Improved asymptotic analysis for dynamical probe method
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Yong-Gwan Ji
Abstract
We concerned with the asymptotic analysis for the dynamical probe method which is a reconstruction scheme to identify an anomaly inside a heat conductor from the Neumann-to-Dirichlet map. In this paper an inclusion was considered as an anomaly and we succeeded giving an improved asymptotic behavior of the indicator function defined in terms of the Neumann-to-Dirichlet map to identify not only the location of the inclusion but also some of its physical properties simultaneously. The two major improvements made for analyzing the asymptotic behavior of the indicator function are as follows. Firstly, we can know the distance to the boundary of unknown inclusion as we probe it from its outside. This improvement can avoid overshooting the boundary points as much as possible if we probe it from outside the inclusion numerically. Secondly, we can know the value of heat conductivity of inclusion as we probe close to the inclusion even without touching it.
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: 49771-01
Funding statement: Partially supported by National Research Foundation of Korea (No. 49771-01).
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Articles in the same Issue
- Frontmatter
- Inversions of the windowed ray transform
- Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs–Divisia indices and forecasting
- Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales
- An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter
- Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems
- Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems
- Accuracy estimates of Gauss–Newton-type iterative regularization methods for nonlinear equations with operators having normally solvable derivative at the solution
- On convergence rates for asymptotic discrepancy principle
- Identification of an unknown coefficient in KdV equation from final time measurement
- Improved asymptotic analysis for dynamical probe method
Articles in the same Issue
- Frontmatter
- Inversions of the windowed ray transform
- Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs–Divisia indices and forecasting
- Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales
- An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter
- Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems
- Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems
- Accuracy estimates of Gauss–Newton-type iterative regularization methods for nonlinear equations with operators having normally solvable derivative at the solution
- On convergence rates for asymptotic discrepancy principle
- Identification of an unknown coefficient in KdV equation from final time measurement
- Improved asymptotic analysis for dynamical probe method
