A weakly overlapping domain decomposition preconditioner for the finite element solution of elliptic partial differential equations

We present a new two-level additive Schwarz domain decomposition preconditioner which is appropriate for use in the parallel finite element solution of elliptic partial differential equations (PDEs). As with most parallel domain decomposition methods each processor may be assigned one or more subdomains, and the preconditioner is such that the processors are able to solve their own subproblem(s) concurrently. The novel feature of the technique proposed here is that it requires just a single layer of overlap in the elements which make up each subdomain at each level of refinement, and it is shown that this amount of overlap is sufficient to yield an optimal preconditioner. Some numerical experiments-posed in both two and three space dimensions-are included to confirm that the condition number when using the new preconditioner is indeed independent of the level of mesh refinement on the test problems considered

Prevention of stroke in atrial fibrillation: desired and real

The analysis of the data ot the register of patients with atrial fibrillation (retrospective part -1860 patients, prospective observation - 498 patients), which were observed in the period 2009-2017 in outpatient facilities and hospitals in Moscow, is presented. The dynamics of the appointment of antithrombotic drugs of various groups in routine clinical practice and in conditions of observation in an anticoagulant room on the basis of a day hospital were studied. The results are compared with data from other domestic observational studies of patients with atrial fibrillation. Other ways to improve the quality of antithrombotic prophylaxis are discussed.Представлен анализ данных регистра пациентов с фибрилляцией предсердий (ретроспективная часть -1860 пациентов, проспективное наблюдение - 498 пациентов), наблюдавшихся в период 2009-2017годы в амбулаторных учреждениях и стационарах г. Москвы. Исследована динамика назначения антитромботических препаратов различных групп в рутинной клинической практике и в условиях наблюдения в антикоагулянтном кабинете на базе дневного стационара. Результаты сопоставлены с данными других отечественных наблюдательных исследований пациентов с фибрилляцией предсердий. Обсуждаются другие способы повышения качества антитромботической профилактики

Multilevel preconditioning operators on locally modified grids

Systems of grid equations that approximate elliptic boundary value problems on locally modified grids are considered. The triangulation, which approximates the boundary with second order of accuracy, is generated from an initial uniform triangulation by shifting nodes near the boundary according to special rules. This ”locally modified” grid possesses several significant features: this triangulation has a regular structure, the generation of the triangulation is rather fast, this construction allows to use multilevel preconditioning (BPX-like) methods. The proposed iterative methods for solving elliptic boundary value problems approximately are based on two approaches: The fictitious space method, i.e. the reduction of the original problem to a problem in a

Density of quasilocalized states along the resonance curves in continuum = Особенности плотности квазилокальных состояний вдоль резонансных кривых в сплошном спектре

Densities of quasilocalized states are calculated and analyzed for a one-dimensional system with a point defect and an FCC crystal with a planar defect. The density of states displays a pronounced peak that is positioned near the energy (frequency) of resonant transmission of a particle (wave) through the defect but slightly shifted from this energy. The peak nears the resonance frequency and sharpens, tending to a Ϩ function, as the continuum edge is approachedyesBelgorod State Universit

Density of quasilocalized states along the resonance curves in continuum=Особенности плотности квазилокальных состояний вдоль резонансных кривых в сплошном спектре

yesDensities of quasilocalized states are calculated and analyzed for a one-dimensional system with a point defect and an FCC crystal with a planar defect. The density of states displays a pronounced peak that is positioned near the energy (frequency) of resonant transmission of a particle (wave) through the defect but slightly shifted from this energy. The peak nears the resonance frequency and sharpens, tending to a Ϩ function, as the continuum edge is approachedBelgorod State Universit

Multilevel preconditioning operators on locally modified grids

Systems of grid equations that approximate elliptic boundary value problems on locally modified grids are considered. The triangulation, which approximates the boundary with second order of accuracy, is generated from an initial uniform triangulation by shifting nodes near the boundary according to special rules. This "locally modified" grid possesses several significant features: this triangulation has a regular structure, the generation of the triangulation is rather fast, this construction allows to use multilevel preconditioning (BPX-like) methods. The proposed iterative methods for solving elliptic boundary value problems approximately are based on two approaches: The fictitious space method, i.e. the reduction of the original problem to a problem in an auxiliary (fictitious) space, and the multilevel decomposition method, i.e. the construction of preconditioners by decomposing functions on hierarchical grids. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh size. The construction of the grid and the preconditioning operator for the three dimensional problem can be done in the same way