Finite elements

A constitutive model is a Python class where the relationship between fluxes and gradients is encoded in SymPy. At every stage the mathematics is visible, inspectable, and differentiable. The framework handles Jacobians, C code generation, and PETSc integration. You handle the physics.

One of the less glamorous but important problems in a finite element framework is this: how does the user assign values to a field variable, and how does the framework ensure that PETSc sees those values correctly, in parallel, without the user needing to keep track themselves?

What actually happens between the moment you write a mathematical expression in underworld3's python layer and the moment PETSc receives a finite element term in the form of compiled C code ?

Underworld is a code for geodynamics — mantle convection, lithospheric deformation, subduction, ice flow. We solve coupled, nonlinear PDEs with complex rheologies using Lagrangian particles to track material history. The project has been running for 20 years: why did we start again ?

Introducing Underworld3: Mathematically Self-Describing Modelling in Python for Desktop, HPC and Cloud.

CITCOM is a geodynamics modelling code based on the finite element method that is designed for planetary evolution modelling where large spatial variations and strong non-linearities occur in the material properties.