Efficient integral equation solvers for large-scale frequency domain electromagnetic scattering problems

用于大规模频域电磁散射问题的高效积分方程求解器

• 批准号: 1312169
• 负责人: Catalin Turc
• 金额: $ 14.43万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1312169&HistoricalAwards=false
• 关键词: Efficient; integral; equation; solvers; large

The investigator proposes to develop highly-parallel, efficient, accurate and rapidly-convergent algorithms for evaluation of the interaction between waves and geometrically complex structures. The family of algorithms to be developed by the investigator will focus mainly on (1) The design of a general methodology based on approximations of Dirichlet-to-Neumann operators capable of producing intrinsically well-conditioned boundary integral equation formulations for a wide suite of scattering problems with all types of boundary conditions, (2) The implementation of these formulations within a computational toolbox that delivers fast, high-order solvers for scattering problems which can also handle geometries described by CAD models produced by all of the major CAD engines, and (3) The design and Finite Element and Boundary Element implementation of non-overlapping Domain Decomposition Methods (DDM) for the solution of Maxwell's equations based on quasi-optimal transmission conditions. The proposed approach consists of the following main elements: (a) High-order integral equation solvers that rely on high-order surface representations that accept as input commercial CAD formats as well as triangulations and even point clouds; (b) Pseudodifferential calculus-based design of coercive approximations of Dirichlet-to-Neumann operators that on one hand leads to well-conditioned integral equation formulations that require small numbers of Krylov-subspace iterations for a wide range of electromagnetic problems and on the other hand leads to transmission conditions that optimize the norm of the iteration operators that lie at the heart of non-overlapping Domain Decomposition Methods for the solution of Maxwell's equations; and (c) Use of equivalent sources, FFT-based acceleration algorithms to achieve fast integral solvers. The algorithms that are to be developed as part of the proposed work are of fundamental significance to diverse applications such as radar, electronic circuits, antennas, communication devices, photonics. The simulation of electromagnetic wave propagation in complex structures gives rise to a host of significant computational challenges that result from oscillatory solutions, low-fidelity representations of complex geometries, and ill-conditioning in the low and high-frequency regimes. The recent efforts of the investigator and his collaborators resulted in the development and analysis of a highly efficient computational methodology which resolved several of these difficulties and whose extension, proposed hereby, will enable the investigator to fulfill an ambitious plan: to simulate with high fidelity realistic scattering environments.

研究者提出的提案要开发高度平行，有效，准确和快速构造的算法，以评估波和几何复杂结构之间的相互作用。研究人员将要开发的算法家族将主要集中在（1）基于一般方法的设计基于Dirichlet到Neumann操作员的近似值，能够生成本质上良好条件良好的边界积分公式，以在所有类型的边界条件中散布的散布问题，这些散布的范围在所有类型的边界条件下都可以在这些散布的问题上进行，该工具的实现，（2）（2）（2）可在（2）实现的范围，（2）（2）可在（2）由所有主要CAD发动机生成的CAD模型所描述的几何形状，以及（3）基于准最佳透射条件的Maxwell方程解决方案的非重叠域分解方法（DDM）的设计和有限元和边界元素实现。所提出的方法由以下主要要素组成：（a）依赖于接受为输入商业CAD格式的高阶表面表示的高阶积分方程求解器，甚至是三角形，甚至点云； （b）基于假数分化的计算，一方面是基于Dirichlet到Neumann操作员的强制性近似的设计，这些操作员一方面会导致良好条件的积分方程公式，需要少量的Krylov-Spasspace迭代率，以使多种电磁问题的范围范围范围内导致型号的型号，以使其在不良型号的情况下进行隔离型号的序列，以使其在不良的域中，并在不及时的情况下进行了效果。麦克斯韦方程的解决方案； （c）使用等效源，基于FFT的加速算法来实现快速积分求解器。作为拟议工作的一部分开发的算法对于雷达，电子电路，天线，通信设备，摄影等潜水员应用具有至关重要的意义。复杂结构中电子波传播的模拟导致了许多重大的计算挑战，这些挑战是由振荡溶液，复杂几何形状的低效率表示以及在低频和高频方案中造成的不良条件。研究人员及其合作者的最新努力导致对高效的计算方法的开发和分析，该方法解决了这些困难中的几个，其扩展（特此）将使研究人员能够实现雄心勃勃的计划：以高忠诚度现实的散射环境模拟。