复杂大腔体电磁散射问题的高效数值方法

项目名称： 复杂大腔体电磁散射问题的高效数值方法

项目编号： No.11201392

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 杜魁

作者单位： 厦门大学

项目金额： 22万元

中文摘要： 随着军事科技中隐身技术的发展需要，如何降低目标物体的雷达散射截面以及精确预测复杂目标已成为当今重要的研究课题。本项目要给出以飞行器进气道为代表的复杂大腔体电磁散射问题的高效数值方法。由于解具有高振荡特性，该类问题的数值计算极具挑战性，现有的数值方法不能很好的处理它们，新的数值方法有待我们去研究。本项目中我们将给出腔体电磁散射问题的基于波数的稳定性分析，高阶数值离散方法及相应的误差分析，并针对数值离散所得大型不定线性方程组设计波数无关高效预条件子及求解器。预期通过本项目的研究，给出复杂大腔体电磁散射问题的高精度数值模拟软件，为设计满足工业和军事领域需要的复杂腔体数值模拟方面做好准备。

中文关键词： 腔体问题；稳定性；张量有限元；快速算法；

英文摘要： As the development of the stealth technology in military, how to reduce the radar cross section of an object and accurate prediction of complex targets such as aircrafts with cavities have become important research topics. In this project we will give effcient numerical methods for electromagnetic scattering from large complex cavities. As well known, the computation is especially challenging when the cavities are large compared to the wavelength because of the highly oscillatory nature of the solutions. Existing numerical methods can not handle such problems well. Some new methods are needed. For cavity problems，we will study the wave number based stability analysis. Some high-order numerical methods and the corresponding error analysis will be given. For the resulting large-scale indefinite linear equations, we will design efficient preconditioners and solvers which are independent of the wave number. By this project, we expect to provide high-precision numerical simulation of electromagnetic scattering from large complex cavities, which will meet the needs of industrial and military applications.

英文关键词： cavity problems；stability；tensor-product finite element；fast algorithms；