Natural preconditioning and iterative methods for saddle point systems

The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness---in terms of rapidity of convergence---is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends

Thermospheric heating at high latitudes as observed from intercosmos-Bulgaria-1300 and dynamics explorer-B

This paper reports the results of the first direct comparison of near simultaneous measurements obtained by the INTERCOSMOS-BULGARIA-1300 and the DYNAMICS EXPLORER-B satellites. The ICB-1300 is in a near circular orbit at a mean height of about 850 km. The DE-B satellite in an elliptical orbit is sometimes directly below the ICB-1300 satellite providing an opportunity to investigate the response of the thermosphere to particle fluxes from the magnetosphere. Energy fluxes in the range 0.2-15 keV are obtained from an energetic particle analyzer on board the ICB-1300 satellite. The thermospheric composition and density are obtained by a neutral gas mass spectrometer (NACS) on the DE-B satellite. During the period 20 August-20 November, 1981, observations show tht the times and locations of maxima in magnetospheric energy deposition coincide with regions of maximum thermospheric upwelling characterized by composition changes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25883/1/0000446.pd

A multiscale virtual element method for the analysis of heterogeneous media

We introduce a novel heterogeneous multiscale method for the elastic analysis of two-dimensional domains with a complex microstructure. To this end, the multiscale finite element method is revisited and originally upgraded by introducing virtual element discretizations at the microscale, hence allowing for generalized polygonal and nonconvex elements. The microscale is upscaled through the numerical evaluation of a set of multiscale basis functions. The solution of the equilibrium equations is performed at the coarse scale at a reduced computational cost. We discuss the computation of the multiscale basis functions and corresponding virtual projection operators. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples

Finite element pressure stabilizations for incompressible flow problems

Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis

Ion Temperature Estimation with Ion Trap Data from Rockets & Setellites

151-154A method is presented to estimate the ion temperature (T) alongwith the space vehicle potential (ɸs) from the ion trap measurements of collector current (I) versus the retarding grid potential (ɸs) . The relationship between I and ɸs is a non-linear equation of the unknown parameters T and ɸs The method consists of finding an appropriate theoretical curve which fits the observed data points by applying a new minimization procedure for the coefficient of variation. This method is always convergent and is illustrated by an example where the initial values chosen are widely different from the real ones

Spectral mimetic least-squares method for div-curl systems

In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test problems. For N> 1 optimal convergence rates on an orthogonal and a curvilinear mesh are observed. For N= 1 the method does not converge.Aerodynamic