The Helmholtz equation describes linear, time-harmonic wave problems that arise in engineering applications such as aeronautics and electromagnetic applications. Its discretization by means of finite elements leads to indefinite, severely ill-conditioned problems for which standard iterative methods encounter difficulties. While direct solvers can be employed in 2D, in 3D they are prohibitive due to their costs. The development of iterative techniques and preconditioners, that are able to cope with the Helmholtz equation, is hence an important task.
Due to their inherent parallelism, domain decomposition methods are able to handle large problems and are hence of particular interest when dealing with the typically large systems arising from Helmholtz problems. The aim of this project is the development of a domain decomposition method that is an efficient preconditioner for the Helmholtz equation, building on the methods that have already been developed in this field.
This project is supported by the HP2C initiative.
Prof. Dr. Rolf Krause; ; PI; ICS Institute of Computational Science