Goethe Center for Scientific Computing (G-CSC)

Goethe University Frankfurt

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Research Front Page

G-CSC Poster

Report 2006 to 2011

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Report 2005 to 2010

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Report 1999 to 2006

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Computational Pharmacy:
Diffusion of xenobiotics through human skin.
Computational Neuroscience:
Signal transduction and processing in the brain.
Mathematical Finance:
High-dimensional option pricing problems.
Credit risk modelling and assessment.
Chemical and Process Engineering:
Multidimensional population balances coupled with fluid flow and disperse systems.
Detailed simulation of rising bubbles in liquid Fluid-fluid extraction
Environmental Science:
Ground water flow and transport.
Flow in porous media.
Density driven flow in porous media.
Transport, diffusion, sorption, dispersion and decay of radioactive pollutions in groundwater.
Remediation of aquifers.
Natural attenuation.
Long-term waste disposals
Computational Fluid Dynamics:
Incompressible and compressible Navier-Stokes Equations,
Large-Eddy Simulation,
Multi-phase flow,
low Mach-number flow,
non-Newtonian flows
Computational Electromagnetics:
Eddy current problems,
Coupling of electromagnetics with fluid flow
Laminar diffusion flames with detailed Chemistry for realistic industrial configurations.
Numerical Geometry and Visualization:
Reconstruction of the Heidelberg Castle before destruction.


Fast solvers for large systems of equations:
Parallel adaptive multigrid methods,
Incomplete LU (ILU),
Algebraic Multigrid (AMG),
Frequency Filtering,
Adaptive Filtering,
Filtering Algebraic Multigrid (FAMG),
homogenization and multigrid,
Coarse Graining Multigrid (CNMG),
interface reduction,
Domain Decomposition.
Multiscale Numerics and Homogenization:
Linking Homogenization with numerical multiscale methods fast computation of effective models and their parameters.
Finite volume methods,
Flux-based Method of Characteristics,
Discontinuous Galerkin methods,
Whitney elements,
sparse grids,
higher order sparse grid methods.
Inverse Modelling and Optimisation:
Optimisation multigrid,
SQP multigrid,
reduced SQP methods.
Numerical methods for high dimensional problems:
Sparse Grids,
Dimensional Reduction
Integro-differential equations:
Panel clustering for population balances.
Grid generation:
Generating combined hexahedral/tetrahedral grids for domains with thin layers and other complicated substructures.
Image processing:
Non-linear anisotropic filtering, segmentation, reconstruction.
Numeric Geometry and Visualization:
Parallel internet based ray tracing.

Software Tools

Simulation system UG:
With the simulation system UG we have created a general platform for the numerical solution of partial differential equations in two and three space dimensions on serial and on parallel computers. UG supports distributed unstructured grids, adaptive grid refinement, derefinement/coarsening, dynamic load balancing, mapping, load migration, robust parallel multigrid methods, various discretizations, parallel I/O, and parallel visualization of 3D grids and fields. The handling of complex three-dimensional geometries is made possible by geometry and grid generation using special interfaces and integrated CAD preprocessors. This software package has been extensively developed in the last four years and has got two awards in this period: 1999 at SIAM Parallel Processing, San Antonio, Texas, and HLRS Golden spike award 2001. Based on this platform, simulation tools for various problems from Bioscience, Environmental Science and CFD are being developed. UG is widely distributed around the world, more than 300 groups licensed it.
The development of the parallel programming model DDD (Dynamic Distributed Data) distributing data objects on a multiprocessor system. DDD is based on message passing, thus it does not require the system to provide global information. It allows a smooth integration of parallelization in the software tool UG.
The simulation tool d3f allows to compute the density driven groundwater flow in the presence of strong density variations e.g. around saltdomes. This unique software allows for the first time a solution of the full equations in realistic geometries.
In co-operation with the GRS Braunschweig and scientists from the universities of Freiburg, Bonn, and the ETH Z├╝rich a special software package r3t based on UG was developed. This novel software tool allows the simulation of the transport and retention of radioactive contaminants (up to 160 radionuclides) in large complex three-dimensional model areas.
As a counterpart to UG we developed the library SG (structured grids). It makes use of all structures known in logically rectangular grids. Currently we use it in Image Processing and Computational Finance projects. In the future we will couple it with UG.
In co-operation with B. Sakmann (MPI) we developed the Neuron Reconstruction Algorithm (NeuRA). It allows the automatic reconstruction of Neuron geometries from confocal microscopic data using a specially adjusted blend of non-linear anisotropic filtering, segmentation and reconstruction.
ARTE, TKD_Modeller:
We developed two grid generators for the treatment of highly anisotropic structures. ARTE generates tetrahedral meshes including prisms in thin layers, TKD_Modeller generates hexahedral meshes for mainly plane parallel domains.
Tool for internet based parallel rendering using POVRAY.
Parallel Visualization subsystem of UG.