Efficient finite element assembly of high order Whitney forms

This study presents an efficient method for the finite element assembly of high order Whitney elements. The authors start by reviewing the classical assembly technique and by highlighting the most time consuming part. Then, they show how this classical approach can be reformulated into a computationally efficient matrix-matrix product. They also address the global orientation problem of the vector valued basis functions. They conclude by presenting numerical results for a three-dimensional wave propagation problem.