Efficient Spectral-Element Methods in Polar Coordinates for Complex Geometries with Piecewise-Smooth Boundaries
Sheng Chen, Weiwei Sun, Shuai Wu · SIAM Journal on Scientific Computing · 2025
Abstract. An efficient spectral-element method is proposed for handling complex geometries. By utilizing this approach significant advancements are made in approximating domains with piecewise-smooth boundary curves, enabling the effective solution of partial differential equations (PDEs) in both interior and exterior complex geometries. Rigorous convergence analyses are provided, along with the integration of log orthogonal functions (LOFs) to enhance computational accuracy and stability, particularly in addressing corner singularities. This study establishes a robust framework for the application of spectral methods in complex geometries, offering valuable tools for practical PDE computations.