The economic performance of Portuguese and Spanish regions: A network dynamic approach

This paper contributes to further understanding the economic performance of Portuguese and Spanish regions, using a stochastic network approach. The empirical analysis is made at the territorial level of NUT 3 regions and covers the period 1995-2008. The performance of regions is based on GDP per capita at Purchasing Power Standards. The network analysis is based on a metric space built from the correlation coefficients between the log-difference of annual growth rates. The metric space and the corresponding topological coefficients are compared with the independent performance of randomly generated data. The metric space is graphically represented along the 3 dominant eigenvalues and the strongest connections are selected and represented in a network of Iberian regions. The main purpose of this research is to find the most relevant geographical and demographic determinants of regional development, namely a “border effect”, an “interiority (without border) effect”, a “coastal effect”, a “metropolitan effect” and an “ultra periphery effect”.

Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map

We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method. Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances

Panel discussion

Economic development ; Economic conditions