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Robust and Efficient Numerical Methods for Electromagnetic Wave Propagation in Complex Media

复杂介质中电磁波传播的鲁棒高效数值方法

基本信息

批准号：
2011943
负责人：
Jichun Li
金额：
$ 25.22万
依托单位：
University of Nevada Las Vegas
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-08-01 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2011943&HistoricalAwards=false
关键词：
Robust Efficient Numerical Methods Electromagnetic

项目摘要

This project will develop novel mathematical modeling and robust computational methods for simulating wave propagation in complex media such as metamaterials and graphene. This interdisciplinary research has direct applications in nanotechnology and materials through the advancement of discovery and understanding of new phenomena in nanooptics and stealth technology brought by metamaterials and graphene. Graphene can be used to generate picosecond laser pulses because of its wide absorption range, fast decay, and high stability properties. Graphene can be used in sensors to concurrently sense mass, gas, tension, diseases, and explosives; graphene can be used in low-cost display screens of mobile devices, lithium-ion batteries with fast recharge capacity, hydrogen storage for fuel cell-powered cars, and low-cost fuel cells and water desalination, etc. All of these applications benefit from accurate and efficient numerical algorithms for solving the associated mathematical models by reducing the cost of physical experiments. This project will provide support for one PhD student per year. The focus of this project is to develop and analyze robust and efficient finite element methods for solving electromagnetic wave propagation problems in complex media. Theoretical analysis and practical algorithms will be developed with the following objectives: (1) Further explore some perfectly matched layer (PML) models recently developed for metamaterials, develop and analyze time-domain finite element methods using both edge elements and discontinuous Galerkin methods for solving them; (2) Explore graphene models and efficient FEM algorithms to simulate wave propagation in graphene; (3) Develop robust and efficient a posteriori error estimators for time-dependent Maxwell’s equations in metamaterial and graphene, explore possible superconvergence points for high-order triangular and tetrahedral edge elements; (4) Develop, and analyze efficient numerical methods for Maxwell's equations with random inputs with applications for random metamaterials. The developed algorithms and codes in the project will lead to a better understanding of metamaterials and graphene, and their physical effects, so that researchers can design and use them in applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目将开发新的数学建模和强大的计算方法，用于模拟波在超材料和石墨烯等复杂介质中的传播。这种跨学科的研究通过发现和理解超材料和石墨烯带来的纳米光学和隐形技术中的新现象的进步，在纳米技术和材料中有直接的应用。石墨烯可以用来产生皮秒激光脉冲，因为它的吸收范围宽，衰减快，稳定性高。石墨烯可用于传感器，同时感测质量、气体、张力、疾病和爆炸物;石墨烯可用于移动的设备的低成本显示屏、具有快速再充电能力的锂离子电池、用于燃料电池驱动的汽车的氢存储，以及低成本燃料电池和水脱盐，所有这些应用都受益于用于通过减少物理计算的成本来求解相关联的数学模型的精确且有效的数值算法。实验该项目每年将为一名博士生提供支持。该项目的重点是开发和分析用于解决复杂介质中电磁波传播问题的强大而有效的有限元方法。本研究的主要目标是：（1）深入研究目前发展起来的超材料完全匹配层（PML）模型，发展和分析边缘元和间断Galerkin方法求解PML模型的时域有限元方法;（2）探索石墨烯模型和有效的有限元算法，模拟波在石墨烯中的传播;（3）为超材料和石墨烯中的时间相关麦克斯韦方程组开发鲁棒和有效的后验误差估计器，探索高阶三角形和四面体边缘单元的可能超收敛点;（4）开发和分析具有随机输入的麦克斯韦方程组的有效数值方法，并应用于随机超材料。该项目中开发的算法和代码将使人们更好地理解超材料和石墨烯及其物理效应，以便研究人员能够设计并在应用中使用它们。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。