Scope of asymmetries in the Euro area

We discuss the scope of asymmetries in growth and inflation developments in the euro area countries, taking the euro area as the natural benchmark since the establishment of EMU. We start with a descriptive analysis of a set of indicators that can give a first idea of the likelihood of or extent to which Member States can show asymmetries with respect to the euro area. This approach typically leads to a division of countries between a core and a periphery, the former consisting over the 1993-2000 sub-period of Belgium, Germany, France, Italy, Spain and Austria and perhaps the Netherlands. However, it is rather difficult to weight the indicators and to draw a firm line between "insiders" and "outsiders" in this way. Moreover the dichotomy does not provide any information on the true extent of the asymmetries inside the core and periphery. Accordingly, we move to a quantitative approach (SVAR models) that makes it possible to assess two forms of asymmetry: asymmetry stemming from country-specific shocks and asymmetry stemming from differences in the way countries react to symmetric euro area shocks. The asymmetries are measured along two dimensions: growth and inflation developments. We find that over the years 1971-2000 growth in many countries is driven by the symmetric shocks while the opposite holds true for inflation where asymmetric (country-specific) shocks dominate. However regarding growth, the responses of the different countries to the symmetric shocks do not really differ and these shocks are not a major source of divergence. As a consequence, for growth as well as for inflation, the asymmetries with respect to the euro area are mainly the result of genuine asymmetric shocks. We notice a marked decrease in the impact of asymmetric shocks on inflation over the years, a phenomenon that is also present for growth, albeit less pronounced. If the years 1993-2000 can be used to evaluate the current situation, it appears that countries are spread along a line going from close similarity to the euro area (France) to extensive asymmetry (Ireland). Asymmetric shocks are not negligible yet with an average annual impact of around 1 percentage point on country growth or inflation. Some countries usually thought to belong to the core, are still exposed to such average shocks, in terms of growth or in terms of inflation.

Stress intensity factors computation for bending plates with extended finite element method

The modelization of bending plates with through-the-thickness cracks is investigated. We consider the Kirchhoff–Love plate model, which is valid for very thin plates. Reduced Hsieh–Clough–Tocher triangles and reduced Fraejis de Veubeke–Sanders quadrilaterals are used for the numerical discretization. We apply the eXtended Finite Element Method strategy: enrichment of the finite element space with the asymptotic bending singularities and with the discontinuity across the crack. The main point, addressed in this paper, is the numerical computation of stress intensity factors. For this, two strategies, direct estimate and J-integral, are described and tested. Some practical rules, dealing with the choice of some numerical parameters, are underlined

Multivariate structural time series models with dual cycles : implications for measurement of output gap and potential growth

Structural time series models applied to the factor inputs of a production function often lead to small output gaps and consequently to erratic measures of potential growth. We introduce a dual cycle model which is an extension to the multivariate trend plus cycle model with phase shifts à la Rünstler. The dual cycle model is a combination of two types of models: the trend plus cycle model and the cyclical trend model, where the cycle appears in the growth rate of a variable. This property enables hysteresis to be taken into account. Hysteresis is likely to show up in unemployment but it can also affect the capital stock due to the existence of long investment cycles. In the proposed model, hysteresis may affect all the factor inputs of the production function and phase shifts are extended to the dual cycles. Genuine measures of potential growth can be computed that are hysteresis-free and less prone to volatility. A complementary measure of the output gap that takes hysteresis into account can be derivedOutput gap, potential growth, hysteresis, structural time series models

The production function approach to the Belgian output gap, Estimation of a Multivariate Structural Time Series Model

