# Algorithms for Parallel Generic hp-adaptive Finite Element Software

@article{Fehling2022AlgorithmsFP, title={Algorithms for Parallel Generic hp-adaptive Finite Element Software}, author={Marc Fehling and Wolfgang Bangerth}, journal={ArXiv}, year={2022}, volume={abs/2206.06512} }

The hp -adaptive finite element method (FEM) – where one independently chooses the mesh size ( h ) and polynomial degree ( p ) to be used on each cell – has long been known to have better theoretical convergence properties than either h - or p -adaptive methods alone. However, it is not widely used, owing at least in parts to the difficulty of the underlying algorithms and the lack of widely usable implementations. This is particularly true when used with continuous finite elements. Herein, we…

## Figures from this paper

## One Citation

### The deal.II library, Version 9.4

- Computer Science, LinguisticsJournal of Numerical Mathematics
- 2022

An overview of the new features of the finite element library deal, version 9.4.II is provided.

## References

SHOWING 1-10 OF 59 REFERENCES

### Algorithms for massively parallel generic hp-adaptive finite element methods

- Computer Science
- 2020

Algorithms and data structures required for generic hp-adaptive finite element software applicable for both continuous and discontinuous Galerkin methods on distributed memory systems and strategies to determine the type of adaptation based on error estimation and prediction as well as smoothness estimation via the decay rate of coefficients of Fourier and Legendre series expansions are presented.

### PARALLEL SELF-ADAPTIVE hp FINITE ELEMENT METHOD WITH SHARED DATA STRUCTURE

- Computer Science
- 2011

A new parallel algorithm of the self-adaptive hp Finite Element Method (hp-FEM) with shared data structures that generates in a fully automatic mode a sequence of meshes delivering exponential convergence of the prescribed quantity of interest with respect to the mesh size.

### A Comparison of hp-Adaptive Strategies for Elliptic Partial Differential Equations

- Computer ScienceACM Trans. Math. Softw.
- 2014

The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving PDEs because it can achieve an exponential convergence rate…

### Data structures and requirements for hp finite element software

- Computer ScienceTOMS
- 2009

This article discusses generic data structures and algorithms used in the implementation of hp methods for arbitrary elements, and lists the information a description of a finite element has to provide to the generic algorithms for it to be used in an hp context.

### A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version)

- Computer Science
- 2011

This paper presents the results of a numerical experiment to study the convergence properties of the hp-FEM combined with adaptive mesh refinement strategies and summarizes these strategies.

### Parallelization of the multi-level hp-adaptive finite cell method

- Computer ScienceComput. Math. Appl.
- 2017

### Parallel, fully automatic hp-adaptive 3D finite element package

- Computer ScienceEngineering with Computers
- 2007

The paper presents a description of par3Dhp a 3D, parallel, fully automatic hp-adaptive finite element code for elliptic and Maxwell problems. The parallel implementation is an extension of the…

### Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations

- Computer ScienceArXiv
- 2022

This work studies three multigrid variants for matrix-free ﬁnite-element computations on locally reﬁned meshes: geometric local smoothing, geometric global coarsening, and polynomial global…

### The hp‐multigrid method applied to hp‐adaptive refinement of triangular grids

- Computer ScienceNumer. Linear Algebra Appl.
- 2010

A survey of the development of p‐ multigrid and hp‐multigrid, an hp‐ Multigrid algorithm based on the p‐hierarchical basis for the p levels and h‐Hierarchy basis for an h‐Multigrid solution of the p=1 ‘coarse grid’ equations, and numerical convergence results using hp‐adaptive grids are presented.

### Algorithms and data structures for massively parallel generic adaptive finite element codes

- Computer ScienceACM Trans. Math. Softw.
- 2011

This work develops scalable algorithms and data structures for generic finite element methods that consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing, and removes the bottlenecks that typically limit large-scale adaptive finite element analyses.