Matrix representation

Element system matrix

The element system matrix collects individual system matrices as a multi-dimensional array of shape \left[ n_\text{elements} \times n_\text{nodes-per-element} n_\text{dim} \times n_\text{nodes-per-element} n_\text{dim} \right]. An element system matrix

Ke = K[e,:,:]

obeys the following convention:

\underline{f} = \underline{\underline{K}} \underline{u}

where

f_{(n + i d)} \equiv f_i^{(n)}

with n the node number, i the dimension, and d the number of dimensions. For example for a two-dimensional quadrilateral element

\underline{f} =
\big[
    f_x^{(0)},
    f_y^{(0)},
    f_x^{(1)},
    f_y^{(1)},
    f_x^{(2)},
    f_y^{(2)},
    f_x^{(3)},
    f_y^{(3)}
\big]^T