Research 
Main Goal
A main goal is the development of a General Adaptive
Differential Equation Solver, including mathematical basis, mesh
generation and CAD. Key features are:
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generality of models:
coupled multi-physics modeling combining phenomena from solid
mechanics, fluid dynamics, electromagnetics, reaction-diffusion.
Differential-algebraic models.
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generality of discretization:
space-time h-p finite elements in 2d and 3d, stationary and
non-stationary, moving boundaries,...
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automatic quantitative error control
in arbitrary norms, based on a
posteriori error estimates including stability factors computed by
solving linearized dual problems,
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efficiency:
multigrid, explicit/implicit, parallelization,...
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CAD:
coupling of the general solver to advanced tools for geometric
modeling such as ProEngineer,
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mesh-generation:
adaptive mesh refinement within the solver with updating of CAD
geometry, and coupling to mesh generators (e.g. the in-house mesh generator M3d),
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optimization, including feed-back to CAD,
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automatic modeling:
computational based subgrid modeling,
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applications
to fluids, solids, electromagnetics, chemistry, and multi-physics,
including aspects of optimization and automatic modeling.
realization of the general solver on different levels of complexity
for educational purposes.
Building blocks
Our research has three main components,
Theory, Applications and Software.
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Theory
Our focus is finite element analysis, especially a posteriori error estimation and
adaptivity. We are also active in the fields of computational modeling, optimization
and large-scale industrial problems.
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Applications
Application areas of special interest are
Electromagnetics
Mechanics
Chemistry
Material processing
Multi-physics
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Software
We are working on a general solver capable of handling complex
geometries and large-scale problems.
Although very capable and rich-featured, the current state
of the solver is "in-house".
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Learn more
To learn more about our activities, follow the links below.
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