Keynote
Scalable non-linear solvers for finite elements discretizations of the Cai-Hu model
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The Cai-Hu model describes the branching structure of biological transportation networks, such as leaf venations and vascular systems, as the gradient flow of an energy functional. The minimization of such functional results in a time-dependent, non-linear reaction-diffusion system of equations that interacts with an ill-conditioned algebraic equation for the transported quantity. In this talk, we will discuss the development and implementation of scalable, fully non-linear solvers for low-order finite-element discretizations of the model and present numerical results that validate the robustness and scalability of the solvers.