The development of numerical methods for the simulation of coupled systems as well as its implementation on high performance computers are central areas of focus at the Institute of Scientific Computing. This requires the projects to exhibit significant fundamental research as well as practical relevance.
Of particular interest is the coupling of multi-physics and multi-scale problems - either stochastic or deterministic - as well as the development of software for the purpose of "computational" coupling of existing simulation on parallel computing.
Fluid-structure coupling is a technically important class of multiphysics problems. The institute participates in the graduate colleague for fluid-structure coupling in Braunschweig for more than three years by now within which a partitioning method for the efficient solution of such problems has been developed using black-box solvers for both sub- problems (pure fluid and pure structure). This includes the implementation on a parallel computer.
Moreover, a method for the efficient calculation of long-term Monte-Carlo simulations of wind turbines by using adjunct/dual solutions and non-linear Galerkin-reductions has been developed. In a research project based on these results offshore wind turbines will be simulated where a coupling of structure, aerodynamics, hydromechanics and the soil and foundation is required.
The use of adaptive techniques is a challenge to simulate coupled systems. Such techniques will be developed in a research project where time-space finite elements as well as the least-square finite element method with strongly coupled codes will be used.
Another project simulates systems with non-deterministic material behaviour, e. g. stochastic ground water flow. Thereof, efficient numerical methods for the solution of the resulting equations as well as adaptive methods have been created and the inclusion of existing solvers for the treatment of the space related part is worked on.
For the simulation of coupled systems the efficient reuse and combination of existing software for the simulation of a higher system is emphasized within the research in our institute. This is highly desirable from both the economic and scientific point of view. The institute also develops methods for a sub-project of "COSIWIT" supported by the BMBF where strong mathematic coupling by weak software coupling is anticipated.
A new class of discretization methods are mesh-free methods and particle methods. They will be applied in a current project on the simulation of viscous gas flow in combustion chambers. This is where classic FEM-methods have to remesh continuously.
The simulation of non-linear reaction-diffusion equations with probabilistic cellular automata requires the coupling of several time and space scales (multiscale problem). Procedures have been developed for the examination of the arising samples with the mean- field analysis or cluster- and correlation-analysis. These procedures employ the above methods automatically according to the description of the cellular automation. Furthermore, the simulation system JCASim has been developed which is able to couple different cellular automata simulations.
A further important aspect for the computing of complex coupled systems is the administration of distributed calculation and storage resources. A visionary approach for this is grid computing which has the aim to create a world-wide distributed infrastructure for distributed computing. As a research contribution the institute is working on the import of the distributed optimization system PLATON into a grid application in cooperation with the interdisciplinary working group INOBS.