The element stiffness matrix in 3D FEM problems is build as follows:
$$ K = \int\limits_{[-1,1]^3} B^T C B\, |J| \mathrm{d}r\, \mathrm{d}s\, \mathrm{d}t$$
The integral can be solved using e.g. Gauss quadrature method.
But for me it seems to computational expensive if you perform the above equation for, e.g., 500.000 hexahedral elements. Thus I was wondering if there is an additional approximation or something else done to reduce the computational effort.
Question: Is there some kind of approximation method used to solve the two matrix-matrix products as well as the determinant or are they computed explicitly for each element?