报告题目:Inverse Problem and Scientific Computing Seminar I

报告人：鲁汪涛（浙江大学）、王珏（杭州师范大学）

报告时间：2022年09月09日 9:30－11:30

报告地点：理学楼A110

报告1题目：Wave scattering in layered orthotropic media I: A stable PML and a high-accuracy boundary integral equation method

报告人1：鲁汪涛（浙江大学）

摘要：In anisotropic media, the standard perfectly matched layer (PML) technique suffers irrevocable instability in terminating the unbounded problem domains. It remains an open question whether a stable PML-like absorbing boundary condition exists. For wave scattering in a layered orthotropic medium, this question is affirmatively answered in this talk. In each orthotropic medium, the permittivity tensor uniquely determines a change of coordinates that transforms the governing anisotropic Helmholtz equation into an isotropic Helmholtz equation in the new coordinate system. This leads us to propose a novel Sommerfeld radiation condition (SRC) to rigorously characterize outgoing waves in the layered orthotropic medium. Naturally, the SRC motivates a regionalized PML (RPML) to truncate the scattering problem, in the sense that a standard PML is set up in the new coordinate system in each orthotropic region. It is revealed that the RPML is unconditionally stable compared with the unstable uniaxial PML. A high-accuracy boundary integral equation (BIE) method is developed to solve the resulting boundary value problem. Numerical experiments are carried out to validate the stability of the RPML and the accuracy of the BIE method, showing exponentially decaying truncation errors as the RPML parameters increase.

报告人介绍：鲁汪涛, 2007年中国科学技术大学学士，2012年中国科学技术大学博士，并于同年获得香港城市大学联合培养博士学位。2017年8月回浙江大学工作，获国家海外高层次人才青年项目资助，并任百人计划研究员。2021年获浙江省自然科学基金杰出青年项目资助。主持国家自然科学基金面上项目一项，并参与多项国家级项目。

报告2题目：Some results on numerical research for Navier-Stokes Equations 

报告人2：王珏（杭州师范大学）

摘要：We are concerned with the development of numerical research for the 2D vorticity-stream function formulation and its application in vortex merging at high Reynolds numbers. A novel numerical method for solving the vorticity-stream function formulation of the Navier-Stokes equations at high Reynolds number is presented.  A verification algorithm that has the analytical solution is designed to demonstrate the feasibility and effectiveness of the proposed scheme. Furthermore, the proposed scheme is applied to study the vortex merging problem. Ample numerical experiments are performed to show some essential features of the merging of multiple vortices at high Reynolds numbers. Meanwhile, considering the importance of the inversion for the initial position of the vorticity field, we present an iteration algorithm for the reconstruction of the initial position parameters.

王珏，2010年获哈尔滨工程大学博士学位，随后在吉林大学数学研究所完成博士后研究工作，2018年赴美国Purdue大学访问交流一年。曾历任哈尔滨工程大学讲师，副教授、博士生导师。现任杭州师范大学副教授。主要研究数学物理反问题及其相关的偏微分方程数值解法，发表科研论文20余篇，主持完成国家自然科学青年基金一项、其它科研项目3项，参与完成国家级项目2项。

邀请人：张磊