Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension $k$ is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by $76\times$ times the computational cost of the on-line stage of standard POD for configurations using more than $300,000$ model variables. The tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table

EXTREME PROGRAMMING AND RATIONAL UNIFIED PROCESS – CONTRASTS OR SYNONYMS?

The agile movement has received much attention in software engineering recently. Established methodologies try to surf on the wave and present their methodologies a being agile, among those Rational Unified Process (RUP). In order to evaluate the statements we evaluate the RUP against eXtreme Programming (XP) to find out to what extent they are similar end where they are different. We use a qualitative approach, utilizing a framework for comparison. RUP is a top-down solution and XP is a bottom-up approach. Which of the two is really best in different situations has to be investigated in new empirical studies.extreme programming

How to Stabilize the Cereals Market in a Transition Economy

The Romanian cereals market is in a state of transition, because the grain marketing system is characterized by high risk for market participants. The current situation of grain market is used to estimate the necessity solutions to stabilize the market.grain grading system, price monitory systems, commodity exchange, Agribusiness, Q13,

CHARACTERISTICS AND EVALUATION METHODS OF THE CASE TOOLS

The acronym CASE – Computer Assisted Software Engineering – is the term used to indicate a collection of methods, tools and processes used in the development of software products with the assistance of the computer.IPSE