Volume 32, Issue 4

A novel analytical approach to the synthesis of electrical (e.g., analogue, digital or microwave) filters is proposed. This approach allows to obtain the lowest possible order filters with given involved specification including, e.g., many pass- and stopbands, narrow transition bands, high attenuation at the stopbands and low magnitude oscillations at the passbands. Comparison to other existing approaches is given.

The paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

This work is devoted to computations of invariant pairs associated with separated groups of finite eigenvalues of large regular non-linear matrix pencils. It is proposed to combine the method of successive linear problems with a Newton-type method designed for partial linear eigenproblems and a deflation procedure. This combination is illustrated with a typical hydrodynamic spatial stability problem.

A system of Navier-Stokes equations with a right-hand side is considered in the case when the system approximately describes the motion of a thin layer of a viscous incompressible fluid in an annular domain under the action of external electromagnetic force. The problem possesses an unstable two-stream nonstationary main flow and a set of quasistationary solutions of vortex type for the tested range of parameters. A method of study of the general dynamic pattern is proposed in the paper. The method is based on the construction of control boundary conditions specified on the internal boundary of the annulus and providing the stabilization of considered unstable modes. The problem of boundary stabilization of the main and secondary flows is also solved numerically and we obtained that it is sufficient to take into account only a part of unstable modes in the construction of stabilizing conditions for the main flow. The method based on the partial stabilization of the main flow is first proposed for stabilization of secondary flows, which essentially simplifies the implementation of the algorithm. Formulations of the problems and numerical algorithms are presented.

We propose and investigate a new nonconforming finite element method for the diffusion equation on general triangular and tetrahedral meshes. We prove that the method results in the condensed system for the Lagrange multipliers with a diagonally dominant M-matrix. We also prove that the proposed method is monotone with respect to the solution function on the interfaces between mesh cells.

The paper is related to a coupled problem describing piezoelectric effects in an elastic body. For this problem, we deduce majorants of the distance between the exact solution and any approximation in the respective energy class of functions satisfying the boundary conditions. The majorants are fully computable and do not contain mesh dependent constants. They vanish if and only if an approximate solution coincides with the exact one and provide guaranteed upper bounds of errors in terms of the natural energy norm associated with the coupled problem studied.

The existence of a nonsingular matrix is proved for any space of square symmetric matrices with a trivial quadratic kernel. Some corollaries from this result are obtained for construction of solvers of nonlinear equations and problems of conditional optimization with a Jacobi matrix of incomplete rank based on the theory of p -regularity for p = 2. Some remarks for the case p ⩾ 3 are presented.