Mathematical Sciences: Scientific Computing in Mechanics

斯科特 研究人员开发了一种科学计算的方法，结合了数值分析，计算机科学方面的研究，以及力学模型问题的解决方案。 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高阶，混合方法离散化在二维和三维），粒子传输的扩散加速技术，并行计算机的算法。 这项研究包括对每个算法的分析，得出了一个严格的理由，它准确地近似研究中的现象。 最后，研究涉及原型实现的算法在计算机程序中通过技术，可以确保一个强大的，易于维护的代码。 与相关学科的专家合作，这些计算机程序用于研究各个领域的基本物理现象。 该项目的总体目标是改善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规模多维模型。 这些模型是计算机模拟的基础，用于工程设计、制造过程、环境建模和补救技术的开发，以及生物技术的各个方面。 这项研究涉及到为现有技术难以解决的几个问题开发新的算法。 它强调高性能计算机在现实模拟中的有效使用。

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.