C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Modelling, Analysis and Simulation Modelling, Analysis and SimulationImproving the parallel performance of a domain decomposition preconditioning technique in the Jacobi-Davidson method for large scale eigenvalue problems M. Genseberger This report discusses the aspect that the original strategy can be improved. For large scale eigenvalue problems that need a massively parallel treatment this aspect turns out to be nontrivial. The impact on the parallel performance will be shown by results of scaling experiments up to 1024 cores. REPORT MAS-R0805 AUGUST 20082000 Mathematics Subject Classification: 65F15, 65N25, 65F10, 65N55, 65Y05

The correction equation in the Jacobi-Davidson method is effective in a subspace orthogonal to the current eigenvector approximation, while for the continuation of the process only vectors orthogonal to the search subspace are of importance. Such a vector is obtained by orthogonalizing the (approximate) solution of the correction equation against the search subspace. As an alternative, a variant of the correction equation can be formulated that is restricted to the subspace orthogonal to the current search subspace. In this paper, we discuss the effectivity of this variant. Our investigation is also motivated by the fact that the restricted correction equation can be used for avoiding stagnation in case of defective eigenvalues. Moreover, this equation plays a key role in the inexact TRQ method [19].

Although phosphorus loadings are considered the main pressure for most shallow lakes, winddriven resuspension can cause additional problems for these aquatic ecosystems. We quantified the potential effectiveness of measures to reduce the contribution of resuspended sediments, resulting from wind action, to the overall light attenuation for three comparable shallow peat lakes with poor ecological status in the Netherlands: Loosdrecht, Nieuwkoop, and Reeuwijk (1.8-2.7 m depth, 1.6-2.5 km fetch). These measures are: 1. wave reducing barriers, 2. water level fluctuations, 3. capping of the sediment with sand, and 4. combinations of above. Critical shear stress of the sediments for resuspension (V crit), size distribution, and optical properties of the suspended material were quantified in the field (June 2009) and laboratory. Water quality monitoring data (2002-2009) showed that light attenuation by organic suspended matter in all lakes is high. Spatial modeling of the impact of these measures showed that in Lake Loosdrecht limiting wave action can have significant effects (reductions from 6% exceedance to 2% exceedance of V crit), whereas in Lake Nieuwkoop and Lake Reeuwijk this is less effective. The depth distribution and shape of Lake Nieuwkoop and Lake Reeuwijk limit the role of wind-driven resuspension in the total suspended matter concentration. Although the lakes are similar in general appearance (origin, size, and depth range) measures suitable to improve their ecological status differ. This calls for care when defining the programme of measures to improve the ecological status of a specific lake based on experience from other lakes.