Mathematical Sciences: Conference on Inverse Problems in Differential Equations: Computational Algorithms; March 10-14, 1991, College Station, Texas

这笔赠款部分用于资助将于1991年3月10日至14日在德克萨斯农工大学举行的一次会议和研讨会。这次会议的主题是偏微分方程逆问题，源于科学和工程中的各种问题。高速计算机的出现使得人们可以尝试解决具有巨大社会和经济价值的大规模问题，例如CAT扫描和油藏模拟。非唯一性问题是数值算法发展中的一个关键问题。确定必要的数据量以便最多存在一个解决方案是一个重要的问题；但是，通常可以重新定义“解决方案类”以“回答”这个问题。即使这并不合理，这个问题也可能被重新表述为一个情况要好得多的“足够接近”的问题。CAT扫描起作用，或者潜艇的特征可以通过反射声波检测出来，这一事实表明，复杂的逆问题即使得不到解决，至少也可以协商。与会者将讨论是否能找到数值可实现的方法，为阻抗层析成像、反向散射和频谱方法以及重叠边界数据等子领域中的一些密切相关的重新表述问题提供唯一的解决方案。参与者将在研讨会气氛中测试这些算法。//

This grant is to partially support a conference and workshop to be held March 10-14, 1991 at Texas A&M University. The topic of the conference, inverse problems in partial differential equations, arises from a wide variety of problems in science and engineering. The availability of high speed computers has allowed attempts at large scale problems of enormous social and economic value, for example, the CAT scan and oil reservoir simulations. The question of non-uniqueness is a critical one for the development of numerical algorithms. Determining the necessary amount of data in order that at most one solution can exist is an important question; however, often one can redefine the "solution class" in order to "answer" this question. Even when this is not reasonable, the problem may be reformulated into a "sufficiently close" problem for which the situation is much better. The very fact that CAT scans work or that features of submarines can be detected by using reflected sound waves shows that complex inverse problems can be, if not solved, at least negotiated. The conference participants will discuss whether one can find numerically implementable methods that give a unique solution to some closely related reformulation of problems in the subareas of impedance tomography, inverse scattering and spectral methods, and overposed boundary data. The participants will test these algorithms in a workshop atmosphere. //