Hybrid Hermite-Discontinous Galerkin Methods with Applications to Elastic and Electromagnetic Waves

混合 Hermite-不连续 Galerkin 方法在弹性波和电磁波中的应用

基本信息

批准号：
1319054
负责人：
Daniel Appelo
金额：
$ 25.82万
依托单位：
University of New Mexico
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2013
资助国家：
美国
起止时间：
2013-09-15 至 2017-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1319054&HistoricalAwards=false
关键词：
Hybrid Hermite Discontinous Galerkin Methods

项目摘要

The Principal Investigator proposes to carry out an interdisciplinary comprehensive research program combining the development, analysis and optimization of a new class of numerical methods, with their application to problems in seismology and electromagnetics. The novel methods hybridizes arbitrary-order Hermite approximations with arbitrary-order discontinuous Galerkin methods. The combination of these two methods will result in a new class of hybrid methods able to handle complex geometries and with unprecedented computational efficiency through large time steps and high-resolution. The methods have very large computation to communication ratio and are well suited for implementation on current and emerging supercomputer systems, enabling the solution of complex, multiple-scale evolutionary systems. The proposed unified analysis of discontinuous Galerkin methods and Hermite methods will require new tools and theories to be developed and will lead to a new theoretical framework for the analysis of hybrid methods. The proposal will consider methods for both first and second order formulations of the governing equations of elasticity and electromagnetics. The research will have broader impacts in technology and science, as well as in the training of the next generation of computational scientists. As recent events in Japan have shown, earthquakes are a societal problem throughout the world. To better mitigate seismic hazard, effective prevention and prediction is needed. Careful assessment of seismic hazards through accurate computational predictions can lead to appropriate building codes. This can be of enormous impact for human life and societal welfare in the case of a large seismic event in a densely populated area as the greater Los Angeles or the San Francisco bay. The broader impacts of the proposed activities also include education. The project will involve graduate students who will gain experience in state-of-the-art computational science. The research will be performed at the University of New Mexico, a Hispanic serving institution that also serves a large body of native Americans, allowing active recruitment and education of students from underrepresented groups.

首席研究员建议开展一项跨学科综合研究计划，结合一类新型数值方法的开发、分析和优化，并将其应用于地震学和电磁学问题。该新颖方法将任意阶 Hermite 近似与任意阶不连续 Galerkin 方法混合在一起。这两种方法的结合将产生一类新型混合方法，能够处理复杂的几何形状，并通过大时间步长和高分辨率实现前所未有的计算效率。这些方法具有非常大的计算通信比，非常适合在当前和新兴的超级计算机系统上实现，从而能够解决复杂的多尺度进化系统。所提出的对不连续伽辽金方法和埃尔米特方法的统一分析将需要开发新的工具和理论，并将为混合方法的分析带来新的理论框架。该提案将考虑弹性和电磁学控制方程的一阶和二阶公式的方法。该研究将对技术和科学以及下一代计算科学家的培训产生更广泛的影响。日本最近发生的事件表明，地震是全世界的一个社会问题。为了更好地减轻地震灾害，需要有效的预防和预测。通过准确的计算预测仔细评估地震危害可以制定适当的建筑规范。如果在大洛杉矶或旧金山湾等人口稠密地区发生大型地震，这可能会对人类生活和社会福利产生巨大影响。拟议活动的更广泛影响还包括教育。该项目将涉及研究生，他们将获得最先进的计算科学的经验。这项研究将在新墨西哥大学进行，这是一所拉美裔服务机构，也为大量美国原住民提供服务，允许积极招募和教育来自代表性不足群体的学生。