Determination of volumetric material data from boundary measurements

What is it about?

For decades, procedures have been sought to determine material properties from data measured at the boundary. One such example is Calderon's problem, where temperature and normal heat fluxes are given on the boundary, and the distribution of conductivity of the material in the volume is sought. We show that for this case, which is governed by the Laplace equation, the resulting conductivity is still significantly different from the target (or real) distribution sought. While the normal fluxes recovered are very close to the prescribed ones, the tangential fluxes can differ considerably.This implies that the estimation of field conductivities (or generally field data) from boundary data is a far more difficult than previously assumed when the governing partial differential equation in the domain is a Laplacian. This has consequences for material parameter assessments (e.g. for routine maintenance checks of structures), electrical impedance tomography, and many other applications.

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