Mathematical Sciences: Scientific Computation in Mechanics

提出了一种结合数值分析、计算机科学方面的研究和力学模型问题的解决方法的科学计算方法。三个研究领域是该提案的重点：不可压缩流体动力学的计算问题（包括自由边界问题，变密度问题和三维高阶离散化问题），计算化学（分子动力学模拟），以及并行计算机上科学算法的自动编程。该提案的总体目标是改进软件的基础，以解决涉及大规模、涉及力学的多维模型的科学和技术问题。这项研究将涉及开发新的算法来解决一些现有技术难以解决的问题。它还将包括对每个算法的分析，得出一个严谨的理由，证明它准确地近似于所研究的现象。最后，提出的研究将涉及通过技术在计算机程序中实现算法的原型，这些技术可以确保健壮且易于维护的代码。这项研究将改进许多重要工业过程的计算建模。其中一门课程包括制作摄影胶片、缝纫线、挤压金属和保鲜膜等各种各样的东西。另一个涉及生物医学应用，例如新药的开发。另一个影响对某些有毒气体泄漏的分析。

An approach to scientific computation is proposed that incorporates research in numerical analysis, aspects of computer science, and solution of model problems in mechanics. Three research areas are the focus of the proposal: computational problems in incompressible fluid dynamics (including free-boundary problems, problems with variable density and high-order discretizations in three dimensions), computational chemistry (molecular dynamics simulations), and automated programming of scientific algorithms on parallel computers. The overall objective of the proposal is to improve the foundations for software for solving problems in science and technology that involve large scale, multidimensional models involving mechanics. The research will involve the development of new algorithms for several problems too difficult to solve by existing techniques. It will also include an analysis of each algorithm, yielding a rigorous justification that it accurately approximates the phenomena under study. Finally, the proposed research will involve prototype implementations of the algorithms in computer programs via techniques that can assure a robust and easliy maintained code. This research will improve computational modeling of many important industrial processes. One class involves such diverse things as making photographic film, sewing thread, extruded metals and Saran Wrap. Another involves biomedical applications, for example in the development of new pharmaceuticals. Another impacts the analysis of certain toxic gas spills.