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

这笔拨款部分用于支持将于1991年3月10日至14日在德州农工大学举行的会议和研讨会。本次会议的主题是偏微分方程中的逆问题，它源于科学和工程中的各种各样的问题。高速计算机的可用性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的一个关键问题。确定必要的数据量以便最多存在一种解决方案是一个重要问题；然而，为了“回答”这个问题，通常可以重新定义“解决方案类”。即使这是不合理的，问题也可能被重新表述为一个“足够接近”的问题，这样情况会好得多。CAT扫描可以工作，或者潜艇的特征可以通过反射声波来探测，这一事实表明，复杂的逆问题即使不能解决，至少也可以协商解决。会议参与者将讨论是否可以找到数值上可实现的方法，为阻抗层析成像，逆散射和光谱方法以及叠加边界数据等子领域中一些密切相关的问题的重新表述提供独特的解决方案。参与者将在研讨会的氛围中测试这些算法。//

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. //