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Reconstruction of unknown inclusions based on the diffusion model
发布时间: 2018-10-30     08:52   【返回上一页】 发布人:王海兵


北京师范大学数学科学学院

 

偏微分方程学术报告

 

报告题目:Reconstruction of unknown inclusions based on the diffusion model 

报告人:王海兵 教授(东南大学)

时间地点:2018年11月2日 下午2:00-3:00, 后主楼1124.

邀请人:李海刚

报告摘要:

Consider the problem of reconstructing unknown inclusions inside a diffusive medium from boundary measurements, which arises from active thermography and diffuse optical tomography. It is formulated as an inverse boundary value problem for the diffusion equation. We introduce two non-iterative methods for reconstructing the boundary of the unknown inclusion. One is a sampling-type method, which is based on the characterization of the solution to the so-called Neumann-to-Dirichlet map gap equation. The second is a direct algorithm for locating small inclusions, which is based on the asymptotic expansion for the weighted boundary measurement. Some close relations between them are discussed. Numerical results are also presented to show the efficiency and stability of the proposed methods.