论文标题
与随机输入数据的麦克斯韦源问题的共形映射的多项式混乱扩展
Conformally Mapped Polynomial Chaos Expansions for Maxwell's Source Problem with Random Input Data
论文作者
论文摘要
广义多项式混乱（GPC）的扩展已很好地确定了许多应用领域的不确定性传播。尽管与蒙特卡洛技术相比，相关的计算工作可能会减少，但是，进一步的收敛加速对于解决高参数敏感性的问题可能很重要。在这项工作中，我们建议使用保形图来构建转换的GPC基础，以增强收敛顺序。所提出的基础仍然具有正交性属性，因此有助于计算许多统计特性，例如敏感性和力矩。相应的替代模型是通过使用映射的正交规则来计算的，可以通过伪谱投影计算，从而提高了成本精度比率。我们使用随机输入数据将方法应用于麦克斯韦的源问题。特别是，给出了光光栅耦合器的参数有限元模型的数值结果。
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for instance, further convergence acceleration may be important to tackle problems with high parametric sensitivities. In this work, we propose the use of conformal maps to construct a transformed gPC basis, in order to enhance the convergence order. The proposed basis still features orthogonality properties and hence, facilitates the computation of many statistical properties such as sensitivities and moments. The corresponding surrogate models are computed by pseudo-spectral projection using mapped quadrature rules, which leads to an improved cost accuracy ratio. We apply the methodology to Maxwell's source problem with random input data. In particular, numerical results for a parametric finite element model of an optical grating coupler are given.
