A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Rational molecular dynamics scheme for predicting optimum concentration loading of nano-additive in phase change materials

The present study deals with the diffusion and phase transition behaviour of paraffin reinforced with carbon nano-additives namely graphene oxide (GO) and surface functionalized single walled carbon nanotubes (SWCNT). Bulk disordered systems of paraffin hydrocarbons impregnated with carbon nano-additives have been generated in realistic equilibrium conformations for potential application as latent heat storage systems. Ab initio molecular dynamics(MD) in conjugation with COMPASS forcefield has been implemented using periodic boundary conditions. The proposed scheme allows determination of optimum nano-additive loading for improving thermo-physical properties through analysis of mass, thermal and transport properties; and assists in determination of composite behaviour and related performance from microscopic point of view. It was observed that nanocomposites containing 7.8% surface functionalised SWCNT and 55% GO loading corresponds to best latent heat storage system. The propounded methodology could serve as a by-pass route for economically taxing and iterative experimental procedures required to attain the optimum composition for best performance. The results also hint at the large unexplored potential of ab-initio classical MD techniques for predicting performance of new nanocomposites for potential phase change material applications. (C) 2015 Author(s).

Onset of plane layer magnetoconvection at low Ekman number

We study the onset of magnetoconvection between two infinite horizontal planes subject to a vertical magnetic field aligned with background rotation. In order to gain insight into the convection taking place in the Earth's tangent cylinder, we target regimes of asymptotically strong rotation. The critical Rayleigh number Ra-c and critical wavenumber a(c) are computed numerically by solving the linear stability problem in a systematic way, with either stress-free or no-slip kinematic boundary conditions. A parametric study is conducted, varying the Ekman number E (ratio of viscous to Coriolis forces) and the Elsasser number. (ratio of the Lorentz force to the Coriolis force). E is varied from 10(-9) to 10(-2) and. from 10(-3) to 1. For a wide range of thermal and magnetic Prandtl numbers, our results verify and confirm previous experimental and theoretical results showing the existence of two distinct unstable modes at low values of E-one being controlled by the magnetic field, the other being controlled by viscosity (often called the viscous mode). It is shown that oscillatory onset does not occur in the range of parameters we are interested in. Asymptotic scalings for the onset of these modes are numerically confirmed and their domain of validity is precisely quantified. We show that with no-slip boundary conditions, the asymptotic behavior is reached for E < 10(-6) and establish a map in the (E, Lambda) plane. We distinguish regions where convection sets in either through the magnetic mode or through the viscous mode. Our analysis gives the regime in which the transition between magnetic and viscous modes may be observed. We also show that within the asymptotic regime, the role played by the kinematic boundary conditions is minimal. (C) 2015 AIP Publishing LLC.

PLUTO plus : Near-Complete Modeling of Affine Transformations for Parallelism and Locality

Affine transformations have proven to be very powerful for loop restructuring due to their ability to model a very wide range of transformations. A single multi-dimensional affine function can represent a long and complex sequence of simpler transformations. Existing affine transformation frameworks like the Pluto algorithm, that include a cost function for modern multicore architectures where coarse-grained parallelism and locality are crucial, consider only a sub-space of transformations to avoid a combinatorial explosion in finding the transformations. The ensuing practical tradeoffs lead to the exclusion of certain useful transformations, in particular, transformation compositions involving loop reversals and loop skewing by negative factors. In this paper, we propose an approach to address this limitation by modeling a much larger space of affine transformations in conjunction with the Pluto algorithm's cost function. We perform an experimental evaluation of both, the effect on compilation time, and performance of generated codes. The evaluation shows that our new framework, Pluto+, provides no degradation in performance in any of the Polybench benchmarks. For Lattice Boltzmann Method (LBM) codes with periodic boundary conditions, it provides a mean speedup of 1.33x over Pluto. We also show that Pluto+ does not increase compile times significantly. Experimental results on Polybench show that Pluto+ increases overall polyhedral source-to-source optimization time only by 15%. In cases where it improves execution time significantly, it increased polyhedral optimization time only by 2.04x.

Inverse Polynomial Based Explicit Guidance for Lunar Soft Landing During Powered Braking

In this paper an explicit guidance law for the powered descent phase of the soft lunar landing is presented. The descent trajectory, expressed in polynomial form is fixed based on the boundary conditions imposed by the precise soft landing mission. Adapting an inverse model based approach, the guidance command is computed from the known spacecraft trajectory. The guidance formulation ensures the vertical orientation of the spacecraft during touchdown. Also a closed form relation for the final flight time is proposed. The final time is expressed as a function of initial position and velocity of the spacecraft ( at the start of descent) and also depends on the desired landing site. To ensure the fuel minimum descent the proposed explicit method is extended to optimal guidance formulation. The effectiveness of the proposed guidance laws are demonstrated with simulation results.