A multivariate structural time series model is applied to the factor inputs of a production function (or components thereof) to estimate the Belgian output gap. The usefulness of capacity utilization is also investigated but the variable is not given a prominent status. The number of independent cycles - there may be more than one - and the frequencies retained in the cycles are not restricted a priori. To allow for leads and lags between variables, phase shifts à la Rünstler are introduced at a later stage. Additivity of leads and lags is not imposed. Over 1983-2004, a 3.5 years periodicity is found in the cycles. At that periodicity, the cycles in the participation and unemployment rates are negligible. Two independent cycles hide behind the cycles of the other variables: hours, TFP and capacity utilization. A common cycle restriction is rejected, even allowing for idiosyncratic cycles. The cycles present in the whole data set cannot be subsumed in a single measure such as capacity utilization. Phase shifts are significant, with hours leading by as much as 3 quarters and capacity utilization lagging but additivity of leads and lags is rejected. The resulting output gap has much in common with the NBB business survey indicator.Business cycle, output gap, phase shifts, structural time series models

Asymmetric growth and inflation developments in the acceding countries: a new assessment

In this paper, we use a SVAR model in order to study the asymmetry of growth and inflation developments in the acceding countries vis-à-vis the euro area over the years 1995-2003. The model combines two strands of the literature, the explanation in terms of country-specific and euro area shocks, and a further split between supply and demand shocks. The four structural shocks may all create asymmetries vis-à-vis the euro area. It appears that country-specific shocks are the main source of growth or inflation divergence, rather than the distinct way in which acceding countries react to euro area shocks. But whereas country-specific supply shocks are mainly responsible for growth divergence, country-specific demand shocks are mainly responsible for inflation asymmetry. Hence, a low asymmetry in terms of growth does not necessarily imply a low asymmetry in terms of inflation, although the latter is particularly important for countries aiming to join the euro area. There is some evidence that both asymmetries were on the fall over the last years of the sample

Scope of asymmetries in the Euro area

We discuss the scope of asymmetries in growth and inflation developments in the euro area countries, taking the euro area as the natural benchmark since the establishment of EMU. We start with a descriptive analysis of a set of indicators that can give a first idea of the likelihood of or extent to which Member States can show asymmetries with respect to the euro area. This approach typically leads to a division of countries between a core and a periphery, the former consisting over the 1993-2000 sub-period of Belgium, Germany, France, Italy, Spain and Austria and perhaps the Netherlands. However, it is rather difficult to weight the indicators and to draw a firm line between "insiders" and "outsiders" in this way. Moreover the dichotomy does not provide any information on the true extent of the asymmetries inside the core and periphery. Accordingly, we move to a quantitative approach (SVAR models) that makes it possible to assess two forms of asymmetry: asymmetry stemming from country-specific shocks and asymmetry stemming from differences in the way countries react to symmetric euro area shocks. The asymmetries are measured along two dimensions: growth and inflation developments. We find that over the years 1971-2000 growth in many countries is driven by the symmetric shocks while the opposite holds true for inflation where asymmetric (country-specific) shocks dominate. However regarding growth, the responses of the different countries to the symmetric shocks do not really differ and these shocks are not a major source of divergence. As a consequence, for growth as well as for inflation, the asymmetries with respect to the euro area are mainly the result of genuine asymmetric shocks. We notice a marked decrease in the impact of asymmetric shocks on inflation over the years, a phenomenon that is also present for growth, albeit less pronounced. If the years 1993-2000 can be used to evaluate the current situation, it appears that countries are spread along a line going from close similarity to the euro area (France) to extensive asymmetry (Ireland). Asymmetric shocks are not negligible yet with an average annual impact of around 1 percentage point on country growth or inflation. Some countries usually thought to belong to the core, are still exposed to such average shocks, in terms of growth or in terms of inflation

A two-scale solver for linear elasticity problems in the context of parallel message passing

