Mixed boundary value problem from a perspective of a desperate statistician

Eugene Demidenko

DHMC / Dartmouth Mathematics Dept

Many problems of physics and engineering can be modeled by a partial differential equation with mixed boundary conditions (BC) yet surprisingly little effort has been made in this direction. The goal of the talk is to attract mathematicians to this important problem and illustrate mixed BC for Laplace equation applied to electrical impedance tomography. The advantages of an analytical solution versus finite element/volume is emphasized, e.g. for the problem of optimal measurements in the case of inverse problem. We have derived an analytical solution to the potential distribution on the homogeneous disk with unknown electrode surface impedance and conductivity expressed as Fourier series. This solution is used to estimate bad contact in the case of electrical impedance tomography measurements as a part of our breast cancer detection project funded by National Institutes of Health.

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