Topological and shape gradient strategy for solving geometrical inverse problems
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TLDR
In this paper, a technique for shape reconstruction based on the topological and shape gradients is presented, which considers the shape as a superposition of very thin elliptic inclusions to get a first approximation.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2013-04-15 and is currently open access. It has received 22 citations till now. The article focuses on the topics: Topological quantum number & Inverse problem.read more
Citations
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Analyses of internal structures and defects in materials using physics-informed neural networks
TL;DR: In this article , a general framework based on physics-informed neural networks for identifying unknown geometric and material parameters is presented, which can be applied to other inverse problems in different applications, targeting material characterization, quality assurance, and structural design.
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Topological sensitivity analysis for the modified Helmholtz equation under an impedance condition on the boundary of a hole
TL;DR: In this paper, a topological sensitivity analysis for the modified Helmholtz equation with an impedance condition prescribed on the boundary of a hole is presented, which is then used for numerical simulations for an inverse problem.
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A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem
TL;DR: In this article, a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology was developed.
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Topology optimization of electric machines based on topological sensitivity analysis
Peter Gangl,Ulrich Langer +1 more
TL;DR: Ohtake et al. as mentioned in this paper proposed a gradient-based ON/OFF method for the optimization of an electric motor in the nonlinear case and showed numerical results obtained by applying the on/off method to the optimization.
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One-iteration reconstruction algorithm for geometric inverse source problem
Mourad Hrizi,Maatoug Hassine +1 more
TL;DR: In this article, a new reconstruction method based on the Kohn-Vogelius formulation and the topological gradient method was proposed to detect the shape and location of the unknown source term from additional boundary conditions.
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Topological sensitivity analysis
TL;DR: In this article, the authors proposed an alternative way to compute the topological derivative based on the shape sensitivity analysis concepts, which leads to a more simple and constructive formulation than the ones found in the literature.
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Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction
TL;DR: In this paper, an asymptotic formula for the steady-state voltage potential in the presence of a finite number of diametrically small inhomogeneities with conductivity different from the background conductivity was derived.
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Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
Michael Vogelius,Darko Volkov +1 more
TL;DR: In this article, the authors consider solutions to the time-harmonic Maxwell's Equations of a TE (transverse electric) nature and provide a rigorous derivation of the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter.
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On uniqueness of recovery of a discontinuous conductivity coefficient
TL;DR: In this paper, the authors consider the problem of retrouver le coefficient a de l'equation elliptique div(a⊇u)=0 dans un domaine Ω avec la condition aux limites u=φ sur ∂Ω quand ∂u/∂N est donnee pour tout φ (regulier).