Mathematical Sciences: Scientific Computing in Mechanics

研究人员斯科特开发了一种科学计算的方法，它结合了数值分析、计算机科学的各个方面的研究，并解决了力学中的模型问题。三个研究领域是该项目的重点：不可压缩流体动力学的计算问题(包括自由边界问题和二维和三维的高阶混合方法离散)，粒子传输的扩散加速技术，以及并行计算机的算法。这项研究包括对每种算法的分析，得出了它准确地近似于所研究的现象的严格理由。最后，这项研究涉及在计算机程序中通过能够确保健壮和易于维护的代码的技术来实现算法的原型。这些计算机程序与相关学科的专家合作，用于研究各种领域的基本物理现象。该项目的总体目标是改善用于解决科学和技术问题的软件基础，这些问题涉及连续介质力学中的大型多维模型。这些模型是计算机模拟的基础，用于制造过程中的工程设计、环境建模和补救技术的开发，以及生物技术的各个方面。这项研究涉及为现有技术难以解决的几个问题开发新的算法。它强调在现实模拟中高效使用高性能计算机。

Scott The investigator develops an approach to scientific computation 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 project: computational problems in incompressible fluid dynamics (including free--boundary problems and high-order, mixed method discretizations in two and three dimensions), diffusion acceleration techniques for particle transport, and algorithms for parallel computers. This research includes an analysis of each algorithm, yielding a rigorous justification that it accurately approximates the phenomenon under study. Finally, the research involves prototype implementations of the algorithms in computer programs via techniques that can assure a robust and easily maintained code. In collaboration with specialists in related disciplines, these computer programs are used to study basic physical phenomena in a variety of areas. The overall objective of the project is to improve the foundations for software for solving problems in science and technology that involve large scale, multidimensional models in continuum mechanics. These models are the basis for computer simulation used in engineering design in manufacturing processes, in environmental modeling and the development of remediation techniques, and in various aspects of biotechnology. The research involves the development of new algorithms for several problems too difficult to solve by existing techniques. It emphasizes the efficient use of high-performance computers in realistic simulations.