The task of providing aa optimal analysis of the state of the atmosphere requires the development of novel computational tools that facilitate an efficient integeration of observational data into models. In this paper we discuss some of the computational tools developed for the assimilation of chemical data imo atmospheric models. We perform a theoretical analysis of discrete and cominuous adjoints for stiff differential equation solvers. Software tools particularly tailored for direct and adjoint sensitivity analysis of chemical systems are presented. The adjoint of the state-of-the-art model STEM-III is discussed, together with ozone assimilation results for a realistic test problem.

/pdf/computational-aspects-of-chemical-data-assimilation-into-361kpge3o0.pdf

Numerische Mathematik 1

Computational aspects of chemical data assimilation into atmospheric models

Following the phenomenological approach of gestaltists, sparse monocular depth cues such as T- and X-junctions and the local convexity are crucial to identify the shape and depth relationships of depicted objects. According to Kanizsa, mechanisms called a modal and modal completion permit to transform these local relative depth cues into a global depth reconstruction. In this paper, we propose a mathematical and computational translation of gestalt depth perception theory, from the detection of local depth cues to their synthesis into a consistent global depth perception. The detection of local depth cues is built on the response of a line segment detector (LSD), which works in a linear time relative to the image size without any parameter tuning. The depth synthesis process is based on the use of a nonlinear iterative filter which is asymptotically equivalent to the Perona-Malik partial differential equation (PDE). Experimental results are shown on several real images and demonstrate that this simple approach can account a variety of phenomena such as visual completion, transparency and self-occlusion.

Monocular Depth by Nonlinear Diffusion

The most successful equations for the modeling of ocean wave phenomena are the free–surface Euler equations. Their solutions accurately approximate a wide range of physical problems from open–ocean transport of pollutants, to the forces exerted upon oil platforms by rogue waves, to shoaling and breaking of waves in nearshore regions. These equations provide numerous challenges for theoreticians and practitioners alike as they couple the difficulties of a free boundary problem with the subtle balancing of nonlinearity and dispersion in the absence of dissipation. In this paper we give an overview of, what we term, “Boundary Perturbation” methods for the analysis and numerical simulation of this “water wave problem”. Due to our own research interests this review is focused upon the numerical simulation of traveling water waves, however, the extensive literature on the initial value problem and additional theoretical developments are also briefly discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

/pdf/boundary-perturbation-methods-for-water-waves-4kkl3fjpmk.pdf

Boundary Perturbation Methods for Water Waves

Reconstructing the Complete 3D Shape of Faces from Partial Information (Rekonstruktion der dreidimensionalen Form von Gesichtern aus partieller Information)

The design of mechanisms for building micro-tools can be viewed as a shape optimization problem with a peculiar objective function. We propose such an optimization method based on homogenization, which is called topology optimization.

/pdf/optimal-design-of-micro-mechanisms-by-the-homogenization-13o6wsktp9.pdf

Numerische Mathematik 1

Citations

Computational aspects of chemical data assimilation into atmospheric models

Monocular Depth by Nonlinear Diffusion

Boundary Perturbation Methods for Water Waves

Reconstructing the Complete 3D Shape of Faces from Partial Information (Rekonstruktion der dreidimensionalen Form von Gesichtern aus partieller Information)

Optimal design of micro-mechanisms by the homogenization method

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