Adaptive mesh refinement for geophysical inversion
Geophysical inversion is an optimization problem subject to partial differential equation (PDE) constraints. These constraints can be efficiently approximated using standard PDE discretization methods which, in many cases, require the refinement of mesh at some locations. Usually, the locations for refinement are unknown before the inversion, or are moved during the inversion. Zhi Li's PhD research aims to develop a mechanism to determine where to carry out the refinement by automatically and independently modifying the computational mesh. In order to implement refinement adaptively, this project will design a suitable posteriori error estimation and efficient data structure to facilitate mesh refinement and mesh coarsening.