New Exponential Integrators and Applications

新的指数积分器和应用

• 批准号: 1115978
• 负责人: Mayya Tokman
• 金额: $ 30万
• 依托单位: University of California - Merced
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115978&HistoricalAwards=false
• 关键词: New; Exponential; Integrators; Applications

The need to numerically solve initial value problems for large stiff systems of ordinary differential equations (ODEs) arises in an overwhelming majority of scientific and engineering fields. Traditionally implicit solvers have been used to overcome the stability restrictions on the time step and improve computational efficiency compared to explicit schemes. Recently, however, exponential integrators emerged as an efficient alternative to commonly used techniques. While several of such integrators have been proposed, significant research efforts are needed to construct, analyze and optimize these integrators. The PI proposed a class of new exponential propagation iterative schemes of Runge-Kutta type (EPIRK) which are designed to maximize computational efficiency for solving very large stiff systems. The research sponsored by this grant will produce new EPIRK methods designed to have good scalability on parallel high-performance computing platforms. The study of the new integrators will produce methodologies for construction of efficient exponential schemes and explore properties of these methods. An important part of the project is the development of adaptive versions of the algorithms and implementation of new integrators as a general-use software package for both serial and parallel platforms. The software will be used to study several application problems in plasma physics and biomodeling and will be made widely available.In a variety of scientific and engineering applications researchers want to predict behavior of complex systems which evolve on a wide range of temporal and spatial scales. Such systems, for instance, arise in many geo-engineering applications such as storing greenhouse gases, extraction of oil and gas from highly porous and fractured media or managing groundwater resources. Another example of a multiscale problem is modeling magnetic reconnection, one of the most fundamental processes in astrophysical and laboratory plasmas that governs such important phenomena as solar flares, magnetic substorms in the Earth?s magnetosphere and dynamics of magnetic fusion experiments. Computer modeling has become an essential tool in studying such systems. However, in order to be able to simulate the behavior of these systems on a computer advanced mathematical tools that offer exceptional efficiency on high-performance computing platforms have to be developed. The numerical techniques that will result from this project will allow prediction of the behavior of a wide range of complex systems of scientific and engineering interest over the parameter regimes inaccessible to standard methods.

大型刚性常微分方程组初值问题的数值求解在绝大多数科学和工程领域中都有着广泛的应用。 传统的隐式求解器已被用来克服时间步长的稳定性限制，并提高计算效率相比，显式格式。然而，最近，指数积分器出现作为一个有效的替代常用的技术。 虽然已经提出了几个这样的积分器，需要大量的研究工作来构建，分析和优化这些积分器。PI提出了一类新的龙格-库塔型（EPIRK）的指数传播迭代格式，旨在最大限度地提高计算效率，解决非常大的刚性系统。这项研究将产生新的EPIRK方法，旨在在并行高性能计算平台上具有良好的可扩展性。新的积分器的研究将产生有效的指数计划的建设方法，并探讨这些方法的性能。 该项目的一个重要组成部分是开发自适应版本的算法和实施新的积分器作为通用软件包的串行和并行平台。该软件将用于研究等离子体物理和生物建模中的几个应用问题，并将广泛提供。在各种科学和工程应用中，研究人员希望预测在广泛的时间和空间尺度上演化的复杂系统的行为。例如，此类系统出现在许多地球工程应用中，例如储存温室气体、从高度多孔和破碎的介质中提取石油和天然气或管理地下水资源。多尺度问题的另一个例子是模拟磁重联，这是天体物理学和实验室等离子体中最基本的过程之一，它控制着太阳耀斑、地球磁亚暴等重要现象。的磁层和磁聚变实验的动力学。计算机建模已成为研究此类系统的重要工具。然而，为了能够在计算机上模拟这些系统的行为，必须开发在高性能计算平台上提供卓越效率的高级数学工具。从这个项目中产生的数值技术将允许在标准方法无法达到的参数范围内预测科学和工程兴趣的各种复杂系统的行为。