This paper pushes further the intrinsic capabilities of the GFEM$^{gl}$ global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local problems. Regarding local problems, a specific scheduling strategy is introduced. Then, to measure correctly the convergence of the iterative process, we introduce a reference solution that revisits the product of classical and enriched functions. As a consequence, we are able to propose a purely matrix-based implementation of the global-local problem. The distributed approach is then compared to other parallel solvers either direct or iterative with domain decomposition. The comparison addresses the scalability as well as the elapsed time. Numerical examples deal with linear elastic problems: a polynomial exact solution problem, a complex micro-structure, and, finally, a pull-out test (with different crack extent). 1: C. A. Duarte, D.-J. Kim, and I. Babu\v{s}ka. A global-local approach for the construction of enrichment functions for the generalized fem and its application to three-dimensional cracks. In Advances in Meshfree Techniques, Dordrecht, 2007. SpringerComment: To be published in Computer Methods in Applied Mechanics and Engineering. Revision: mainly introduction, conclusion and Fig3 update

A phase-field model for cohesive fracture

In this paper, a phase-field model for cohesive fracture is developed. After casting the cohesive zone approach in an energetic framework, which is suitable for incorporation in phase-field approaches, the phase-field approach to brittle fracture is recapitulated. The approximation to the Dirac function is discussed with particular emphasis on the Dirichlet boundary conditions that arise in the phase-field approximation. The accuracy of the discretisation of the phase field, including the sensitivity to the parameter that balances the field and the boundary contributions, is assessed at the hand of a simple example. The relation to gradient-enhanced damage models is highlighted, and some comments on the similarities and the differences between phase-field approaches to fracture and gradient-damage models are made. A phase-field representation for cohesive fracture is elaborated, starting from the aforementioned energetic framework. The strong as well as the weak formats are presented, the latter being the starting point for the ensuing finite element discretisation, which involves three fields: the displacement field, an auxiliary field that represents the jump in the displacement across the crack, and the phase field. Compared to phase-field approaches for brittle fracture, the modelling of the jump of the displacement across the crack is a complication, and the current work provides evidence that an additional constraint has to be provided in the sense that the auxiliary field must be constant in the direction orthogonal to the crack. The sensitivity of the results with respect to the numerical parameter needed to enforce this constraint is investigated, as well as how the results depend on the orders of the discretisation of the three fields. Finally, examples are given that demonstrate grid insensitivity for adhesive and for cohesive failure, the latter example being somewhat limited because only straight crack propagation is considered

The inequality level-set approach to handle contact: membrane case

International audienceBackground: Contact mechanics involves models governed by inequality constraints. Even for the simplest contact problem, inequalities arise from the lack of information on the contact zone position. In addition to increasing the difficulty to solve such problems, an unknown contact zone makes it difficult to use an appropriate mesh and to represent efficiently phenomena on the contact zone boundary. Nevertheless these phenomena are often crucial to have an accurate representation of the problem such as weak discontinuity of the displacement.Methods: In this paper, we propose a method specifically designed to solve inequality constraint problems linked to an unknown domain without remeshing. In order to do so, level sets coupled with X-FEM is used to define the unknown domain and take into account the specific behavior at the contact zone boundary. The key idea of the method is to split the problem involving inequality constraints into two problems. In the first problem, the unknown domain is set and therefore it only involves equalities. Nevertheless, the constraints might be violated, meaning the set domain has to be changed. Then, the other problem is a shape optimization of this domain and leads to an updated set domain. These two problems are iterated up to convergence of the algorithm. Moreover, the addition of adhesion to the problem will be considered.Results: The studied case in this paper is a membrane in the context of small deformations. First, a 1D example will be given to illustrate the method with and without adhesion. Then 2D cases will be studied. Finally an example with an evolving load will be given. Comparison will be made with a classical active-set method.Conclusions: The ILS is proved to be an efficient method giving a convincing accuracy for the contact boundary without need of re-meshing. It is also able to naturally handle adhesion

Stability of incompressible formulations enriched with X-FEM

The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic ows occurs as in forming processes. The use of mixed nite element methods is known to prevent the locking of the nite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the nite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (XFEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement eld makes it possible to treat surfaces of discontinuity inside nite elements. In this paper, some strategies are proposed for the enrichment of mixed nite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the nite element convergence rate is preserved and the inf-sup condition is passed