Efficient preconditioners for problems with multiple scales

Problems with multiple scales and multiple phases cover a wide range of research and application in science and industry, as for instance in computational physics and -mechanics, materials science, biomedical engineering, and petroleum engineering. Tradit ional numerical methods for such equations face severe difficulties due to the size of the problem and the numerical ill--conditioning often caused by the strong heterogeneity and the different scales processes. The accurate description of the mathemati cal model, and advanced numerical methods that rely on the description are key to enabling computer simulations in a feasible time. The main objective of the project is to develop such reliable and efficient algorithms for multiscale problems. As primary applications, we will consider problems related to the shape optimization of heterogeneous materials like the microstructures and the microfluidic biochips. The robustness and accuracy of the iterative solution methods will have an enormous impact on the overall performance of the optimization routines, both in terms of computing time and memory. Simply by way of improving the accuracy and the speed of computation, this project will have a positive impact on the industries, e.g. the automotive-, medical -, and petroleum industries. The purpose of this project is to establish long term research collaboration between the two applied science institutions from Germany and Norway. The cooperation will include both exchange of students, as well as transfer of knowledge between the two research groups.