Tianyuan Mathematical Center
in Southwest China

Application of Immersed Finite Elements to Interface Inverse Problems

[Math. Dept.]

June 29, 2018  15:30-16:30

E409  School of Mathematics

SPEAKER

Tao Lin (Department of Mathematics, Virginia Tech)

ABSTRCT

This talk is about a fixed mesh method for solving interface inverse problems for an elliptic boundary value problem that is posed in a domain formed with different materials. These inverse problems are to determine the interface that separates different materials by some measurements, either on the boundary and/or in the interior of the domain, about the solution to the boundary problem. We formulate these interface inverse problems as shape optimization problems whose objective functionals depend on the interface. Both the governing partial differential equations and objective functionals are discretized accurately by an immersed finite element (IFE) method on a fixed mesh independent of interface. The formulas for the shape sensitivities of the discretized objective functions are derived within the IFE framework that can be computed accurately and efficiently through the discretized adjoint method. We demonstrate features of this IFE-based shape optimization algorithm by a group of representative interface inverse/design problems.

SUPPORTED BY

Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University