Physics-regularized learning (MATH+ EF3-4)

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Carsten Gräser (FU Berlin), Prof. Dr. Christof Schütte (FU Berlin/ZIB)

Jan 01, 2019 — Dec 31, 2021

Goals and achievements This methodologically oriented project was devoted to the development and numerical analysis of learning algorithms for (typically large) data sets exploiting a priori knowledge in terms of an auxiliary physical model formulated as partial differential equation. We ...

Stochastic analysis of particle systems: Langevin dynamics and the Dean-Kawasaki model (MATH+ AA1-3)

Prof. Dr. Peter K. Friz (TU Berlin), Prof. Dr. Ralf Kornhuber, Prof. Dr. Nicolas Perkowski (HU Berlin)

Jan 01, 2019 — Dec 31, 2021

Naturally emerging stochastic models for particle systems in the Life Sciences are often questionable or even meaningless from a mathematical point of view. The goal of this project is to develop mathematically rigorous formulations and solution concepts together with a stochastic and numerical ...

Langevin dynamics of particles in membranes (A07)

Prof. Dr. Carsten Gräser (FU Berlin), Prof. Dr. Luigi Delle Site (FU Berlin), Prof. Dr. Ralf Kornhuber (FU Berlin)

Jul 01, 2018 — Jun 30, 2022

The interplay of proteins and curvature of lipid bilayers is well-known to regulate cell morphology and a variety of cellular functions, such as trafficking or signal detection. Here, interplay not only means that proteins can induce curvature by shaping and remodeling the membrane, but also that ...

Fault networks and scaling properties of deformation accumulation (B01)

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Onno Oncken (GFZ Potsdam), Dr. Matthias Rosenau (GFZ Potsdam), Prof. Dr. Alexander Mielke (WIAS)

Jul 01, 2018 — Jun 30, 2022

In the second funding period of this project, we plan to extend our numerical simulations to single faults in viscoelastic materials and, in parallel, concentrate on the investigation of multiscale fault networks. In particular, we will develop analogue experiments that involve networks of ...

Integrated Research Training Group (Z02)

Prof. Dr. Ralf Kornhuber (FU Berlin)

Jul 01, 2018 — Jun 30, 2022

The Integrated Research Training Group (IRTG) provides advanced, programme-specific structured training and support for all PhD students of the CRC 1114. The central aims of the IRTG are first, to equip PhD students with knowledge and skills for successful research work and academic performance ...

Advanced techniques for entropy-based moment methods for linear kinetic equations

Dr. Graham Kaland (FU Berlin)

Dec 06, 2016 — Nov 21, 2019

Linear kinetic equations model many physical phenomena, e.g. radiative transport, but remain challenging to simulate. The entropy- based moment method is a discretization which has attractive theoretical properties but so far no practical implementation. We will investigate several new techniques ...

Reliable joint simulations for orthopaedic decision making in hip surgery

Prof. Dr. Ralf Kornhuber (FU Berlin), Dr. Stefan Zachow (ZIB)

Jun 01, 2017 — Dec 31, 2018

This project aims at estimating the unknown parameters of a physics-based joint model together with a systematic sensitivity analysis, to ensure the reliability of a computer-assisted surgery planning tool developed in previous Matheon projects A17/CH1. The estimation shall be carried out using a ...

Understanding of microstructure evolution in copper indium selenide (CISe) and copper gallium indium selenide (CGSe)

Prof. Dr. Ralf Kornhuber (FU Berlin)

Nov 01, 2012 — Dec 31, 2018

Photovoltaic devices, which operate by directly converting solar energy into electricity, have become rapidly one of the most important “clean” energy sources. The optimization of thin-film solar cells for such use has been mainly a trial-and-error process. A detailed understanding of the ...

Fault networks and scaling properties of deformation accumulation

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Onno Oncken (GFZ Potsdam), Dr. Matthias Rosenau (GFZ Potsdam), Prof. Dr. Alexander Mielke (WIAS)

Oct 01, 2014 — Jun 30, 2018

Earthquake statistics reveal scale invariance over 10 orders of magnitude of the earthquake strength as expressed, e.g., by the famous Gutenberg–Richter power law. Well- established explanations for earthquake activity in the lithosphere are based on strain accumulation and stress release along ...

