CAREER: Towards Robust and Efficient High-Order Adaptive Computational Methods for Conservation Laws in Complex Geometries -- Analysis, Implementation, and Applications

职业：复杂几何守恒定律的稳健高效高阶自适应计算方法——分析、实现和应用

• 批准号: 0132967
• 负责人: Jan Hesthaven
• 金额: $ 33万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0132967&HistoricalAwards=false
• 关键词: CAREER; Towards; Robust; Efficient; Order

The purpose of the CAREER effort is to take some important steps towards the development and application of new, adaptive, high-order accurate methods for solving conservation laws. While the technical emphasis will be on efficient implicit time-stepping methods and techniques for local error and regularity estimation, the effort will maintain a focus on large scale, realistic applications from the applied sciences and engineering, and the use of national high performance computing facilities. The complexity of this multidisciplinary task, the development of a computational platform focusing on educational elements, and the fundamental nature of the problems being considered will provide a stimulating environment in which to train future computational scientists in emerging computational techniques for solving conservation laws.Application of basic physical principles of conservation of mass, momentum, and energy has proven itself to lead to accurate and reliable mathematical models of the physical world surrounding us. Such models, known as conservation laws, display a richness, much like the physical world, that continues to challenge developers of computational techniques for solving such problems. The mere universality of such models, however, warrants that new and improved methods be developed to enable the efficient and robust modeling of problems in areas as diverse as the dynamics of fluids and gases, optical communication and high-speed electronics, applications in electromagnetic radiation, or even climate modeling. Hesthaven proposes to develop new adaptive high-order methods for such problems and to train computational scientists in this area.

职业生涯努力的目的是朝着开发和应用新的、自适应的、高精度的方法来解决守恒律问题迈出重要的一步。虽然技术重点将是用于局部误差和正则性估计的高效隐式时间步进方法和技术，但努力将继续侧重于应用科学和工程的大规模、现实应用，以及使用国家高性能计算设施。这项多学科任务的复杂性，一个专注于教育因素的计算平台的开发，以及正在考虑的问题的基本性质，将提供一个激励环境，在其中培训未来的计算科学家解决守恒定律的新兴计算技术。质量、动量和能量守恒的基本物理原理的应用已经证明，它本身导致了我们周围物理世界的准确和可靠的数学模型。这类被称为守恒定律的模型展示了丰富的内容，就像物理世界一样，它继续挑战着解决这类问题的计算技术的开发人员。然而，仅仅是这些模型的普遍性，就需要开发新的和改进的方法，以便能够对各种领域的问题进行高效和健壮的建模，这些领域包括流体和气体动力学、光学通信和高速电子、电磁辐射应用，甚至气候建模。Hesthaven建议为这类问题开发新的自适应高阶方法，并在这一领域培训计算科学家。