Efficient, accurate and rapidly convergent algorithms for solutions of wave propagation problems in configurations complex material and geometrical features

TurcDMS-1008076研究人员开发了高效、准确和快速收敛的算法，用于评估电磁场与复杂结构之间的相互作用。具体地说，研究人员和他的合作者开发了一系列算法，主要集中在(1)包含几何奇异性的区域中波传播问题的快速、高阶数值解，以及(2)可穿透电磁周期结构的散射问题，特别强调与光子晶体和负折射率材料(NIM)设计相关的共振问题。研究人员致力于开发和实现一个基于积分方程组的大规模并行计算框架，该框架能够产生具有实际复杂性的波散射问题的快速和高阶解。该方法包括以下主要内容：(A)非光滑区域中边界积分方程解的奇异性的高阶解分解；(B)基于伪微积分的良好积分方程组的设计和分析，从而针对广泛的电磁传输问题产生少量的Krylov子空间迭代；以及(C)使用等效源、基于FFT的加速算法以及利用新可用的图形处理单元(GPU)计算平台来显著提高计算时间和能力。作为该项目的一部分开发的算法对各种应用具有基本意义，如电磁干扰和兼容性(电子电路)、介质/磁性涂层导体和复合材料(光子晶体和负折射率材料)。电磁波在复杂结构中传播的模拟带来了一系列重大的计算挑战，这些问题是由非强制公式、振荡解、几何奇异性、共振和高频病态引起的。研究人员和他的合作者最近的努力导致了一种高效的计算方法的开发，该方法解决了其中的几个困难，其扩展使一个雄心勃勃的计划得以实现：模拟具有高动态范围的高保真真实散射环境。

TurcDMS-1008076 The investigator develops efficient, accurate and rapidlyconvergent algorithms for evaluation of the interaction betweenelectromagnetic fields and complex structures. Specifically, theinvestigator and his collaborators develop a family of algorithmsthat focus mainly on (1) Fast, high-order numerical solutions forwave-propagation problems in domains that contain geometricsingularities, and (2) Scattering problems from penetrableelectromagnetic periodic structures, with a particular emphasison resonant problems relevant to the design of photonic crystalsand Negative Index Materials (NIM). The investigatorconcentrates on development and implementation of a massivelyparallel computational framework based on integral equationformulations capable of producing fast and high-order solutionsof wave scattering problems of realistic complexity. Theapproach consists of the following main elements: (a) High-orderresolution of the singularities of the solutions of the boundaryintegral equations in non-smooth domains; (b)Pseudodifferential-calculus-based design and analysis ofwell-conditioned integral equation formulations leading to smallnumbers of Krylov-subspace iterations for a wide range ofelectromagnetic transmission problems; and (c) Use of equivalentsources, FFT-based acceleration algorithms, and implementationsthat take advantage of the newly available Graphic ProcessingUnits (GPUs) computational platforms to dramatically enhancecomputational times and capabilities. The algorithms that are developed as part of this projectare of fundamental significance to diverse applications such aselectromagnetic interference and compatibility (electroniccircuits), dielectric/magnetic coated conductors, and compositemeta-materials (photonic crystals and Negative Index Materials). The simulation of electromagnetic wave propagation in complexstructures gives rise to a host of significant computationalchallenges that result from non-coercive formulations,oscillatory solutions, geometric singularities, resonances, andill-conditioning in the high-frequency regime. The recentefforts of the investigator and his collaborators resulted in thedevelopment of a highly efficient computational methodology thatresolved several of these difficulties and whose extensionenables the fulfillment of an ambitious plan: to simulate withhigh fidelity realistic scattering environments with a highdynamic range.