New structures in geometric numerical integration

几何数值积分的新结构

• 批准号: DP140100640
• 负责人: Prof Reinout Quispel
• 金额: $ 47.9万
• 依托单位: La Trobe University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-05-23 至 2018-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100640
• 关键词: New; structures; geometric; numerical; integration

Many scientific phenomena in physics, astronomy, chemistry, and geoscience, are modelled by differential equations (DEs). Generally DEs have no closed form solutions, and one must rely on numerical integration. Traditionally this is done using, for example, Runge-Kutta methods or linear multistep methods, respectively finite difference or finite element methods. Recently, however, novel so-called ‘geometric’ integration methods that preserve qualitative features of many DEs exactly (as opposed to traditional methods) have been discovered, leading to crucial stability improvements. Combining aspects of dynamical systems theory and traditional numerical DEs, this project will improve, extend, and systematise this new field of geometric integration.

物理学，天文学，化学和地球科学中的许多科学现象都是由不同方程式建模的（DES）。通常，DES没有封闭形式的解决方案，并且必须依靠数值集成。传统上，这是使用例如runge-kutta方法或线性多步法方法，分别有限差异或有限元方法来完成。然而，最近，已经发现了保留许多DES的定性特征（与传统方法相反）的新型所谓“几何”整合方法，从而导致了至关重要的稳定性改善。结合动态系统理论的各个方面，该项目将改善，扩展和系统化这一新的几何整合领域。