The ultraspherical spectral element method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:436

Article

Fortunato, Daniel¹  Hale, Nicholas²  Townsend, Alex³ 

[1] Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA

[2] Stellenbosch Univ, Dept Math Sci, ZA-7602 Stellenbosch, South Africa

[3] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

关键词: Spectral element method;    Ultraspherical spectral method;    Hierarchical Poincare-Steklov method;    hp-adaptivity;   

DOI  :  10.1016/j.jcp.2020.110087

来源: Elsevier

【 摘 要 】

We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincare-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured quadrilateral or triangular meshes. Properties of the ultraspherical spectral method lead to almost banded linear systems, allowing the element method to be competitive in the high-polynomial regime (p > 5). The hierarchical Poincare-Steklov scheme enables precomputed solution operators to be reused, allowing for fast elliptic solves in implicit and semi-implicit time-steppers. The resulting spectral element method achieves an overall computational complexity of O(p(4)/h(3)) for mesh size hand polynomial order p, enabling hp-adaptivity to be efficiently performed. We develop an open-source software system, ultraSEM, for flexible, user-friendly spectral element computations in MATLAB. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free