Search results for "Inverse conductivity problem"

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Spectral approach to D-bar problems

2017

We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2017 Wiley Periodicals, Inc.

[ MATH ] Mathematics [math]Spectral approachInverse conductivity problemBar (music)General MathematicsElectrical-impedance tomographyFOS: Physical sciences2 dimensions010103 numerical & computational mathematics01 natural sciencesDiscrete systemsymbols.namesakeConvergence (routing)FOS: MathematicsApplied mathematicsUniquenessStewartson-ii equationsMathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]Electrical impedance tomographyReconstruction algorithmsNumerical-solutionMathematicsNonlinear Sciences - Exactly Solvable and Integrable SystemsApplied MathematicsNumerical Analysis (math.NA)Integral equation010101 applied mathematicsFourier transformsymbolsUniquenessExactly Solvable and Integrable Systems (nlin.SI)
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Reconstruction from boundary measurements for less regular conductivities

2012

In this paper, following Nachman's idea and Haberman and Tataru's idea, we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz domain $\Omega$ from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$. In the appendix the authors and R. M. Brown recover the gradient of a $C^1$-conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$.

Mathematics - Analysis of PDEs35R30Inverse conductivity problemCalderón problemAstrophysics::High Energy Astrophysical PhenomenaBourgain's spaceFOS: MathematicsMathematics::Analysis of PDEsDirichlet-to-Neumann mapMathematics::Spectral TheoryBoundary integral equationAnalysis of PDEs (math.AP)
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