Collaborative Research: Adaptive Hybridized DG Methods for Acoustic and Electromagnetic Scattering

合作研究：声学和电磁散射的自适应混合 DG 方法

• 批准号: 1216857
• 负责人: Ronald Hoppe
• 金额: $ 14.88万
• 依托单位: University of Houston
• 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: 2012-08-01 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1216857&HistoricalAwards=false
• 关键词: Collaborative; Research; Adaptive; Hybridized; DG

In this project, the investigator and his colleagues will develop, analyze, and implement quasi-optimal adaptive hybridized Discontinuous Galerkin methods for acoustic and electromagnetic scattering problems as described by the Helmholtz equation and the time-harmonic Maxwell equation on bounded domains in two and three dimensional domains using general local bases. These methods feature traditional piecewise polynomial bases as well as special purpose wave elements, and multilevel preconditioned iterative solvers on adaptively refined simplicial, quadrilateral, and hexahedral meshes. The adaptive mesh refinement is driven by residual-type a posteriori error estimators. In particular, the team will prove convergence of the adaptive solution process as well as its quasi-optimality in terms of the computational complexity with respect to a properly specified approximation class. High quality software implementations will be used to test the algorithms and inform the analysis.Advances in the state of the art in numerical methods for performing acoustic and electromagnetic simulations have potentially high impact in several applications. As an example more accurate simulation of acoustic wave propagation can be used to considerably enhance resolution of medical ultra sound scans, and thus expand the reach of non-invasive diagnostics. The emphasis of this project is the development of novel numerical methods that compute provably accurate approximations of physical acoustics and electromagnetics phenomena.

在这个项目中，研究人员和他的同事将开发、分析和实现准最优自适应混合不连续伽辽金方法，用于解决声学和电磁散射问题，如使用通用局部基在二维和三维域中有界域上的亥姆霍兹方程和时谐麦克斯韦方程所描述的。这些方法具有传统的分段多项式基以及专用波单元，以及自适应细化单纯形、四边形和六面体网格上的多级预处理迭代求解器。自适应网格细化由残差型后验误差估计器驱动。特别是，该团队将证明自适应求解过程的收敛性及其在计算复杂性方面相对于正确指定的近似类的准最优性。高质量的软件实现将用于测试算法并为分析提供信息。用于执行声学和电磁仿真的数值方法的最新进展在多种应用中具有潜在的巨大影响。例如，可以使用更准确的声波传播模拟来显着提高医疗超声扫描的分辨率，从而扩大非侵入性诊断的范围。该项目的重点是开发新颖的数值方法，计算物理声学和电磁学现象的可证明准确的近似值。