Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes

02/23/2021
by   Matthew W. Scroggs, et al.
0

We develop an approach to generating degree-of-freedom maps for arbitrary order finite element spaces for any cell shape. The approach is based on the composition of permutations and transformations by cell sub-entity. Current approaches to generating degree-of-freedom maps for arbitrary order problems typically rely on a consistent orientation of cell entities that permits the definition of a common local coordinate system on shared edges and faces. However, while orientation of a mesh is straightforward for simplex cells and is a local operation, it is not a strictly local operation for quadrilateral cells and in the case of hexahedral cells not all meshes are orientable. The permutation and transformation approach is developed for a range of element types, including Lagrange, and divergence- and curl-conforming elements, and for a range of cell shapes. The approach is local and can be applied to cells of any shape, including general polytopes and meshes with mixed cell types. A number of examples are presented and the developed approach has been implemented in an open-source finite element library.

READ FULL TEXT

page 13

page 20

research
12/31/2022

Dimensions of exactly divergence-free finite element spaces in 3D

We examine the dimensions of various inf-sup stable mixed finite element...
research
03/27/2021

A Construction of C^r Conforming Finite Element Spaces in Any Dimension

This paper proposes a construction of local C^r interpolation spaces and...
research
10/01/2021

Virtual elements on agglomerated finite elements to increase the critical time step in elastodynamic simulations

In this paper, we use the first-order virtual element method (VEM) to in...
research
07/03/2020

Training of Deep Learning Neuro-Skin Neural Network

In this brief paper, a learning algorithm is developed for Deep Learning...
research
10/29/2019

High order approximation of Hodge Laplace problems with local coderivatives on cubical meshes

In mixed finite element approximations of Hodge Laplace problems associa...
research
02/03/2023

A Hybrid Training Algorithm for Continuum Deep Learning Neuro-Skin Neural Network

In this brief paper, a learning algorithm is developed for Deep Learning...
research
11/08/2019

Finite element simulation of ionicelectrodiffusion in cellular geometries

Mathematical models for excitable cells are commonly based on cable theo...

Please sign up or login with your details

Forgot password? Click here to reset