Mathematical Sciences: Scientific Computing in Mechanics

研究人员开发了一种科学计算方法，该方法结合了数值分析、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，二维和三维的混合方法离散化），粒子传输的扩散加速技术，以及并行计算机的算法。这项研究包括对每个算法的分析，得出一个严格的理由，即它准确地近似于所研究的现象。最后，研究涉及通过技术在计算机程序中实现算法的原型，以确保鲁棒性和易于维护的代码。与相关学科的专家合作，这些计算机程序被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进软件的基础，以解决涉及连续介质力学中大规模、多维模型的科学和技术问题。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发展，以及生物技术的各个方面。这项研究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.