L. D’Amore1 , R. Arcucci2 , L. Marcellino3 and A. Murli2 1. Department of Mathematics and Application, University of Naples Federico II, Italy. 2. Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC), Italy. 3. Department of Applied Sciences, University of Naples Parthenope, Italy. Received 30 January, 2012; accepted in revised form 22 December, 2012 Abstract: The most significant features of Data Assimilation (DA) are that both the models and the observations are very large and non-linear (of order at least O(108 )). Further, DA is an ill-posed inverse problem. Such properties make the numerical solution of DA very difficult so that, as stated in , ”solving this problem in ”real-time” it is not always pos- sible and many different approximations to the basic assimilation schemes are employed”. Thus, the exploitation of advanced computing environments is mandatory, reducing the computational cost to a suitable turnaround time. This activity should be done according to a co-design methodology where software requirements drive hardware design decisions and hardware design constraints motivate changes in the software design to better fit within those constraints. In this paper, we address high performance computation issues of the three dimensional DA scheme underlying the oceanographic 3D-VAR assimilation scheme, named Ocean- VAR, developed at CMCC (Centro Euro Mediterraneo per i Cambiamenti Climatici), in Italy. The aim is to develop a parallel software architecture which is able to effectively take advantage of the available high performance computing resources. c 2012 European Society of Computational Methods in Sciences, Engineering and Technology
Devendra Kumar, M.K. Kadalbajoo Received 5 August, 2011; accepted in revised form 22 July, 2012 Abstract: This paper is devoted to the numerical study for a class of boundary value problems of second-order differential equations in which the highest order derivative is multiplied by a small parameter ǫ and both the convection and reaction terms are with negative shift. To obtain the parameter-uniform convergence, a piecewise uniform mesh (Shishkin mesh) is constructed, which is dense in the boundary layer region and coarse in the outer region. Parameter-uniform convergence analysis of the method has been given. The method is shown to have almost second-order parameter-uniform convergence. The effect of small delay δ on the boundary layer has also been discussed. To demonstrate the performance of the proposed scheme several examples having boundary layers have been carried out. The maximum absolute errors are presented in the tables.
Received 14 December, 2010; accepted in revised form 25 April, 2012 Abstract: A three-field finite element scheme designed for solving systems of partial dif- ferential equations governing stationary viscoelastic flows is studied. It is based on the simulation of a time-dependent behavior. Once a classical time-discretization is performed, the resulting three-field system of equations allows for a stable approximation of velocity, pressure and extra stress tensor, by means of continuous piecewise linear finite elements, in both two and three dimension space. This is proved to hold for the linearized form of the system. An advantage of the new formulation is the fact that it implicitly provides an algo- rithm for the iterative resolution of system non-linearities. Convergence in an appropriate sense applying to these three flow fields is demonstrated.