data in a least-square sense and minimisation of the objective function. This approach can also be considered with noisy boundary Cauchy data. The simplicity and efficiency of this method is illustrated in several numerical examples.

AB - In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy data in a least-square sense and minimisation of the objective function. This approach can also be considered with noisy boundary Cauchy data. The simplicity and efficiency of this method is illustrated in several numerical examples.

KW - Inverse geometric problem

KW - Laplace equation

KW - Least-square problem

KW - Method of fundamental solution

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DO - 10.3390/fractalfract6020066

M3 - Article

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ER -

The Method of Fundamental Solutions for the 3D Laplace Inverse Geometric Problem on an Annular Domain

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Keywords

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