The analysis of multigrid algorithms for cell centered finite difference methods

In this paper, we examine multigrid algorithms for cell centered finite difference approximations of second order elliptic boundary value problems. The cell centered application gives rise to one of the simplest non-variational multigrid algorithms. We shall provide an analysis which guarantees that the W-cycle and variable V-cycle multigrid algorithms converge with a rate of iterative convergence which can be bounded independently of the number of multilevel spaces. In contrast, the natural variational multigrid algorithm converges much more slowly.     

Comparison of the GMRES and ORTHOMIN for the black oil model in porous media

This paper deals with the application of the GMRES algorithm to a three‐dimensional, three‐phase black oil model used in petroleum reservoir simulation. Comparisons between the GMRES and ORTHOMIN algorithms in terms of storage and total flops per restart step are given. Numerical results show that the GMRES is faster than the ORTHOMIN for large‐scale simulation problems. The GMRES uses only as much as 63% of the CPU time of the ORTHOMIN for some of the problems tested. Copyright © 2005 John Wiley & Sons, Ltd.     

Localization of sphingomyelin in cholesterol domains by imaging mass spectrometry

The location of each lipid in a palmitoyloleoylphosphatidylcholine/18:0 sphingomyelin/cholesterol monolayer system is laterally resolved using imaging time-of-flight secondary ion mass spectrometry (TOF-SIMS) without the necessity of adding fluorescent labels. This system of coexisting immiscible liquid phases shows cholesterol domains with sizes and shapes comparable to those in the fluorescence microscopy literature. The results show that SM localizes with cholesterol and that palmitoyloleoylphosphatidylcholine is excluded. Moreover, the segregation is not complete, and there is a small amount of both phospholipids distributed throughout.     

Sphingomyelin/phosphatidylcholine and cholesterol interactions studied by imaging mass spectrometry

Label-free imaging mass spectrometry is utilized the first time to study lipid-lipid interactions in a model membrane system. Ternary lipid mixtures of cholesterol (CH), sphingomyelin (SM), and phosphatidylcholine (PC) on supported Langmuir-Blodgett films are investigated as a mimic of the cellular membrane. The unique chemical specificity and imaging capability allow identification and localization of each lipid molecule in the membranes. The SM and PC in each ternary mixture vary in their acyl chain saturation with both, either, or neither one double bonded at the same position of their acyl chain. For the ternary mixtures with SM and PC both saturated or unsaturated, all the lipids are evenly distributed in the molecule-specific images. However, domain structures were observed for the two mixtures with either SM or PC unsaturated. In both films, the saturated lipid, whether it is SM or PC, colocalized with CH while the unsaturated lipid was excluded from the CH domains. These results strongly suggest that acyl chain saturation, rather than the specific interactions between SM and CH, is the dominating factor for SM colocalization with CH in the raft areas of the cellular membranes.