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...

Almost multiplier is rather a new concept in the theory of almost functions. In this paper we discussion the boundedness of almost multipliers on some special Banach algebras, namely stable algebras. We also define an adjoint and extension for almost multiplier.

‎In this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎The equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎Such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

This paper compares the continuous and discrete adjoint-based automatic aerodynamic optimization. The objective is to study the trade-off between the complexity of the discretization of the adjoint equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution. First, this p...

In this paper we present a discrete adjoint approach for the optimization of unsteady, turbulent flows. While discrete adjoint methods usually rely on the use of the reverse mode of Automatic Differentiation (AD), which is difficult to apply to complex unsteady problems, our approach is based on the discrete adjoint equation directly and can be implemented efficiently with the use of a sparse f...

The goal of this paper is to introduce an adjoint approach for calculating stream depletion in a river that is hydraulically connected to an aquifer. This paper presents the coupled forward and adjoint equations of flow in an unconfined aquifer, a confined aquifer, and in a river. Flow in the river is assumed to follow Manning’s equation, and the river is assumed to have a wide, rectangular cro...

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl–Titchmarsh half-line m-coefficients (and 2 ...

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L = A +V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J. We establish optimal estimates on the position of the spectrum of L with respect to the spectrum of A and we obtain norm bounds on the operator angles betw...

The modal analysis and seismic response of a vibrating cantilever, with or without tip mass rotary inertia, are investigated in this study using shear deformable beam model including the effect vertical load. Based on existing approaches, an original method is proposed that does not use fourth-order uncoupled equations to determine deflection rotation. In fact, approach presented herein transfo...