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

这笔赠款将部分支持一次会议和讲习班 将于1991年3月10日至14日在德克萨斯A M大学举行。 会议的主题，局部反问题 微分方程，产生于各种各样的问题， 科学与工程学高速计算机的可用性 使得人们可以尝试解决大规模的社会问题， 和经济价值，例如CAT扫描和油藏 仿真。 非唯一性问题是一个关键问题 用于数值算法的开发。 确定 必要的数据量，以便最多一个解决方案可以 存在是一个重要的问题;然而，通常可以重新定义 “解决方案类”，以“回答”这个问题。 甚至 当这不合理时，问题可以重新表述为 一个“足够接近”的问题， 好多了 CAT扫描有效的事实， 潜艇可以通过使用反射声波来探测。 复杂的逆问题即使不能解决， 谈判。 与会者将讨论是否可以 找到数值上可实现的方法， 问题的一些密切相关的重新表述的解决方案， 阻抗层析成像、逆散射和光谱成像的子区域 方法和重叠边界数据。 参与者将测试 在研讨会的气氛中讨论这些算法。//

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. //