Reduced-order methods for a parametrized model for erythropoiesis involving structured population equations with one structural variable

Abstract

The thesis investigates a one-dimensional, hyperbolic evolution equation containing one structural variable, with a particular focus on a model of erythropoiesis developed by Fürtinger et al. in 2012. Three di erent discretization techniques which all result in so-called high-fidility or detailed solutions are introduced and discussed. The methods used include Finite Differences and a polynomial representation of the structural variable. Viewed from the perspective of Optimal control, the model takes the form of a Parametrized Partial Di erential Equation (P2DE) where both the control and other data values are treated as parameters of the equation. This places the problem into a multi-query context, making model order reduction (MOR) techniques conceivable. Reduced basis (RB) strategies are employed to reduce the dimension of the utilized discretization spaces with a Galerkin projection. The reduced space is generated by applying a Greedy algorithm with methods including both the addition of single snapshots as well as Proper Orthogonal Decomposition (POD). In order to assess the error between the detailed and the reduced solution, two a-posteriori estimators are introduced and analyzed. Algorithmically, an offine/online decomposition scheme is used to enable e cient computations of both the reduced solutions and the estimators. Lastly, numerical experiments are presented to evaluate the feasibility of model order reduction techniques for the problem at hand.