We consider the shallow water magnetohydrodynamic (SWMHD) equations, in which multiscale phenomena appear in geophysics, astrophysics, and energy production applications. However, capturing both large and small scales numerically requires an exact treatment of the physically-observed divergence-free condition of the magnetic field and typically a very fine spatial grid. An alternative to requiring a fine spatial…

There are several challenges associated with inverse problems in which the unknown parameters can be modeled as piecewise constant functions. We model the unknown parameter using multiple level sets to represent the piecewise constant function. Adopting a Bayesian approach, we impose prior distributions on both the level set functions that determine the piecewise constant regions…

When dealing with large compartment models it can often be challenging to track how a small component of the model affects the overall system. This is an issue when trying to determine if a model is in its "simplest form" or if there are components that can be removed without significantly affecting the model's behavior.…