Fourier and Microlocal Methods for Computational Wave Propagation

Speaker: 陈曦 (复旦大学)

Time: 2025-11-26 10:00-11:00
Location: 1610, SIMIS

Abstract:

Wave propagation is ubiquitous in physical phenomena. Mathematically, Fourier and microlocal methods serve as robust tools for elucidating the analytical and geometric structures of wave propagation. However, wave propagation in numerical simulation and inversion remains highly challenging in both traditional computational mathematics and machine learning, owing to the highly oscillatory nature of waves and the complexity of propagation media. The integration of Fourier and microlocal methods into computational wave propagation proves useful in reducing computational cost. This talk shall discuss several existing works and recent advances from this perspective.

波传播是物理现象中普遍存在的现象。在数学层面，傅里叶方法与微局部方法是阐明波传播解析结构与几何结构的可靠工具。然而，受波的高振荡特性及传播介质的复杂性影响，数值模拟与反演中的波传播问题，在传统计算数学与机器学习领域仍极具挑战性。将傅里叶与微局部方法融入计算波传播，被证实有助于降低计算成本。本报告将从这一视角，探讨相关既有研究成果及最新进展。

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About Speaker:

Xi Chen is an Associate Professor at the Shanghai Center for Mathematical Sciences, Fudan University, with a joint appointment at the Center for Applied Mathematics and the School of Mathematical Sciences. He received his PhD from the Australian National University, followed by postdoctoral fellowships at Fudan University and the University of Cambridge prior to his return to Fudan. His research interests include microlocal analysis, inverse problems in mathematical physics, and the numerical computation of PDEs.