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.

首席研究者建议执行一项跨学科的综合研究计划，该计划结合了一类新的数值方法的开发，分析和优化，并将其应用于地震学和电磁学中的问题。这种新方法将任意阶的Hermite近似值与任意阶不连续的Galerkin方法杂交。这两种方法的组合将导致一类新的混合方法能够通过大的时间步骤和高分辨率来处理复杂的几何形状以及前所未有的计算效率。这些方法具有非常大的计算与通信比率，并且非常适合在当前和新兴的超级计算机系统上实现，从而实现了复杂的多尺度进化系统的解决方案。提出的对不连续的Galerkin方法和Hermite方法的统一分析将需要开发新的工具和理论，并将为分析混合方法分析带来新的理论框架。该提案将考虑弹性和电磁学方程的一阶和二阶公式的方法。这项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大的影响。正如日本最近发生的事件所表明的那样，地震是世界各地的一个社会问题。为了更好地减轻地震危害，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导致适当的建筑法规。如果在人口稠密的地区，作为大洛杉矶或旧金山湾，这可能会对人类生活和社会福利产生巨大影响。拟议活动的更广泛的影响还包括教育。该项目将涉及将获得最先进计算科学经验的研究生。这项研究将在新墨西哥大学进行，这是一家西班牙裔服务机构，还为大量美洲原住民提供服务，允许积极招募和教育代表人数不足的群体。