  The finite element method is a well-established method for the numerical
solution of partial differential equations (PDEs), both linear and nonlinear.
However, the repeated reassemblage of finite element matrices for nonlinear
PDEs is frequently pointed out as one of the bottlenecks in the computations.
The second bottleneck being the large and numerous linear systems to be solved
arising from the use of Newton's method to solve nonlinear systems of
equations. In this paper, we will address the first issue. We will see how
under mild assumptions the assemblage procedure may be rewritten using a
completely loop-free algorithm. Our approach leads to a small matrix-matrix
multiplication for which we may count on highly optimized algorithms.
