Mathematical Sciences: Spectral Methods and Corner Singularities

本文研究的是一种数值解法， 多维问题的谱方法。 目的是 保持这些方法的快速收敛， 否则由于底层中的角奇异性而丢失 溶液 本研究所采用的方法， 奇异基函数，将附加快速收敛 解的平滑部分的切比雪夫展开。 角点奇点出现在各种各样的问题中， 重要的工程应用。 这项工作应导致 提高应用领域的计算能力，例如 驱动空腔流、扭转裂纹梁和对流 在核反应堆中。

This research deals with the numerical solution of multidimensional problems by spectral methods. The aim is to retain the rapid convergence of these methods that might otherwise be lost due to corner singularities in the underlying solution. The approach adopted in this research uses appropriate singular basis functions which will append the rapidly converging Chebyshev expansion for the smoother part of the solution. Corner singularities occur in a variety of problems with important engineering applications. This work should lead to increased computational ability in application areas such as driven cavity flows, cracked beams with torsion, and convection in nuclear reactors.