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.

职业努力的目的是采取一些重要步骤来开发和应用新的、自适应的、高阶精确的方法来求解守恒定律。虽然技术重点将放在用于局部误差和规律性估计的有效隐式时间步长方法和技术上，但工作重点仍是应用科学和工程的大规模、实际应用以及国家高性能计算设施的使用。这项多学科任务的复杂性、专注于教育元素的计算平台的开发以及所考虑问题的基本性质将提供一个刺激的环境，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已证明可以为我们周围的物理世界建立准确可靠的数学模型。这种被称为守恒定律的模型显示出丰富的内容，就像物理世界一样，这继续对解决此类问题的计算技术开发人员提出挑战。然而，这些模型的普遍性足以保证开发新的和改进的方法，以便能够对流体和气体动力学、光通信和高速电子、电磁辐射应用等不同领域的问题进行有效和鲁棒的建模，甚至是气候建模。 Hesthaven 提议针对此类问题开发新的自适应高阶方法，并培训该领域的计算科学家。