Domain Decomposition and Multilevel Techniques for Preconditioning Operators

Introduction In recent years, domain decomposition methods have been used extensively to efficiently solve boundary value problems for partial differential equations in complex{form domains. On the other hand, multilevel techniques on hierarchical data structures also have developed into an effective tool for the construction and analysis of fast solvers. But direct realization of multilevel techniques on a parallel computer system for the global problem in the original domain involves difficult communication problems. I this paper, we present and analyze a combination of these two approaches: domain decomposition and multilevel decomposition on hierarchical structures to design optimal preconditioning operators

SERUM LEVEL AND PRODUCTION OF CYTOKINES BY PBMC IN PATIENTS WITH ATOPIC DERMATITIS

The рарег presents the results of measurements of cytokine levels in serum and conditioned medium of PBMC cultures from the patients with atopic dermatitis with the exacerbation and remission in comparison with the healthy donors. We have shown that the serum levels of the key cytokines IL-5 and IL-13, proinflammatory cytokines IL-1β and IL-6 and the main Th1 cytokine — IFNγ — were higher compared to healthy donors. In the conditioned media of peripheral blood mononuclear cells in contrast, we have found a significant decrease of the spontaneous secretion of key cytokines IL-10 and IL-17. We have shown that the stimulated secretion of IL-5 and IL-13, IL-12 and INF-γ is significantly reduced in comparison with the control level. Only IL-1β revealed a statistically significant higher level of stimulated secretion without exacerbation of atopic dermatitis. The contemporary therapy has no effect on cytokine production

ОСОБЕННОСТИ ПРОЦЕССОВ ФОРМИРОВАНИЯ МИКРОВКЛЮЧЕНИЙ В КРИСТАЛЛАХ МУЛЬТИКРЕМНИЯ, ВЫРАЩЕННЫХ ИЗ МЕТАЛЛУРГИЧЕСКОГО РАФИНИРОВАННОГО КРЕМНИЯ МЕТОДОМ БРИДЖМЕНА—СТОКБАРГЕРА

Specific features of impurity distribution in multisilicon crystals grown from refined metallurgical silicon by the vertical Bridgman−Stockbarger method have been studied. The chemical composition of metallurgical silicon and multisilicon ingots grown under varying crystallization conditions have been analyzed by mass spectrometry with inductively coupled plasma (ICP−MS) and X−ray spectral electron probe microanalysis (RSMA). The size and distribution nature of microinclusions on the polished etched surfaces and chips of multisilicon crystals have been studied. We have revealed multicomponent microinclusions up to 100 micron in size in the multisilicon ingots grown at high crystallization speeds (1.5 cm/h) and low−component microinclusions one micron in size in the multisilicon ingots grown at a crystallization speed of from 0.5 to 1 cm/h.Исследованы особенности распределения примесей в кристаллах мультикремния, выращенных из металлургического рафинированного кремния вертикальным методом Бриджмена—Стокбаргера. Методами масс−спектрометрии с индуктивно связанной плазмой и рентгеноспектрального электронно−зондового микроанализа проведены комплексные исследования химического состава металлургического кремния и слитков мультикремния, выращенных при различных условиях кристаллизации. Изучены размеры и характер распределения микровключений на полированных, травленых поверхностях и сколах кристаллов мультикремния. Выявлены многокомпонентные (состоящие из трех и более элементов) микровключения размером до 100 мкм в слитках мультикремния, выращенных при высоких скоростях (1,5 см/ч) кристаллизации, и малокомпонентные микровключения размером до 1 мкм в слитках мультикремния, полученных при скоростях кристаллизации от 0,5 до 1 см/ч

Variable preconditioning procedures for elliptic problems

For solving systems of grid equations approximating elliptic boundary value problems a method of constructing variable preconditioning procedures is presented. The main purpose is to discuss how an efficient preconditioning iterative procedure can be constructed in the case of elliptic problems with disproportional coefficients, e.g. equations with a large coefficient in the reaction term (or a small diffusion coefficient). The optimality of the suggested technique is based on fictitious space and multilevel decom- position methods. Using an additive form of the preconditioners, we intro- duce factors into the preconditioners to optimize the corresponding conver- gence rate. The optimization with respect to these factors is used at each step of the iterative process. The application of this technique to two-level $p$-hierarchical precondi- tioners and domain decomposition methods is considered too

The hierarchical preconditioning having unstructured grids

In this paper we present two hierarchically preconditioned methods for the fast solution of mesh equations that approximate 2D-elliptic boundary value problems on unstructured quasi uniform triangulations. Based on the fictitious space approach the original problem can be embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner by decomposing functions on it are well defined. We implemented the corresponding Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration having optimal computational costs. Several numerical examples demonstrate the efficiency of the artificially constructed hierarchical methods which can be of importance in the industrial engineering, where often only the nodal coordinates and the element connectivity of the underlying (fine) discretization are available