.png){kind=icon}
.png){kind=icon}
Return
The ultraspherical spectral element method
.png){kind=icon}
OA
AI
DOI：10.1016/j.jcp.2020.110087.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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.
Keywords:
Spectral element method
Ultraspherical spectral method
Hierarchical Poincare-Steklov method
hp-adaptivity
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
3.8
Papers:
1.5W
Citations:
7.4W
View more organizations