The areas of mathematics most related to computational mechanics are partial differential equations, linear algebra and numerical analysis.
The boundary element technique is in general less popular, but has a niche in certain areas including acoustics engineering, for example.
The most widely used programming language in the scientific community, including computational mechanics, is Fortran.
Because of its very natural way of expressing mathematical computations, and its built-in visualization capacities, the proprietary language/environment MATLAB is also widely used, especially for rapid application development and model verification.
that would be very difficult or impossible to treat using analytical methods have been successfully simulated using the tools provided by computational mechanics.