High Order and Efficient Numerical Methods for Simulating Electromagnetic Phenomena

模拟电磁现象的高阶高效数值方法

• 批准号: 1619713
• 负责人: Wei Cai
• 金额: $ 17万
• 依托单位: University of North Carolina at Charlotte
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2018-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1619713&HistoricalAwards=false
• 关键词: Order; Efficient; Numerical; Methods; Simulating

New materials with special properties are necessary in the search for new clean energy sources and advanced medical devices. Electromagnetic phenomena play a key role in the design of new materials such as meta-materials and conducting materials. Meta-materials, assembled with blocks of meta-atoms of naturally available components, have provided a wide range of new possibilities to design man-made materials with special properties. Novel devices using meta-materials have been proposed including perfect lens and sub-diffraction-limited imaging for medical applications, light harvest in clear energy solar cells. In addition, understanding the conducting flow of a charged system is essential for studying confined nuclear thermal reactions for the exploration of new clean energy sources.The computational simulation of electromagnetic phenomena is challenging, owing to the demand of highly accurate and efficient numerical methods that not only represent the correct physics in the magnetic induction equation but also resolve the multiple scattering and local field enhancements from random objects in meta-materials. To meet these requirements, the PIs will accomplish the following two tasks in this project: (1) to develop a highly efficient volume integral equation method for Maxwell equations for very accurate computation of multiple scatterings of large number of regular or random objects employed in the construction of meta-materials; (2) to devise a high order constrained transport finite element method for the magnetic induction equations in the magneto-hydrodynamics problem so the global divergence free condition on the magnetic field is preserved. The research findings will be disseminated through journal publications and software tool development.

寻找新的清洁能源和先进的医疗设备需要具有特殊性能的新材料。电磁现象在超材料和导电材料等新材料的设计中发挥着关键作用。超材料由天然成分的超原子块组装而成，为设计具有特殊性能的人造材料提供了广泛的新可能性。已经提出了使用超材料的新型设备，包括用于医疗应用的完美透镜和亚衍射限制成像、透明能源太阳能电池中的光收集。此外，了解带电系统的传导流动对于研究约束核热反应以探索新的清洁能源至关重要。电磁现象的计算模拟具有挑战性，因为需要高精度和高效的数值方法不仅代表了磁感应方程中的正确物理场，而且还解决了超材料中随机物体的多重散射和局部场增强问题。为了满足这些要求，PI将在该项目中完成以下两项任务：（1）开发一种高效的麦克斯韦方程体积积分方程方法，用于非常精确地计算在物理场中使用的大量规则或随机物体的多次散射。超材料的构造； (2) 为磁流体动力学问题中的磁感应方程设计一种高阶约束输运有限元方法，从而保持磁场的全局无散度条件。研究结果将通过期刊出版物和软件工具开发来传播。