Coupling Schemes and Inexact Newton for Multi-Physics and Coupled Optimization Problems

This book targets mathematical solutions and software for complex numerical simulation and optimization problems. The combination of different models and software modules and the need for massively parallel execution on supercomputers are main characteristics. The work consists of two parts: (i) Surface coupled fluid- structure interaction simulations, and (ii) analysis of medical MR imaging data of brain tumor (glioblastoma multiforme) patients. In (i), the author presents new and powerful quasi-Newton methods to establish highly accurate simulations by combining different aspects such as fluid flow and arterial wall deformation in, e. g., hemodynamics simulations. In (ii) focus lies on (a) facilitating the transfer of information such as functional brain regions from a statistical healthy atlas brain to the individual patient brain, and (b) to allow for patient specific tumor progression simulations based on the estimation of biophysical parameters via inverse tumor growth simulation. Scheufele presents a joint medical image registration and biophysical inversion strategy, targeting at facilitating diagnosis, aiding and supporting surgical planning, and improving the efficacy of brain tumor therapy.