2025年12月26日 地点：环境楼316 |
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时间 |
具体安排 |
14:30-15:30 |
报告人：郭玉坤（哈尔滨工业大学） 题目：Reconstruction of the biharmonic wave source from phaseless data 摘要：This talk concerns an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multifrequency phaseless measurements. In the first step, we establish a phase retrieval formula by introducing some artificial auxiliary point sources to the inverse source system. We show that the phase information can be uniquely determined and estimate the stability of this phase retrieval approach. Next, the Fourier method is adopted to reconstruct the source function from the phased multifrequency data. Numerical results will be presented to illustrate the performance of the proposed method. |
15:30-16:30 |
报告人：汪贤超（哈尔滨工业大学） 题目：A Monotonicity-Based Regularization Approach to Shape Reconstruction for the Helmholtz Equation 摘要：In this talk, we introduce 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 main advantages of our new approach are that this is a convex data-fitting problem that does not require additional PDE solutions. The global convergence and stability of the method are rigorously established to demonstrate the theoretical soundness. In addition, several numerical experiments are conducted to verify the effectiveness of the proposed approach in shape reconstruction.
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