A new class of the structured matrices related to the discrete skew-self-adjoint Dirac systems is introduced. The corresponding matrix identities and inversion procedure are treated. Analogs of the Schur coefficients and of the Christoffel-Darboux formula are studied. It is shown that the structured matrices from this class are always positive-definite, and applications for an inverse problem f...

In this talk we give an overview of recent developments on adaptive higher order Discontinuous Galerkin discretizations for the use in computational aerodynamics at the DLR in Braunschweig. In particular, this includes some of the most recent developments and results achieved in the EU project ADIGMA. Important quantities of interest in aerodynamic flow simulations are the aerodynamic force coe...

The search for the temperature disturbance causing transition between regular and Mach reflections in a dual solution domain is addressed in an optimization statement. The gradient of the discrepancy between the current and target flow fields was calculated using the adjoint equations. The control was determined by a gradient based optimization. The flowfield simulation is verified via a poster...

The a posteriori error evaluation based on differential approximation of a finitedifference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Lagrange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic boundi...

In this paper, an optimal control problem for the stationary NavierStokes equations in the presence of state constraints is investigated. Existence of optimal solutions is proved and first order necessary conditions are derived. The regularity of the adjoint state and the state constraint multiplier is also studied. Lipschitz stability of the optimal control, state and adjoint variables with re...

We consider parabolic SPDEs driven by purely spatial noise, and show the existence of solutions with random initial data and forcing terms. We perform error analysis for the semi-discrete stochastic finite element method applied to a class of equations with self-adjoint differential operators that are independent of time. The analysis employs the formal stochastic adjoint problem and the corres...

We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF-measures on the lattice of subgroups of the infinite symmetric group SN. The problem is closely related to the theory of characters and factor representations of gro...

Existence criteria for two positive solutions to a nonlinear, even-order stacked deltanabla boundary value problem with stacked, vanishing conditions at the two endpoints are found using the method of Green’s functions. A few examples are given for standard time scales. The corresponding even-order nabla-delta problem is also discussed in detail. c © 2003 Elsevier Science Ltd. All rights reserv...

We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here include weakly as well as strongly singular cases. We illustrate these results on two models which correspond to so-called additive strongly singular perturbations.

Recent applications’ needs/desires have motivated efforts to develop approaches for optimizing Monte Carlo calculations for global distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as response at multiple localized detectors and spectra. Recent efforts at Oak Ridge National Laboratory (ORNL) have led to the development of a variation on the Consistent Adjoint ...