Efficient multi-level hp-finite elements in arbitrary dimensions

TL;DR

This paper introduces an efficient, scalable framework for multi-level hp-finite element bases applicable in any dimension, demonstrating improved performance and convergence in complex simulations.

Contribution

The authors develop a data-oriented, multi-level hp-basis construction method that extends to arbitrary dimensions and optimizes performance without increasing computational costs.

Findings

No increase in runtime or memory compared to classical p-version FEM.

Achieved expected convergence rates in dynamic refinement and derefinement.

Demonstrated efficiency with a new open-source library.

Abstract

We present an efficient algorithmic framework for constructing multi-level hp-bases that uses a data-oriented approach that easily extends to any number of dimensions and provides a natural framework for performance-optimized implementations. We only operate on the bounding faces of finite elements without considering their lower-dimensional topological features and demonstrate the potential of the presented methods using a newly written open-source library. First, we analyze a Fichera corner and show that the framework does not increase runtime and memory consumption when compared against the classical p-version of the finite element method. Then, we compute a transient example with dynamic refinement and derefinement, where we also obtain the expected convergence rates and excellent performance in computing time and memory usage.