Computational Mechanics - Overview

Overview

Computational mechanics (CM) is interdisciplinary. Its three pillars are mathematics, computer science, and mechanics. Computational fluid dynamics, computational thermodynamics, computational electromagnetics, computational solid mechanics are some of the many specializations within CM.

The areas of mathematics most related to computational mechanics are partial differential equations, linear algebra and numerical analysis. The most popular numerical methods used are the finite element, finite difference, and boundary element methods in order of dominance. In solid mechanics finite element methods are far more prevalent than finite difference methods, whereas in fluid mechanics, thermodynamics, and electromagnetism, finite difference methods are almost equally applicable. The boundary element technique is in general less popular, but has a niche in certain areas including acoustics engineering, for example.

With regard to computing, computer programming, algorithms, and parallel computing play a major role in CM. The most widely used programming language in the scientific community, including computational mechanics, is Fortran. Recently, C++ has increased in popularity. The scientific computing community has been slow in adopting C++ as the lingua franca. 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.

Some examples where computational mechanics have been put to practical use are vehicle crash simulation, petroleum reservoir modeling, biomechanics, glass manufacturing, and semiconductor modeling.

In the last century, especially in the second half thereof, computational mechanics has had profound influences on science and technology. Complex systems that would be very difficult or impossible to treat using analytical methods have been successfully simulated using the tools provided by computational mechanics. With the incorporation of quantum, molecular and biological mechanics into new models, CM is poised to play an even bigger role in the future.