applied math

Joint Applied Math/Inverse Problems Seminar at Colorado State University

Thursday 2:00-3:00PM, Online

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Zoom Meeting link  
Meeting ID: 963 0995 0719
Passcode: 384535

Spring 2021

Jab 21   Feb 25   Mar 04   Apr 04   Apr 22  


 
 
 
Jan 21   Back to top

Mikyoung Lim

Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST)

Title  Reconstruction of a conductivity inclusion using the Faber polynomials

Abstract  In this talk, I present analytical shape recovery methods for the conductivity inclusion in two dimensions, obtained in collaboration with Doosung Choi and Junbeom Kim. For a simply connected planar domain, there exists a function that conformally maps a region outside a circular disk to the region outside the domain. The conformal mapping then defines the so-called Faber polynomials, which form a basis for analytic functions. An electrical inclusion, inserted in a homogeneous background, induces a perturbation in the background potential. This perturbation admits a far-field expansion, whose coefficients are the so-called generalized polarization tensors (GPTs). GPTs can be obtained from the exterior measurements. As a modification of GPTs, we recently introduced the Faber polynomial polarization tensors (FPTs). We design two analytical approaches for the shape recovery of a conductivity inclusion by employing the concept of FPTs. Numerical experiments demonstrate the validity of the proposed analytical methods.

 
 
 
Feb 25   Back to top

Andrew Gillette

Lawrance Livermore National Laboratory

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Mar 04   Back to top

Teemo Saksala

Department of Mathematics, North Carolina State University

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Apr 04   Back to top

Colin Jensen

Department of Mathematics, Colorado State University

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Apr 22   Back to top

Sui Tang

Department of Mathematics, University of California, Santa Barbara

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