Computational approaches to studying non-linear dynamics of the crust and mantle

We outline a mathematical formulation for mantle convection which can deal with the viscoelastic–plastic rheology of the cool parts of the lithosphere. This formulation is then analyzed to expose the numerical challenges inherent in the equations and a suitable solution strategy is outlined. With this strategy in place, we discuss a parallel implementation, explaining how we maintain computational efficiency, in a tiered and modular software environment. We show two examples from geodynamics which demonstrate the capability of the numerical method and its implementation.