Multilevel coarse graining of multiscale problems

Prof. Dr. Christof Schütte (FU Berlin/ZIB), Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Beate Koksch (FU Berlin)

Oct 01, 2014 — Jun 30, 2018

Molecular dynamics and related computational methods enable the description of bio­logical systems with all-atom detail. However, these approaches are limited regarding simulation times and system sizes. A systematic way to bridge the micro-macro scale range between molecular dynamics and ...

Particles in lipid bilayers

Prof. Dr. Carsten Gräser (FU Berlin), Prof. Dr. Carsten Hartmann (BTU), Prof. Dr. Ralf Kornhuber (FU Berlin)

Oct 01, 2014 — Jun 30, 2018

The interplay of proteins and curvature of lipid bilayers is well-known to regulate cell morphology and a variety of cellular functions, such as trafficking or signal detection. Here, interplay not only means that proteins can induce curvature by shaping and re­modeling the membrane, but also ...

Geometric properties in Orlicz spaces, direct sums and Banach spaces of vector-valued functions

Dr. Jan-David Hardtke (FU Berlin)

Feb 01, 2017 — Sep 30, 2017

The aim of this project is to study various types of rotundity and smoothness properties in infinite direct sums of Banach spaces, Köthe-Bochner spaces of vector-valued functions (which include Lebesgue-Bochner and Orlicz-Bochner spaces as special cases), and more generally in so called direct ...

Wear simulation and shape optimization of knee implants. Subproject 4: Uncertainty quantification

Prof. Dr. Ralf Kornhuber (FU Berlin)

Jul 01, 2013 — Jul 31, 2017

One of very common surgeries daily performed in German clinics is the human knee joint replacement. For the market admittance of joint implants, standardized wear tests has to be performed. During the design phase, similar tests are necessary as well. Those tests are very cost and time ...

Reduced basis methods in orthopedic hip surgery planning

Prof. Dr. Ralf Kornhuber (FU Berlin), Dr. Stefan Zachow (ZIB)

Jun 01, 2014 — May 31, 2017

This project aims at the development, analysis and implementation of algorithms for computer-assisted planning in hip surgery and hip joint replacement by fast virtual testing. Fast forward simulations of patient-specific motion of hip joints and implants in 3D shall be enabled by exploiting ...

Variational methods for problems of rate- and state-dependent friction

Prof. Dr. Ralf Kornhuber (FU Berlin)

Jan 01, 2011 — Dec 31, 2014

The model of rate- and state-dependent friction is ubiquitous in geophysics. Even though it is not derived from first principles but phenomenological in nature, it has found applications to a great many materials. Mathematically, it is poorly understood, however. To be precise, there appears to be ...

Multilevel methods on manifold meshes

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Konrad Polthier (FU Berlin), Prof. Dr. Harry Yserentant (TU Berlin)

May 01, 2005 — May 31, 2014

The project addresses the strong needs for multilevel algorithms in CAD and computer graphics, in particular in industrial applications where large surface meshes must be efficiently processed. Typical applications are solutions of PDEs on surfaces, surface optimization, and automatic mesh ...

Adaptive multigrid methods for local and non-local phase field models of solder alloys

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Jürgens Sprekels (WIAS)

Dec 01, 2005 — May 31, 2014

Phase field models provide a well-established framework for the mathematical description of phase transitions on the meso scale. Allen-Cahn equations (non-conserved order parameter) and Cahn-Hilliard equations (conserved order parameter) are typical examples. In such classical phase field models ...

Computational surgery planning

Prof. Dr. Peter Deuflhard (ZIB), Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Oliver Sander (TU Dresden)

Jun 01, 2010 — May 31, 2014

These days, the choice of the optimal surgical procedure still relies heavily on the experience of the surgeon and even small misjudgements can cause detrimental long-term effects. Therefore preoperative planning is very important to reduce these unwanted effects. This project aims to develop a ...

