Optimising finite element matrix calculations using the general technique of element vectorisation

A general algorithm for calculating finite element matrices efficiently on both serial and vector processors is presented. In contrast to other element calculation algorithms, the degree of vectorisation of the proposed algorithm is not limited by the order of the element approximation, thus the potential for increased efficiency is applicable to any existing finite element code. To illustrate the degree of vectorisation and scalar optimisation that can be realised in practice, computation times using a serial computer and a CYBER 205 vector processor are compared for three distinct types of element matrix each having physical significance.