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Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.
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(2010)
Increasing Scots pine (Pinus sylvestris L.) mortality has been recently observed in the dry inner valleys of the European Alps. Besides drought, infection with pine mistletoe (Viscum album ssp. austriacum) seems to play an important role in the mortality dynamics of Scots pines, but how mistletoes promote pine decline remains unclear. To verify whether pine mistletoe infection weakens the host via crown degradation, as observed for dwarf mistletoes, we studied the negative effects of pine mistletoe infestation on the photosynthetic tissues and branch growth of pairs of infested and non-infested branches. Pine mistletoe infection leads to crown degradation in its host by reducing the length, the radial increment, the ramification, the needle length and the number of needle years of the infested branches. This massive loss in photosynthetic tissue results in a reduction in primary production and a subsequent decrease in carbohydrate availability. The significant reduction in needle length due to mistletoe infection is an indication for a lower water and nutrient availability in infested branches. Thus, mistletoe infection might lead to a decrease in the availability of water and carbohydrates, the two most important growth factors, which are already shortened due to the chronic drought situation in the area. Therefore, pine mistletoe increases the risk of drought-induced mortality of its host when growing in a xeric environment.