Willkommen auf den Seiten des Lehrstuhl IX "Wissenschaftliches Rechnen"
Welcome to the homepage of the Chair of Mathematics IX 'Scientific Computing'

Prof. Dr. Alfio Borzi (Chair Holder)

Wissenschaftliches Rechnen - Scientific Computing

bezeichnet die eigenständige wissenschaftliche Disziplin, die sich mit der rechnergestützten numerischen Simulation von Prozessen beschäftigt, wie sie etwa in den Natur-, Ingenieurwesen oder Wirtschaftswissenschaften untersucht werden. Die numerische Simulation tritt dabei neben die beiden klassischen Säulen des Erkenntniserwerbs in den betreffenden Anwendungswissenschaften, nämlich die theoretische Untersuchung und das Experiment. Das wissenschaftliche Rechnen mit seinen zentralen Methodenbereichen Modellierung, Numerische Simulation und Hochleistungsrechnen hat sich zu einer Schlüsseltechnologie für das Verständnis und die Bewältigung wissenschaftlich-technischer Herausforderungen entwickelt. So unterschiedliche komplexe Probleme wie die Gestaltung und Simulation des Einlasskanals eines Zylinderkopfes in Motoren, die Modellierung und Visualisierung von elektrischen Erregungswellen im Gehirn und Herzmuskelgewebe, oder das Design und die Steuerung von Nano- und Mikrosystemen erfordern den Einsatz von wissenschaftlichem Rechnen. Durch wissenschaftliches Rechnen erhält man oft genauso neue Erkenntnisse, wie es bei komplizierten Experimenten in einem Physik- oder Chemielabor passieren kann. Also, man kann mit dem Unerwarteten rechnen.


      

Forschungsschwerpunkte - Reasearch

Marie Curie International Training Network
Multi-ITN STRIKE - Novel Methods in Computational Finance

The computational complexity of mathematical models employed in financial mathematics has witnessed a tremendous growth that requires the development of advanced numerical techniques appropriate for the most present-day applications in financial industry. Besides a series of internationally recognized researchers from academics, leading quantitative analysts from the financial industry also participate in this network. The challenge lies in the necessity of combining transferable techniques and skills such as mathematical analysis, sophisticated numerical methods and stochastic simulation methods with deep qualitative and quantitative understanding of mathematical models arising from financial markets.


Steuerung von Quantensystemen - Control of Quantum Systems

Control of quantum phenomena is becoming central in a variety of systems with present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures. In most cases, quantum control is aiming at quantum devices and molecular systems where there is the need to manipulate quantum states with highest possible precision. The successful application of optimal control theory in this field together with the enormous effort towards nanosciences explains the large growing interest in quantum control problems. Our focus is the development and investigation of fast and robust solvers of finite- and infinite-dimensional quantum control problems within an interdisciplinary scientific environment including biology, chemistry, mathematics, and physics.

Mehrgitterverfahren - Multigrid Methods

Multigrid methods represent one of the most important breakthrough in the development of fast solvers of large-scale algebraic problems. In particular, multigrid principles allow to define iterative schemes with optimal computational complexity for solving discretized partial differential equations (PDEs). More recently, multigrid schemes have been applied successfully to solve PDE optimization problems and inverse problems. Our purpose is the development and analysis of multigrid methods for simulation and optimization with PDE models and the formulation of multigrid optimization schemes for unconstrained optimization.

Robuste Energie-Optimierung bei Gärprozessen in der Produktion von Biogas und Wein: ROENOBIO - Robust energy optimization of fermentation processes for the production of biogas and wine: ROENOBIO

Gärung spielt als grundlegender biochemischer Prozess in vielfältigen technologischen Prozessen eine herausragende Rolle. In diesem Projekt sollen Gärprozesse bei der Produktion von Biogas und Wein räumlich und zeitlich detailliert modelliert und simuliert werden. Durch die kombinierte Untersuchung der Biogas- und der Weinproduktion ist es möglich, Synergieeffekte zu nutzen, da die leichter kontrollierbare Weingärung als Prototyp für die komplexere Biogasgärung betrachtet werden kann. Die Modelle werden basierend auf einem gemeinsamen generischen Grundmodell entwickelt mit dem Ziel, die Prozesse v.a. hinsichtlich des thermischen Energieaufwands zu optimieren, wobei produktspezifische Aspekte wie Gasausbeute (Biogas) oder Aromaprofil (Wein) berücksichtigt werden. Damit gehört dieses Projekt zum Bedarfsfeld Klima/Energie der Hightech-Strategie der Bundesregierung.

Optimierung mit partiellen Differentialgleichungen - PDE Optimization

The purpose of PDE optimization is to define ways of how optimally change, influence, or estimate features of systems modeled by partial differential equations. An important class of problems in PDE optimization results from optimal control applications. Other important classes of optimization problems are shape design, topology, and parameter optimization. Optimization is also an essential tool for solving many inverse problems. Our research work aims at the formulation, approximation, and efficient solution of PDE optimization problems also in the presence of data and model uncertainty.

Bildverarbeitung - Image analysis

The development of tomographic and other non-invasive imaging devices represent an exceptional contribution to medicine, material sciences, and arts. This development has led to a fast growth in the interdisciplinary field of imaging science where mathematics plays a central role providing a rigorous basis for imaging analysis. We investigate mathematical methods and fast algorithms for image processing and computer vision. The main focus is on techniques using partial differential equations and optimization.

Formoptimierung - Shape optimization

Shape optimization is a special class of PDE constrained optimization, where the domain is the optimisation variable. Besides classical applications in CFD, as control of fluids and aerodynamic design, shape optimisation appears in many other application fields as computational acoustics, tomography, inverse design, uncertainties quantification and elasticity. Shape optimization problems are among the most challenging applied mathematics problems that are based on rigorous theoretical ground and involve sophisticated algorithms. Thus, this research area combines analysis and geometry with numerics and scientific computing to form structure exploiting algorithms which enable the consideration of large scale problems.

Advanced nebular spectral synthesis for Supernovae

Supernovae are bright optical "transient stars", appearing and disappearing again within some 100 days. In fact, these objects are stars which explode after having reached the final stages of their lives. How Supernova explosions exactly take place is still unclear. While some Supernovae are certainly due to the collapse of a massive stellar core (Supernovae of Type Ib/Ic/II), others are most probably thermonuclear explosions of white dwarfs stars (Type Ia). With our project, we aim at an improved understanding of Supernovae by calculating accurate Supernova spectra from numerical Supernova models (synthetic spectra) and checking whether these match observed spectra.