The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

Anthropogenic aerosol fraction over the Indian region: model simulations versus multi-satellite data analysis

Anthropogenic aerosols play a crucial role in our environment, climate, and health. Assessment of spatial and temporal variation in anthropogenic aerosols is essential to determine their impact. Aerosols are of natural and anthropogenic origin and together constitute a composite aerosol system. Information about either component needs elimination of the other from the composite aerosol system. In the present work we estimated the anthropogenic aerosol fraction (AF) over the Indian region following two different approaches and inter-compared the estimates. We espouse multi-satellite data analysis and model simulations (using the CHIMERE Chemical transport model) to derive natural aerosol distribution, which was subsequently used to estimate AF over the Indian subcontinent. These two approaches are significantly different from each other. Natural aerosol satellite-derived information was extracted in terms of optical depth while model simulations yielded mass concentration. Anthropogenic aerosol fraction distribution was studied over two periods in 2008: premonsoon (March-May) and winter (November-February) in regard to the known distinct seasonality in aerosol loading and type over the Indian region. Although both techniques have derived the same property, considerable differences were noted in temporal and spatial distribution. Satellite retrieval of AF showed maximum values during the pre-monsoon and summer months while lowest values were observed in winter. On the other hand, model simulations showed the highest concentration of AF in winter and the lowest during pre-monsoon and summer months. Both techniques provided an annual average AF of comparable magnitude (similar to 0.43 +/- 0.06 from the satellite and similar to 0.48 +/- 0.19 from the model). For winter months the model-estimated AF was similar to 0.62 +/- 0.09, significantly higher than that (0.39 +/- 0.05) estimated from the satellite, while during pre-monsoon months satellite-estimated AF was similar to 0.46 +/- 0.06 and the model simulation estimation similar to 0.53 +/- 0.14. Preliminary results from this work indicate that model-simulated results are nearer to the actual variation as compared to satellite estimation in view of general seasonal variation in aerosol concentrations.