NUMERICAL IMPLEMENTATION FOR A 2-D THERMAL INHOMOGENEITY THROUGH THE DYNAMICAL PROBE METHOD

In this paper, we present the theory and numerical implementation for a 2-D thermal inhomogeneity through the dynamical probe method. The main idea of the dynamical probe method is to construct an indicator function associated with some probe such that when the probe touch the boundary of the inclus...

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Bibliographic Details
Published in:Journal of computational mathematics 2010-01, Vol.28 (1), p.87-104
Main Authors: Yi, Lei, Kim, Kyoungsun, Nakamura, Gen
Format: Article
Language:English
Subjects:
Approximation
Boundary value problems
Computational mathematics
Differential equations
Heat equation
Indicator functions
Inhomogeneity
Mathematical constants
Mathematical functions
Nondestructive testing
不均匀
功能指标
动力学
指示函数
探针法
数值算法
狄利克雷
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Summary:In this paper, we present the theory and numerical implementation for a 2-D thermal inhomogeneity through the dynamical probe method. The main idea of the dynamical probe method is to construct an indicator function associated with some probe such that when the probe touch the boundary of the inclusion the indicator function will blow up. From this property, we can get the shape of the inclusion. We will give the numerical reconstruction algorithm to identify the inclusion from the simulated Neumann-to-Dirichlet map.
ISSN:0254-9409
1991-7139
DOI:10.4208/jcm.2009.09-m2935