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

We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. The major loops in the code have been vectorized using the so called array operation in MATLAB, and no low level languages like the C or Fortran has 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. The code is fast and scalable with respect to time.