6月6日 学术报告（两个）

发布时间:2023-05-31

学术报告1

报告题目：Numerical PDEs for Fluid-Structure Interaction (FSI) Problems

主讲人：孙澎涛教授，University of Nevada

报告时间：2023/06/06 10:00-11:00

报告地点：东校园信息管理学院楼B312，腾讯会议：402-568-281

主持人：邹青松教授

摘要：

The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields of engineering, named as fluid-structure interactions (FSI). To understand these phenomena, we need to find an effective way to model and simulate both fluid and structure, simultaneously, by investigating the interaction between them. In general, FSI problems require the fluid and the structure fields at the common interface to share not only the same velocity but also the common traction force. There are currently several major approaches classified with respect to the numerical treatment how the interfacie conditions of FSI are dealt with on the moving interface. In my talk, I will introduce three numerical techniques studied in my research for solving FSI problems: (1) bodyfitted mesh (arbitrary Lagrangian-Eulerian) method, (2) body-unfitted mesh (fictitious domain) method, and (3) meshfree (deep neural network) method.

Our applications to FSI problems range from hydrodynamics (physics) to hemodynamics (biology, physiology), in which the involved structures are either incompressible or compressible and bear a deformable and/or rotational constitutive relation while the surrounding fluid flow is incompressible or nearly incompressible. In particular, our well-developed numerical methods have been successfully applied to several realistic dynamic FSI problems. Some belong to the hydrodynamics that involve a deforming and/or spinning turbine which is immersed in the fluid flow. Others belong to the hemodynamical applications, e.g., a rotating artificial heart pump inside the artery to help on curing the heart-failure patients, and an intravascular stent inside the blood fluid to treat the aneurismal patients. Both applications are to improve the human cardiovascular system and to remedy cardiovascular diseases. Some animations will be shown in this talk to illustrate that the proposed and well analyzed numerical methods can produce high fidelity numerical results for realistic FSI problems in an efficient and accurate fashion.

主讲人简介：

       孙鹏涛博士是内华达大学拉斯维加斯分校（UNLV）数学科学系的正教授。孙博士于1997年获得中国科学院数学研究所博士学位。在2007年加入内华达大学拉斯维加斯分校之前，他曾担任中国科学院、香港理工大学、宾夕法尼亚州立大学和西蒙弗雷泽大学的研究科学家、博士后研究员、研究助理和助理教授。孙博士的主要研究领域是数值偏微分方程和科学与工程计算，在固体力学、流体动力学、燃料电池动力学、流固耦合、血液动力学、电流体动力学等领域的杂项多物理场问题中的应用。孙博士在著名科学期刊上发表了100多篇同行评审的学术文章，自2008年以来，他的研究得到了美国国家科学基金会，西蒙斯基金会和教师机会奖（UNLV）的持续支持。孙博士于2016年获得UNLV理学院杰出研究员奖。

个人主页：https://www.sun.faculty.unlv.edu/

学术报告2

报告题目：A priori error analysis and greedy training algorithms for neural networks solving PDEs

主讲人：洪庆国博士，Pennsylvania State University

报告时间：2023/06/06 11:00-12:00

报告地点：东校园信息管理学院楼B312，腾讯会议：402-568-281

主持人：邹青松教授

摘要：

We provide an a priori error analysis for methods solving PDEs using neural networks. We show that the resulting constrained optimization problem can be efficiently solved using greedy algorithms, which replaces stochastic gradient descent. Following this, we show that the error arising from discretizing the energy integrals is bounded both in the deterministic case, i.e. when using numerical quadrature, and also in the stochastic case, i.e. when sampling points to approximate the integrals. This innovative greedy  algorithm is tested on several benchmark examples to confirm its efficiency and robustness.

主讲人简介：

      洪庆国，博士，美国宾州州立大学Assistant  Research Professor。曾先后在奥地利科学院Radon研究所(RICAM)，德国Duisburg-Essen University，美国宾州州立大学从事博士后研究。目前研究兴趣包括机器学习、迭代法、间断有限元方法及应用。在SIAM J. Numer.  Anal.,  Math. Comp.,  Numer. Math.,  Comput. Methods Appl. Mech. Engrg.，Math. Models Methods Appl. Sci.和中国科学-数学等国内外期刊发表系列论文。