论文标题
快速盖尔金方法用于求解屏幕上的Helmholtz边界积分方程
Fast Galerkin Method for Solving Helmholtz Boundary Integral Equations on Screens
论文作者
论文摘要
我们解决了由Helmholtz和Laplace问题引起的第一类弗雷德·弗雷姆（Fredholm）边界积分方程，该方程在具有差点或诺伊曼条件的三维中有界光滑的屏幕上。提出的Galerkin-Bubnov方法将标准球形谐波的加权方位角投影推向规范磁盘上。我们表明，这些基础允许光谱收敛并提供完全离散的误差分析。数值实验支持我们的主张，结果可与Nyström-type和$ hp $ -Methods相当。
We solve first-kind Fredholm boundary integral equations arising from Helmholtz and Laplace problems on bounded, smooth screens in three-dimensions with either Dirichlet or Neumann conditions. The proposed Galerkin-Bubnov method takes as discretization elements pushed-forward weighted azimuthal projections of standard spherical harmonics onto the canonical disk. We show that these bases allow for spectral convergence and provide fully discrete error analysis. Numerical experiments support our claims, with results comparable to Nyström-type and $hp$-methods.
