论文标题
具有傅立叶延伸的不规则域中椭圆形PDE的光谱搭配方法
A spectral collocation method for elliptic PDEs in irregular domains with Fourier extension
论文作者
论文摘要
基于傅立叶扩展，我们提出了一种超采样搭配方法，用于求解与任意不规则域上具有可变系数的椭圆形偏微分方程。该方法仅在均值节点上使用函数值，该函数值的计算成本和多功能性较低。虽然提出了多种数值实验以证明该方法的有效性，但它表明近似误差迅速到达平稳，由于框架固有的不良条件，自由度的增加。
Based on the Fourier extension, we propose an oversampling collocation method for solving the elliptic partial differential equations with variable coefficients over arbitrary irregular domains. This method only uses the function values on the equispaced nodes, which has low computational cost and versatility. While a variety of numerical experiments are presented to demonstrate the effectiveness of this method, it shows that the approximation error fast reaches a plateau with increasing the degrees of freedom, due to the inherent ill-conditioned of frames.
