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器械时，需要具有特殊性能的新材料。电磁现象在超材料、导电材料等新材料的设计中起着至关重要的作用。超材料由天然成分的元原子块组装而成，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器件，包括用于医疗应用的完美透镜和亚衍射限制成像，以及在清洁能源太阳能电池中的光收集。此外，了解带电系统的导电流动对于研究受限核热反应以探索新的清洁能源是至关重要的。电磁现象的计算模拟是具有挑战性的，因为需要高精度和高效率的数值方法，不仅要代表磁感应方程中的正确物理，而且要解决超材料中随机目标的多次散射和局部场增强。为了满足这些要求，PIS将在本项目中完成以下两项任务：(1)开发一种高效的Maxwell方程的体积积分方程组方法，以非常精确地计算在超材料结构中使用的大量规则或随机物体的多次散射；(2)设计一种高阶约束输运有限元方法来求解磁流体力学问题中的磁感应方程，从而保持磁场的整体无散度条件。研究成果将通过期刊出版物和软件工具开发来传播。

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.