This book presents recent research work that is focused on mathematical solution strategies in the important areas of "Prognostic MR Thermometry for Thermal Ablation of Liver Tumours" and "Energy-efficient High Temperature Processes via Shape Optimization". It is addressed to people who are interested in modern mathematical solutions for real-life applications. In particular, mathematical modelling, simulation and optimization are currently successfully used in various fields of application, such as the energy or health sector. Here, mathematics is often the driving force for new innovations and is most relevant for the success of many interdisciplinary projects. The presented chapters demonstrate the power of this emerging research field and show how society can benefit from applied mathematics.
Nicolas R. Gauger is a Full Professor for Scientific Computing as well as Director of the Computing Center at University of Kaiserslautern (TUK). He has about 20 years of experience in optimization and control with partial differential equations. He has been engaged in several European as well as German projects (BMBF, BMWi, DFG) in this area. His main field of application is in aerospace sciences. in 2019 he has been named an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA).
Axel Klar is Professor of Numerical Analysis at the TU Kaiserslautern. Previously, he has had positions at the FU Berlin and the TU Darmstadt. He obtained a Ph.D. in Applied Mathematics at TU Kaiserslautern. His research interests range from scientific computing for hyperbolic and kinetic equations to modeling of physical and social phenomena using kinetic theory and hyperbolic PDEs.
René Pinnau is Professor of Industrial Mathematics at the TU Kaiserslautern. He obtained a Ph.D. in Applied Mathematics at TU Kaiserslautern and works since 20 years in the fields of modeling, numerical simulation as well as optimisation and control with partial differential equations. In particular, he is interested in optimal semiconductor design and optimisation of radiation dominant processes.
This volume is addressed to people who are interested in modern mathematical solutions for real life applications. In particular, mathematical modeling, simulation and optimization is nowadays successfully used in various fields of application, like the energy- or health-sector. Here, mathematics is often the driving force for new innovations and most relevant for the success of many interdisciplinary projects. The presented chapters demonstrate the power of this emerging research field and show how society can benefit from applied mathematics.
Part I Prognostic MR Thermometry for Thermal Ablation of Liver Tumours.- 1 Sebastian Blauth et al., Mathematical Modeling and Simulation of Laser-Induced Thermotherapy for the Treatment of Liver Tumors.- 2 Matthias Andres and René Pinnau, The Cattaneo Model for Laser-Induced Thermotherapy: Identification of the Blood-Perfusion Rate.- 3 Kevin Tolle and Nicole Marheineke, On Online Parameter Identification in Laser-Induced Thermotherapy.- Part II Energy-efficient High Temperature Processes via Shape Optimisation.- 4 Robert Feßler at al., Feasibility Study on Simulating a 3D Furnace Including the Effects of Reactions and Vaporization.- 5 Thomas Marx et al., Shape Optimization for the SP1-Model for Convective Radiative Heat Transfer- 6 Nicolas Dietrich et al., Diffusive Radiation Models for Optimal Shape Design in Phosphate Production.- 7 Ruben Sanchez at al., Adjoint-based sensitivity analysis in high-temperature fluid flows with participating media.
Modeling, Simulation and Optimization in the Health- and Energy-Sector