High Order and Efficient Numerical Methods for Simulating Electromagnetic Phenomena

在寻找新的清洁能源和先进的医疗设备中，具有特殊性能的新材料是必不可少的。电磁现象在超材料和导电材料等新材料的设计中起着关键作用。由天然成分的元原子块组装而成的超材料，为设计具有特殊性能的人造材料提供了广泛的新可能性。使用超材料的新设备已被提出，包括用于医疗应用的完美透镜和亚衍射限制成像，在清洁能源太阳能电池中收获光。此外，了解带电体系的传导流对于研究限制核热反应以探索新的清洁能源是必不可少的。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，不仅要能正确地表示磁感应方程中的物理性质，而且要能解决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将在本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用于构建超材料的大量规则或随机物体的多次散射；(2)为磁流体动力学问题中磁感应方程设计了一种高阶约束输运有限元法，使磁场的全局散度自由条件保持不变。研究结果将通过期刊出版物和软件工具开发进行传播。

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.