Collaborative Research: Construction, Analysis, Implementation and Application of New Efficient Exponential Integrators

合作研究：新型高效指数积分器的构建、分析、实现和应用

• 批准号: 1419003
• 负责人: Adrian Sandu
• 金额: $ 25万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1419003&HistoricalAwards=false
• 关键词: Collaborative; Research; Construction; Analysis; Implementation

As the scale and complexity of scientific and engineering problems grow, computer simulations become a necessary and integral part of the vast majority of research endeavors. An ability to create a computer model of a process under investigation, whether it comes from physics, economics, biology or some other field, provides not only significant cost savings for a study, but also brings insights inaccessible through experimental procedures alone. The growing complexity with which we describe phenomena of interest requires increasingly more sophisticated computer models. In particular, it is important to be able to simulate many complex processes over very long times, which is a computationally intensive and challenging task. This project is focused on developing new computational methods that allow simulating and studying time evolving phenomena from a wide range of scientific and engineering disciplines over long time intervals of interest. The mathematical and computer tools created during this project will enable researchers to study problems at a scale and complexity not possible with currently available computational tools.This project will advance the state-of-the-art in both the theory and practice of time discretization methods. In the course of the project a complete theoretical framework and high performance implementations of the new generation of exponential time integrators will be developed. The new methods will significantly improve computational efficiency of numerical models in many important areas of science and engineering, and will enable simulations at a scale and complexity that are not currently possible. The research will advance core numerical analysis through the development and study of new classes of exponential propagation iterative (EPI) methods such as split, hybrid, partitioned, and Krylov-based techniques. In addition, specialized efficient schemes will be designed and optimized for a wide range of problems. The theoretical work will be complemented by the creation of a mathematical software package that will provide high quality implementations of the most efficient exponential integrators to the broad scientific community.

随着科学和工程问题的规模和复杂性的增长，计算机模拟成为绝大多数研究努力的必要组成部分。一种创建正在调查过程的计算机模型的能力，无论是来自物理，经济学，生物学还是其他领域，不仅可以为研究提供大量的成本节省，而且还可以通过仅通过实验程序来获得无法获得的见解。我们描述的越来越多的复杂性需要越来越复杂的计算机模型。特别是，能够在很长的时间内模拟许多复杂的过程很重要，这是一项计算密集且具有挑战性的任务。该项目的重点是开发新的计算方法，这些方法允许在长期关注的时间间隔内模拟和研究从广泛的科学和工程学科中的时间发展的现象。 在此项目中创建的数学和计算机工具将使研究人员能够使用当前可用的计算工具进行规模和复杂性研究问题。该项目将在时间离散方法的理论和实践中推进最新的问题。在项目过程中，将开发新一代指数时间集成商的完整理论框架和高性能实现。新方法将显着提高科学和工程许多重要领域的数值模型的计算效率，并将以当前无法实现的规模和复杂性来实现模拟。这项研究将通过开发和研究基于分裂，混合，分区和基于Krylov的技术等新的指数传播迭代方法（EPI）方法来推动核心数值分析。此外，专门的有效方案将针对各种问题进行设计和优化。理论工作将通过创建数学软件包的创建来补充，该软件包将为广泛的科学社区提供最有效的指数集成商的高质量实现。