Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Annoyance and welfare costs from the presence of renewable energy power plants: an application of the contingent valuation method

Sustainability is frequently defined by its three pillars: economically viable, socially equitable, and environmentally bearable. Consequently the evaluation of the sustainability of any decision, public or private, requires information on these three dimensions. This paper focuses on social sustainability. In the context of renewable energy sources, the examination of social sustainability requires the analysis of not only the efficiency but also the equity of its welfare impacts. The present paper proposes and applies a methodology to generate the information necessary to do a proper welfare analysis of the social sustainability of renewable energy production facilities. This information is key both for an equity and an efficiency analysis. The analysis focuses on the case of investments in renewable energy electricity production facilities, where the impacts on local residents’ welfare are often significantly different than the welfare effects on the general population. We apply the contingent valuation method to selected facilities across the different renewable energy power plants located in Portugal and conclude that local residents acknowledge differently the damage sustained by the type, location and operation of the plants. The results from these case studies attest to the need of acknowledging and quantifying the negative impacts on local communities when assessing the economic viability, social equity and environmental impact of renewable energy projects.

A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.