ParIC : A Family of Parallel Incomplete Cholesky Preconditioners

A class of parallel incomplete factorization preconditionings for the solution of large linear systems is investigated. The approach may be regarded as a generalized domain decomposition method. Adjacent subdomains have to communicate during the setting up of the precon­ ditioner, and during the application of the preconditioner. Overlap is not necessary to achieve high performance. Fill­in levels are considered in a global way. If necessary, the technique may be implemented as a global re­ordering of the unknowns. Experimental results are reported for two­dimensional problems

OBV methods. [For solving linear systems Ax = b]

The properties of OB relaxation of Varga iterative methods are investigated, with particular emphasis on diagonal relaxation. Generalizations of the results of Beauwens and Quenon (SIAM J. Numer. Anal., 13, 615-643 (1976)) are presented, and their relations with the works of Axelsson and Gustafsson are indicated. Finally, the combination of this formalism with the Axelsson-Gustafsson analysis to enlarge the scope of the latter is illustrated

Fluid transport and cystogenesis in autosomal dominant polycystic kidney disease

Autosomal dominant polycystic kidney disease (ADPKD) is the most frequent inherited nephropathy. The development and enlargement of cysts in ADPKD requires tubular cell proliferation, abnormalities in the extracellular matrix and transepithelial fluid secretion. Multiple studies have suggested that fluid secretion across ADPKD cyst-lining cells is driven by the transepithelial secretion of chloride, mediated by the apical CFTR channel and specific basolateral transporters. The whole secretory process is stimulated by increased levels of cAMP in the cells, probably reflecting modifications in the intracellular calcium homeostasis and abnormal stimulation of the vasopressin V2 receptor. This review will focus on the pathophysiology of fluid secretion in ADPKD cysts, starting with classic, morphological and physiological studies that were followed by investigations of the molecular mechanisms involved and therapeutic trials targeting these pathways in cellular and animal models and ADPKD patients. This article is part of a Special Issue entitled: Polycystic Kidney Disease