Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements

Abstract: Based on the ideas of the paper [8] by Talal Rahman and Jan Valdman we propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H (div) spaces and Nédélec elements in discretizations of H (curl) spaces. The major loops in the code have been vectorized using the so called array operation in MATLAB, and no low level languages like C or Fortran have been used for the purpose. The implementation is based on having the vectorization part separated, in other words hidden, from the original code thereby preserving its original structure, and its flexibility as a finite element code. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.