Parallel-in-time integration of a kinematic dynamo

The origin of magnetism within planets and stars is of fundamental importance in the natural sciences. Magnetic fields of astrophysical bodies reveal a wealth of information about their interior structure and are linked to near-surface conditions, e.g. on Earth where a strong dipole-dominated field shields the surface (including humans) from incoming solar radiation. They are generated by the motion of an electrically conducting fluid in a so-called dynamo process.  Computer simulations of this process are based on complex mathematical models and come with enormous computational cost: a simulation taking weeks to complete is not uncommon.

Parallel-in-time integration algorithms are a novel way to exploit multiple processors in a computer to speed up such simulations, but they have not yet been studied for the equations describing dynamos in the Earth or sun. The student will explore their performance for the kinematic dynamo, describing the process of magnetic induction by a prescribed fluid flow. The model is commonly used in studies of the solar dynamo and many interesting questions are still unanswered.  The project will explore the potential of parallel-in-time methods to speed up simulations to help provide a better understanding of the generation of solar and planetary magnetic fields.