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Volume 28, Issue 1
Numerical Implementation for a 2-D Thermal Inhomogeneity Through the Dynamical Probe Method

Lei Yi, Kyoungsun Kim & Gen Nakamura

DOI: 10.4208/jcm.2009.09-m2935

J. Comp. Math., 28 (2010), pp. 87-104.

Published online: 2010-02

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  • Abstract

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.

  • Keywords

Heat equation, Dynamical probe method, Neumann-to-Dirichlet map.

  • AMS Subject Headings

35R30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-87, author = {Lei Yi, Kyoungsun Kim and Gen Nakamura}, title = {Numerical Implementation for a 2-D Thermal Inhomogeneity Through the Dynamical Probe Method}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {1}, pages = {87--104}, abstract = {

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 = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m2935}, url = {http://global-sci.org/intro/article_detail/jcm/8509.html} }
TY - JOUR T1 - Numerical Implementation for a 2-D Thermal Inhomogeneity Through the Dynamical Probe Method AU - Lei Yi, Kyoungsun Kim & Gen Nakamura JO - Journal of Computational Mathematics VL - 1 SP - 87 EP - 104 PY - 2010 DA - 2010/02 SN - 28 DO - http://doi.org/10.4208/jcm.2009.09-m2935 UR - https://global-sci.org/intro/article_detail/jcm/8509.html KW - Heat equation, Dynamical probe method, Neumann-to-Dirichlet map. AB -

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.

Lei Yi, Kyoungsun Kim and Gen Nakamura. (2010). Numerical Implementation for a 2-D Thermal Inhomogeneity Through the Dynamical Probe Method. Journal of Computational Mathematics. 28 (1). 87-104. doi:10.4208/jcm.2009.09-m2935
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