Finite element simulations using symbolic computing

In our work on modelling of phase change, fluid flow and heat transfer in materials processes, it is crucial to have complete control of the mathematical models, and the numerical simulation of the models. We have developed a toolbox in Maple which can be used to generate complete finite element codes in 1, 2 or 3 dimensions, from a symbolic specification of the mathematical problem. It has been used to create codes used in our research on welding, crystal growth, flow of viscoelastic liquids and more. The possibility of defining a complex problem in a compact readable form, without compromising the flexibility and accessibility of the model and the numerical methods, has changed the way we use simulations in research radically.