Underworld Goes Global

We recently embarked on a project to develop a spherical version of the Underworld code. It seemed fitting that we should try to complete this monstrous journey in under 80 days and with little more than a carpet bag containing a few clean clothes and a book of finite element methodology to guide the way. We report our adventures along the way. Underworld was designed to model processes at the lithosphere scale and was therefore focused on efficient/accurate treatment of large deformation, history dependent material properties and interfaces. At the scale of interest, the curvature of the Earth can often be neglected and the original Underworld code assumed, for simplicity, a Cartesian geometry. Two important considerations led us to develop a spherical code: 1) that many of the processes of interest at the lithospheric scale are driven by global-scale flows which we are increasingly incorporating directly in models (e.g. convergent boundary processes driven by the buoyancy of subducted slabs); and 2) that mapping observables from {lat, long, depth} to Cartesian coordinates introduces an unnecessary complication to interpretation of the resulting models. (Actuallly, three important considerations ... having flown around the world a number of times, keenly observing the world below, and having failed to observe any vertices or edges ... ) We will discuss our choices in mesh construction, particle advection, integration schemes, parallel decomposition, and the abstractions necessary to keep the underlying code independent of the chosen geometry.