Conference on Highly Ocillatory Problems: Computation, Theory and Applications.

高振荡问题会议：计算、理论和应用。

• 批准号: 0702979
• 负责人: Thomas Hou
• 金额: $ 1万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0702979&HistoricalAwards=false
• 关键词: Conference; Highly; Ocillatory; Problems; Computation

Highly oscillatory problems, ubiquitous in applications, are typically consider to be very difficult theoretically and demanding computationally. However, recent developments provide highly effective means to treat problems with rapid oscillation. The Isaac Newton Institute program brings together professionals concerned in highly oscillatory phenomena, with an emphasis on multiscale modeling, homogenization, symplectic integration, Riemann-Hilbert techniques, highly oscillatory quadrature and exponential integrators, together with theoreticians and with workers in a wide range of applications. Typical grand challenges that we seek to address by this multidisciplinary collaboration are the solution of Schroedinger, Helmholtz and Maxwell equations, as well as long-term integration of equations originating in molecular dynamics.High oscillation pervades a very wide range of applications:electromagnetics, fluid dynamics, molecular modelling, quantum chemistry, computerized tomography, plasma transport, celestial mechanics, medical imaging, signal processing. . . . It has been addressed by a wide range of mathematical techniques, ranging from asymptotic theory, harmonic analysis, theory of dynamical systems, theory of integrable systems and differential geometry. The computation of highly oscillatory problems has spawned a large number of different numerical approaches and algorithms. The purpose of this program is to foster research into different aspects of high oscillation, including the theoretical, the computational and the applied, from a united standpoint and to promote the synergy implicit in an interdisciplinary activity.

高振荡问题在实际应用中普遍存在，理论上非常困难，计算上要求很高。然而，最近的发展提供了非常有效的手段来处理快速振荡的问题。艾萨克·牛顿研究所计划汇集了关注高度振荡现象的专业人士，重点是多尺度建模，均匀化，辛积分，黎曼-希尔伯特技术，高度振荡的正交和指数积分器，以及理论家和广泛应用的工人。通过这种多学科合作，我们寻求解决的典型重大挑战是薛定谔方程、亥姆霍兹方程和麦克斯韦方程的解，以及源自分子动力学方程的长期集成。高振荡渗透到非常广泛的应用领域：电磁学、流体动力学、分子建模、量子化学、计算机断层扫描、等离子体传输、天体力学、医学成像、信号处理。. . .它已经解决了广泛的数学技术，从渐近理论，调和分析，理论的动力系统，理论的可积系统和微分几何。高振荡问题的计算产生了大量不同的数值方法和算法。该计划的目的是从统一的角度促进对高振荡不同方面的研究，包括理论，计算和应用，并促进跨学科活动中隐含的协同作用。