A combined technique for solution of PDE's via the generalized domain decomposition method

The Domain Decomposition Method (DDM) is a powerful approach to solving many types of PDE's. DDM is especially suitable for massively parallel computers. In the past, most research on DDM has focused on the domain splitting technique. In this paper, we focus our attention on use of a combination of techniques to solve each subproblem. The central question with DDM is that of how to deal with the pseudoboundary conditions. Here, we introduce a set of operators which act on the pseudo-boundaries in the solution process, referring to this new procedure as the “Generalized Domain Decomposition Method (GDDM).” We have already obtained convergence factors for GDDM with certain classes of PDE's. These convergence factors show that we can derive exact solutions of the whole problem for certain types of PDE's, and can get superior speed of convergence for other types.     

Continental warming preceding the Palaeocene-Eocene thermal maximum

Marine and continental records show an abrupt negative shift in carbon isotope values at ～55.8?Myr ago. This carbon isotope excursion (CIE) is consistent with the release of a massive amount of isotopically light carbon into the atmosphere and was associated with a dramatic rise in global temperatures termed the Palaeocene-Eocene thermal maximum (PETM). Greenhouse gases released during the CIE, probably including methane, have often been considered the main cause of PETM warming. However, some evidence from the marine record suggests that warming directly preceded the CIE, raising the possibility that the CIE and PETM may have been linked to earlier warming with different origins. Yet pre-CIE warming is still uncertain. Disentangling the sequence of events before and during the CIE and PETM is important for understanding the causes of, and Earth system responses to, abrupt climate change. Here we show that continental warming of about 5?°C preceded the CIE in the Bighorn Basin, Wyoming. Our evidence, based on oxygen isotopes in mammal teeth (which reflect temperature-sensitive fractionation processes) and other proxies, reveals a marked temperature increase directly below the CIE, and again in the CIE. Pre-CIE warming is also supported by a negative amplification of δ(13)C values in soil carbonates below the CIE. Our results suggest that at least two sources of warming-the earlier of which is unlikely to have been methane-contributed to the PETM.     

Parallel genetic algorithm on PVM

In this paper we describe an implementation of some kinds of parallel genetic algorithms on the PVM. Parallel Virtual Machine, a portable parallel environment. We give details of a genetic algorithm running on many small subpopulations with an occasional identification and exchange of their useful information among subpopulations by means of message-passing functions of PVM. In this work, experiments were done to compare the parallel genetic algorithm and traditional sequential genetic algorithms.