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. (c) 2007 Elsevier B.V. All rights reserved.