报告题目：Wavelet-based Methods for Numerically Solving PDEs

报 告 人：Bin Han 教授

报告人所在单位：University of Alberta

报告日期：2025年5月9日

报告时间：10:00 - 11:00

报告地点：光华楼东主楼 2001

报告摘要：Wavelets are widely used in image processing and numerical PDEs. This talk focuses on wavelet-based methods for solving the elliptic interface problem and the Helmholtz equation. The elliptic interface problem involves discontinuous diffusion coefficients and source terms, leading to low regularity solutions 𝑢 ∈𝐻^(1+𝜖) (Ω) with 𝜖<1/2. Helmholtz solutions exhibit high frequencies, causing ill-conditioned indefinite linear systems at large wavenumbers. Current methods require complex treatments at interfaces and lack uniformly bounded condition numbers. We present wavelet basics in Sobolev spaces for numerical PDEs and discuss high-order wavelet methods for 2D elliptic interface problems and Helmholtz equations. Finally, we introduce a second-order wavelet method with proven convergence and uniformly bounded condition numbers. This work is based on joint research with M. Michelle.

个人简介：Dr. Bin Han is a Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. He earned his Ph.D. in Mathematics from the University of Alberta and completed postdoctoral research at Princeton University. His research focuses on numerical partial differential equations, framelets with applications in image processing and data science, wavelet theory, and refinable functions and subdivision schemes. Dr. Han has published extensively in top-tier journals, including SIAM J. Numer. Anal., Appl. Comput. Harmon. Anal., and Found. Comput. Math.