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.

研究者建议开发高度并行，高效，准确和快速收敛的算法，用于评估波和几何复杂结构之间的相互作用。由研究者开发的算法系列将主要集中在（1）基于Dirichlet到Neumann算子近似的一般方法的设计，该近似能够为具有所有类型边界条件的广泛散射问题产生内在良好条件的边界积分方程公式，（2）在计算工具箱中实现这些公式，散射问题的高阶求解器，它也可以处理所有主要CAD引擎产生的CAD模型所描述的几何形状，以及（3）基于准最佳传输条件求解麦克斯韦方程的非重叠区域分解方法（DDM）的设计和有限元与边界元实现。（a）高阶积分方程求解器，其依赖于接受商业CAD格式以及三角剖分甚至点云作为输入的高阶表面表示;（B）狄利克雷-诺依曼算子的强制近似的基于伪微分计算的设计，其一方面导致需要少量Krylov-子空间迭代的电磁问题的范围很广，另一方面导致传输条件，优化规范的迭代算子，在非重叠区域分解方法的核心解决方案的麦克斯韦方程;和（c）使用等效源，FFT-的加速算法，以实现快速积分求解器。作为拟议工作的一部分，将开发的算法是具有根本意义的不同例如雷达、电子电路、天线、通信设备、光子学的应用。电磁波在复杂结构中传播的模拟产生了大量的计算挑战，这些挑战来自振荡解、复杂几何形状的低保真度表示以及低频和高频区域的病态。最近的努力的调查员和他的合作者导致了一个高效的计算方法，解决了这些困难和其扩展，在此提出，将使调查员实现一个雄心勃勃的计划的发展和分析：模拟高保真逼真的散射环境。