--, FETI-DP with different scalings for adaptive coarse spaces, PAMM.
We also introduce cost-efficient variants of the methods in [7, 23] that are based on the ideas of an economic variant of the deluxe scaling given in ; deluxe scaling was introduced in ; see also [2, 5, 6, 20, 29, 33].
Alternatively, we use the approach in, e.g., [25, 34], and introduce scaling weights by
This first approach has been proposed in  and relies on deluxe scaling. In the second approach, first proposed in , any kind of scaling is possible as long it satisfies the partition of unity property (4.2).
Let [D.sub.ij.sup.(l)], l = i, j, be scaling matrices such that
In the following, we define a scaling for the FETI-DP and BDDC method denoted as deluxe scaling, which was first introduced in ; for further applications, see [2, 5, 6, 20, 29, 33].
These estimates did not involve suppositions regarding the scaling of D or M with respect to L.
The scaling of D (reported in meters) with respect to L was determined for 50 protozoa species, 19 invertebrates species, 17 vertebrate species, 47 unicellular algal species, 10 volvocalean species, and 610 multicellular terrestrial plant species.
The scaling of selected groupings of plants and animals was explored.
Scaling formulas for M and D were determined by least-squares regression against L.
Analysis indicated that the scaling exponent for animals did not differ from that of plants ([[Alpha].sub.RMA]= 2.81 [+ or -] 0.061 and [[Alpha].sub.RMA] = 2.95 [+ or -] 0.093, respectively; see table 1).
Statistical analyses (not given) showed that the scaling exponent of the combined data set was biased by the preponderance of data from plant species.