报告题目：A Monotonicity-Based Regularization Approach to Shape Reconstruction for the Helmholtz Equation

报告人：汪贤超 哈尔滨工业大学欧洲杯 副教授

报告时间：2026年11月12日10:00---11:00

报告地点：腾讯会议，会议ID：266-494-910

校内联系人：马世琪 [email protected]

报告摘要：We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of reconstructing the shape of the unknown scatterers.

Our formulation is based on a monotonicity relation between the scattering index and boundary measurements. We use this relation to obtain a pixel-wise constraint on the unknown scattering index, and then minimize a data-fitting functional defined as the sum of all positive eigenvalues of a linearized residual operator. The global convergence and stability of the method are rigorously established to demonstrate the theoretical soundness。

报告人简介：汪贤超，哈尔滨工业大学，副教授。2019年毕业于哈尔滨工业大学，获理学博士学位。目前研究领域为数学物理反问题，主要方向为波动方程反散射问题的数值分析与计算。目前已在“Inverse Problems”、“Journal of Computational Physics”以及SIAM等系列期刊上发表SCI学术论文10余篇，主持国家自然青年基金项目1项和“香江学者计划”项目1项。