Research Area D: Numerical and Computational Mathematics
Most simulations are based on mathematic models which are initially composed of differential equations. The SimTech scientists in Research Area D are there to make these fit for implementation on computers. To this end, they convert the differential equations into algebraic equations systems which can then be solved numerically, i.e. by numbers. This process is called discretisation and some errors are incorporated by nature. The SimTech scientists’ ambitious aim is to quantify these errors, as well as uncertainties in the system description, as exactly as possible and to make them manageable.
Development of self-adaptive computer systems
This helps the team to develop better and exacter solution methods for the systems of equations. In doing so, they advance the topmost goal i.e. to develop self-adaptive computer systems which can play expertly with multi-scales while also coupling various physical processes with each other.
A new mathematical language
Different scales and physical processes call for different mathematical solution strategies e.g. a deformation in a material is calculated on a molecular level in a different fashion compared to a flow phenomenon on a macroscopic level. SimTech intends to clear up these “Babylonian” circumstances and to develop a common mathematical language. SimTech simulations are then to be run with the aid of error indicators, self-adaptive in their choice of where and when to operate on which scales and on when to switch on or cut off physical processes in order to simulate the entire process in an optimum fashion.
Close cooperation with Research Area C
In addition, the individual solution strategies will be speeded up considerably. Together with the methods for model validation and model reduction jointly developed with researchers from Research Area C, self-adaptive systems will help develop simulations which are highly efficient and fit for the future.
SimTech projects related Research Area D can be found in the following Project Networks:
- PN3: Simulation of microstructure evolution
- PN4: Coupled problems in biomechanics and systems biology
- PN5: Multi-phase and multi-physics modelling
- PN6: Model reduction, control and real-time simulation
- PN7: Dynamics and modelling in systems biology