A parallel and adaptive multigrid solver for the solutions of the optimal control of geometric evolution laws in two and three dimensions

We present a problem concerning the optimal control of geometric evolution laws. This is a minimisation problem that aims to find a control ? which minimises the objective functional J subject to some imposed constraints. We apply this methodology to an application of whole cell tracking. Given two sets of data of cell morphologies, we may solve the optimal control problem to dynamically reconstruct the cell movements between the time frame of these two sets of data. This problem is solved in two and three space dimensions, using a state-of-the-art numerical method, namely multigrid, with adaptivity and parallelism.