Adaptive multigrid methods for coupled ice shelf models

Prof. Dr. Ralf Kornhuber (FU Berlin)

May 01, 2012 — Dec 31, 2013

Antarctic ice sheets have been retreating dramatically in recent years, and are expected to shrink even more quickly in the future, with a subsequent rise of sea level. It is then crucial to develop accurate numerical simulation tools of ice sheets that have a high predictive capability. Modelling ...

Adaptive multigrid methods for phase field models

Prof. Dr. Ralf Kornhuber (FU Berlin)

Jan 01, 2003 — Dec 31, 2010

Phase field models provide a well-established framework for the mathematical description of free boundary problems for phase transitions. The diffuse interface is represented by the level sets of a function, called order parameter or phase field, whose value identifies the phases at particular ...

Fast and reliable multilevel algorithms in a virtual orthopaedic surgery lab

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Peter Deuflhard (ZIB)

Jan 01, 2007 — Dec 31, 2010

The goal of this project is to develop robust tools to provide predictions of musculoskeletal loading by coupling generic forward dynamics multi-body systems with inverse dynamics approaches to be used in partner project C-4 for analyzing patient specific data. Such global models are to be coupled ...

Coupled flow processes in energy and environmental research

Prof. Dr. Ralf Kornhuber (FU Berlin)

Jan 01, 2008 — Dec 31, 2010

Modeling of coupled flow processes is an urgent and largely unsolved interdisciplinary problem. They have eminent importance in energy research, geosciences, environmental and climate research, civil engineering and materials science. Common topics of the network: reactive transport of dissolved ...

Adaptive hydrological modeling with application in water resource management

Prof. Dr. Ralf Kornhuber (FU Berlin)

Sep 01, 2007 — Aug 31, 2010

The goal of the joint research project AdaptHydroMod is essentially the development of a general methodology for modeling and simulating coupled hydrological processes. The methods that are constructed in this context are supposed to automatically adapt to various conditions and modifications ...

Modeling and simulation of human motion for osteotomic surgery

Prof. Dr. Peter Deuflhard (ZIB), Prof. Dr. Ralf Kornhuber (FU Berlin)

Jun 01, 2002 — May 31, 2010

The general aim is to assist osteotomic surgery by the development of a virtual lab extending the Amira toolbox, which will then include data pre- and postprocessing, visualization, heterogeneous DAE/PDE modelling, and efficient numerical algorithms. We will start by deriving the detailed ...

Adaptive monotone multigrid methods for option pricing

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Peter Deuflhard (ZIB)

Jan 01, 2005 — May 31, 2006

The project is devoted to the development and implementation of monotone multigrid methods, transparent boundary conditions and adaptive strategies for American option pricing. In cooperation with Deutsche Bank London various kinds of 1- and 2-factor models (local volatility, deterministic ...

Computer oriented mathematics

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Rolf Möhring (TU Berlin), Prof. Dr. Ulrich Kortenkamp (Uni Potsdam), Prof. Dr. Christof Schütte (FU Berlin/ZIB)

Oct 01, 2004 — Dec 31, 2005

This project is devoted to fundamental concepts of scientific computing at the crossover from school to university. The goal of this project is to develop a book titled 'Introduction to computer-oriented mathematics' together with an associated web version. The main issues concern - striking ...

Multigrid methods and Eulerian - Lagrangian methods for modelling flow and transport processes in fractured aquifer systems

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr.-Ing. Rainer Helmig (Uni Stuttgart)

Nov 01, 1999 — Oct 31, 2002

Simulation of groundwater flow and solute transport behaviour in fractured aquifer systems is of major importance when considering waste disposal sites (legacies, permanent waste diposals). In the present project, combined modelling approaches will be applied to the mathematical description of the ...

Adaptive monotone multigrid methods for Signorini's problem in linear elasticity

Prof. Dr. Ralf Kornhuber (FU Berlin)

Apr 01, 1999 — Mar 31, 2002

We present a new approach for solving the Signorini problem with Coulomb friction in linear elasticity. The Signorini problem describes the linearized contact of an elastic body with a rigid foundation. Because it is not known in advance which part of the body's surface will be in contact with the ...

Fast solvers for transonic droplet-loaded gas flow with applications to the simulation of spraying processes

Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Rainer Haag (FU Berlin)

Jul 01, 1997 — Jun 30, 2000