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

高效、准确且快速收敛的算法，用于解决复杂材料和几何特征结构中的波传播问题

• 批准号: 1251859
• 负责人: Catalin Turc
• 金额: $ 4.35万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-30 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1251859&HistoricalAwards=false
• 关键词: Efficient; accurate; rapidly; convergent; algorithms

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.

TurcDMS-1008076 研究人员开发了高效，准确和快速收敛的算法，用于评估电磁场和复杂结构之间的相互作用。 具体来说，研究者和他的合作者开发了一系列算法，主要集中在（1）快速，高阶数值解的波传播问题的域，包含几何奇点，（2）散射问题从可穿透的电磁周期性结构，特别强调共振问题相关的光子晶体和负折射率材料（NIM）的设计。 该软件集中于开发和实现一个基于积分方程公式的并行计算框架，能够产生现实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析：（B）基于伪微分的良好条件积分方程公式的设计和分析，导致大量电磁传输问题的少量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最新可用的图形处理单元（GPU）计算平台的实现，以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根本意义，例如电磁干扰和兼容性（电子电路），介电/磁性涂层导体和复合超材料（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产生了一系列重大的计算挑战，这些挑战来自于非强制性公式、振荡解、几何奇点、共振、高频区的条件反射。 最近的研究人员和他的合作者导致了一个高效的计算方法的发展，解决了这些困难中的几个，其扩展使一个雄心勃勃的计划得以实现：以高保真逼真的散射环境模拟高动态范围。