Absolute value preconditioning for symmetric indefinite linear systems

We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method with the inverse of the absolute value of the matrix as a preconditioner converges to the exact solution of the system in at most two steps. Neither the exact absolute value of the matrix nor its exact inverse are computationally feasible to construct in general. However, we provide a practical example of an SPD preconditioner that is based on the suggested approach. In this example we consider a model problem with a shifted discrete negative Laplacian, and suggest a geometric multigrid (MG) preconditioner, where the inverse of the matrix absolute value appears only on the coarse grid, while operations on finer grids are based on the Laplacian. Our numerical tests demonstrate practical effectiveness of the new MG preconditioner, which leads to a robust iterative scheme with minimalist memory requirements

Method of variational calculation of influence of the propulsion plants of forestry machines upon the frozen and thawing soil grounds

The forests, which grow in the conditions of complete expansion of the perpetually frozen ground, are unique forests in accordance with their taxational characteristics, quality indicators of the felled timber, and the ecological functions, which these forests perform in the nature. They are characterised by the low biological productivity, as well as by the high vulnerability due to climatological changes and human economic activities. It is fair to say that conservation of the permafrost is one of the main functions of the forests, which grow within the cryolithozone. Because of this, it is necessary to ensure special regimes for the forestry management and forest exploitation within the forests of the cryolithozone. We formulated the variational problem in order to determine influence of the changeability of the physical and mechanical properties of the thawing soil ground at the boundary with the permafrost ground. © 2019 SERSC

Detection of mechanical resonance of a single-electron transistor by direct current

We have suspended an Al based single-electron transistor whose island can resonate freely between the source and drain leads forming the clamps. In addition to the regular side gate, a bottom gate with a larger capacitance to the SET island is placed underneath to increase the SET coupling to mechanical motion. The device can be considered as a doubly clamped Al beam that can transduce mechanical vibrations into variations of the SET current. Our simulations based on the orthodox model, with the SET parameters estimated from the experiment, reproduce the observed transport characteristics in detail.Comment: 4 pages, 3 figure

JUSTIFICATION OF THE NEED FOR A UNIFIED APPROACH TO THE MANAGEMENT OF THE PUBLIC EXTERNAL DEBT OF THE PARTICIPATING COUNTRIES OF THE EURASIAN ECONOMIC UNION

In article it is told about the Eurasian Economic Union, stages of his formation and features of his budget, the question of the main macroeconomic indicators of the countries-participants of the Union, and also a question of dynamics and structure of their public debt

Metal-Insulator Transition in 2D: Experimental Test of the Two-Parameter Scaling

We report a detailed scaling analysis of resistivity \rho(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the \rho(T,n) data.Comment: 4 pages, 4 figures, 1 tabl