Alf Emil Løvgren received his Ph.D. degree from the Norwegian University of Science and Technology in 2005, for work done on reduced basis modeling of complex flow systems. This work has since been continued in collaboration with Einar Rønquist at NTNU, Yvon Maday at Paris VI, and Simone Deparis at EPFL. The reduced basis modeling project involves the numerical solution of PDEs on complex geometries, using both finite elements and spectral elements. In principle, the reduced basis method applies to all problems where the same PDE is solved for many different instantiations of some parameter, and compared to traditional solvers the speed-up is tremendous. In the ongoing project the geometry of the computational domain is used as the variable parameter.

Recent activity also includes fluid-structure interaction problems arising in the modeling of the spinal cord and the surrounding cerebrospinal fluid. Modeling fluid-structure interaction problems requires huge computational resources, and a long time goal is to combine the reduced basis modeling with fluid-structure interaction problems in order to speed up the computations.