报告题目:Inverse Problem and Scientific Computing II (2024)
报告人：蒋世东、赖俊、王珏、徐翔等
报告时间：2023年07月03日 13:30-17:30
报告地点：理学楼A110
报告I题目：An overview of integral equation methods and fast algorithms
报告人I：蒋世东 教授 （西蒙斯基金会Flatiron研究所计算数学中心）
摘要：In recent years, integral equation methods have become increasingly popular for solving the boundary value problems governed by the classical partial differential equations of mathematical physics. Such methods have several advantages: they reduce the dimensionality from the volume to the boundary, they lead to well-conditioned linear systems, they are compatible with high-order accurate discretizations in complicated geometry, and they avoid the need for artificial boundary conditions when solving exterior or scattering problems. Fast algorithms, especially the Fast Multipole Method and its descendants, have reduced the computational cost associated with the application and inversion of the relevant integral operators so that they scale linearly or nearly linearly with the system size, despite the fact that the matrices are dense. As a result, many of the core problems in electromagnetics, acoustics, solid and fluid mechanics, molecular dynamics, quantum physics and chemistry, and astrophysics can now be solved extremely efficiently. For such problems, this is leading to a paradigm shift: accurate solutions to large-scale problems can now be obtained using modest computational resources rather than supercomputers. This talk will present an overview of both the integral equation methods and the corresponding fast algorithms, with examples illustrating the fundamental ideas and their practical performance.
报告人介绍：蒋世东于2001年获得纽约大学数学博士学位。2001年至2004年，他在耶鲁大学计算机科学系担任博士后。2004年至2021年，他在新泽西理工学院数学科学系任教，2017年晋升为正教授。自2021年8月起，成为西蒙斯基金会Flatiron研究所计算数学中心的高级研究科学家。他的研究兴趣包括应用数学与计算数学、快速算法和积分方程方法。曾在SIAM Review、CPAM、SISC、ACHA等期刊上发表学术论文多篇。
报告II题目: Far field model of acoustic time reversal method in a layered medium
报告人II：赖俊 研究员 （浙江大学）
摘要：This talk is concerned with the so-called DORT method that uses the eigenfunctions of time-reversal operator to determine the locations of small impenetrable scatterers buried in the lower half-space of an unbounded two-layered medium. We give a rigorous mathematical justification for the DORT method under sound-soft and sound-hard boundary conditions in a two-layered medium. Based on the limited-aperture time-harmonic far field model and an asymptotic analysis for small and distant particles, we show that each sound-soft and sound-hard buried particle gives rise to one and three significant eigenvalues, respectively. Utilizing the imaging result as an initial guess, a Bayesian inversion scheme is proposed to reconstruct the shape of multiple buried extended scatterers more accurately, whose efficiency is illustrated by numerical experiments.
报告人介绍：赖俊，美国密歇根州立大学应用数学博士毕业，曾任纽约大学柯朗数学研究所博士后及讲师，目前任浙江大学数学科学学院研究员，长聘副教授，主要研究声波，电磁波及弹性波方程的散射与反散射问题，在数学知名杂志ACHA，SIAM系列，Math Comp，Inverse Problems等发表文章多篇，主持国家面上项目，并参与基金委重大研究计划，基金委创新群体等研究，2016年入选中组部海外高层次青年人才计划，2019年获十一届全国反问题年会“优秀青年学术奖”，2022年获浙江大学-小米青年学者称号.
报告III题目: Research on the nonradiating sources and their applications
报告人III：王珏 副教授 （杭州师范大学）
摘要：In this talk, we will present a stability result for an inverse random source problem of Helmholtz equation in multi-layered media, where the source function is driven by a spatial Brownian motion. The statistical properties of the random source including expectation and variance are reconstructed from physically realizable measurements. By using multi-frequencies data, the increasing stability for the inverse random source scattering problems can be achieved. More precisely, the stability estimate consists of a Lipschitz stability term and a logarithmically unstable term, and the latter logarithmic term decreases as the upper bound of the frequency grows, which makes the problem have an almost Lipschitz stability. The numerical results demonstrate that the better stability can be obtained by using more frequencies and realizations.
报告人介绍：王珏，2010年于哈尔滨工程大学获得博士学位，随后在吉林大学数学研究所从事博士后研究工作。目前任杭州师范大学，副教授。主要研究数学物理反问题数学理论及其相关的偏微分方程数值解法，特别关注电磁场无损检测反问题及复杂背景下声学和电磁学散射与反散射问题的数学理论和数值算法研究。在Inverse Problems、中国科学等期刊发表科研论文多篇，主持国家自然科学基金面上、青年项目和浙江省自然科学基金等科研项目。
报告IV题目: TBA
报告人IV：徐翔 研究员 （浙江大学）
摘要： TBA
报告人介绍：徐翔，浙江大学数学科学学院长聘副教授。徐翔的研究主要集中在反问题的理论与计算，共发表SCI论文30余篇，部分论文被列为ESI高引论文和Inverse Problems亮点收录。2013年获得曙光青年学术奖，2014年入选“海外高层次人才计划青年项目”、浙江省特聘专家，2016年入选浙江省151人才工程。主持国家自然科学基金面上项目，参与国家自然科学基金委创新群体项目、重大研究计划重点项目、国际（地区）交流合作等多项项目。
邀请人：张磊