Preconditioning the solution of the time- dependent neutron diffusion equation by recycling Krylov subspaces

[EN] Spectral preconditioners are based on the fact that the convergence rate of Krylov subspace methods is improved if the eigenvalues of smallest magnitude of the system matrix are `removed'. In this paper, two preconditioning strategies are studied to solve a set of linear systems associated with the numerical integration of the time dependent neutron di usion equation. Both strategies can be implemented using the matrix-vector product as the main operation and succeed at reducing the total number of iterations needed to solve the set of systems.This work has been partially supported by the Spanish Ministerio de Educacion y Ciencia under projects MTM2010-18674 and ENE2011-22823.González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ. (2014). Preconditioning the solution of the time- dependent neutron diffusion equation by recycling Krylov subspaces. International Journal of Computer Mathematics. 91(1):42-52. https://doi.org/10.1080/00207160.2013.771181S425291

Pin-wise homogenization for SPN neutron transport approximation using the finite element method

[EN] The neutron transport equation describes the distribution of neutrons inside a nuclear reactor core. Homogenization strategies have been used for decades to reduce the spatial and angular domain complexity of a nuclear reactor by replacing previously calculated heterogeneous subdomains by homogeneous ones and using a low order transport approximation to solve the new problem. The generalized equivalence theory for homogenization looks for discontinuous solutions through the introduction of discontinuity factors at the boundaries of the homogenized subdomains. In this work, the generalized equivalence theory is extended to the Simplified P-N equations using the finite element method. This extension proposes pin discontinuity factors instead of the usual assembly discontinuity factors and the use of the simplified spherical harmonics approximation rather than diffusion theory. An interior penalty finite element method is used to discretize and solve the problem using discontinuity factors. One dimensional numerical results show that the proposed pin discontinuity factors produce more accurate results than the usual assembly discontinuity factors. The proposed pin discontinuity factors produce precise results for both pin and assembly averaged values without using advanced reconstruction methods. Also, the homogenization methodology is verified against the calculation performed with reference discontinuity factors. (C) 2017 Elsevier B.V. All rights reserved.The work has been partially supported by the spanish Ministerio de Economía y Competitividad under projects ENE 2014-59442-P and MTM2014-58159-P, the Generalitat Valenciana under the project PROMETEO II/2014/008 and the Universitat Politècnica de València under the project FPI-2013. The work has also been supported partially by the Swedish Research Council (VR-Vetenskapsrådet) within a framework grant called DREAM4SAFER, research contract C0467701Vidal-Ferràndiz, A.; Gonzalez-Pintor, S.; Ginestar Peiro, D.; Demaziere, C.; Verdú Martín, GJ. (2018). Pin-wise homogenization for SPN neutron transport approximation using the finite element method. Journal of Computational and Applied Mathematics. 330:806-821. https://doi.org/10.1016/j.cam.2017.06.023S80682133

Updating the Lambda modes of a nuclear power reactor

[EN] Starting from a steady state configuration of a nuclear power reactor some situations arise in which the reactor configuration is perturbed. The Lambda modes are eigenfunctions associated with a given configuration of the reactor, which have successfully been used to describe unstable events in BWRs. To compute several eigenvalues and its corresponding eigenfunctions for a nuclear reactor is quite expensive from the computational point of view. Krylov subspace methods are efficient methods to compute the dominant Lambda modes associated with a given configuration of the reactor, but if the Lambda modes have to be computed for different perturbed configurations of the reactor more efficient methods can be used. In this paper, different methods for the updating Lambda modes problem will be proposed and compared by computing the dominant Lambda modes of different configurations associated with a Boron injection transient in a typical BWR reactor. (C) 2010 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish Ministerio de Educacion y Ciencia under projects ENE2008-02669 and MTM2007-64477-AR07, the Generalitat Valenciana under project ACOMP/2009/058, and the Universidad Politecnica de Valencia under project PAID-05-09-4285.González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ. (2011). Updating the Lambda modes of a nuclear power reactor. Mathematical and Computer Modelling. 54(7):1796-1801. https://doi.org/10.1016/j.mcm.2010.12.013S1796180154

Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry

To simulate the behaviour of a nuclear power reactor it is necessary to be able to integrate the time-dependent neutron diffusion equation inside the reactor core. Here the spatial discretization of this equation is done using a finite element method that permits h-p refinements for different geometries. This means that the accuracy of the solution can be improved refining the spatial mesh (h-refinement) and also increasing the degree of the polynomial expansions used in the finite element method (p-refinement). Transients involving the movement of the control rod banks have the problem known as the rod-cusping effect. Previous studies have usually approached the problem using a fixed mesh scheme defining averaged material properties. The present work proposes the use of a moving mesh scheme that uses spatial meshes that change with the movement of the control rods avoiding the necessity of using equivalent material cross sections for the partially inserted cells. The performance of the moving mesh scheme is tested studying one-dimensional and three-dimensional benchmark problems. (C) 2015 Elsevier B.V. All rights reserved.This work has been partially supported by the Spanish Ministerio de Ciencia e Innovacion under project ENE2011-22823, the Generalitat Valenciana under projects II/2014/08 and ACOMP/2013/237, and the Universitat Politecnica de Valencia under project UPPTE/2012/118.Vidal-Ferràndiz, A.; Fayez Moustafa Moawad, R.; Ginestar Peiro, D.; Verdú Martín, GJ. (2016). Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry. Journal of Computational and Applied Mathematics. 291:197-208. https://doi.org/10.1016/j.cam.2015.03.040S19720829

Modeling noise experiments performed at AKR-2 and CROCUS zero-power reactors

CORTEX is a EU H2020 project (2017-2021) devoted to the analysis of ’reactor neutron noise’ in nuclear reactors, i.e. the small fluctuations occurring around the stationary state due to external or internal disturbances in the core. One important aspect of CORTEX is the development of neutron noise simulation codes capable of modeling the spatial variations of the noise distribution in a reactor. In this paper we illustrate the validation activities concerning the comparison of the simulation results obtained by several noise simulation codes with respect to experimental data produced at the zero-power reactors AKR-2 (operated at TUD, Germany) and CROCUS (operated at EPFL, Switzerland). Both research reactors are modeled in the time and frequency domains, using transport or diffusion theory. Overall, the noise simulators managed to capture the main features of the neutron noise behavior observed in the experimental campaigns carried out in CROCUS and AKR-2, even though computational biases exist close to the region where the noise-inducing mechanical vibration was located (the so-called ”noise source”). In some of the experiments, it was possible to observe the spatial variation of the relative neutron noise, even relatively far from the noise source. This was achieved through reduced uncertainties using long measurements, the installation of numerous, robust and efficient detectors at a variety of positions in the near vicinity or inside the core, as well as new post-processing methods. For the numerical simulation tools, modeling the spatial variations of the neutron noise behavior in zero-power research reactors is an extremely challenging problem, because of the small magnitude of the noise field; and because deviations from a point-kinetics behavior are most visible in portions of the core that are especially difficult to be precisely represented by simulation codes, such as experimental channels. Nonetheless the limitations of the simulation tools reported in the paper were not an issue for the CORTEX project, as most of the computational biases are found close to the noise source

Schwarz type preconditioners for the neutron diffusion equation

[EN] Domain decomposition is a mature methodology that has been used to accelerate the convergence of partial differential equations. Even if it was devised as a solver by itself, it is usually employed together with Krylov iterative methods improving its rate of convergence, and providing scalability with respect to the size of the problem. In this work, a high order finite element discretization of the neutron diffusion equation is considered. In this problem the preconditioning of large and sparse linear systems arising from a source driven formulation becomes necessary due to the complexity of the problem. On the other hand, preconditioners based on an incomplete factorization are very expensive from the point of view of memory requirements. The acceleration of the neutron diffusion equation is thus studied here by using alternative preconditioners based on domain decomposition techniques inside Schur complement methodology. The study considers substructuring preconditioners, which do not involve overlapping, and additive Schwarz preconditioners, where some overlapping between the subdomains is taken into account. The performance of the different approaches is studied numerically using two-dimensional and three-dimensional problems. It is shown that some of the proposed methodologies outperform incomplete LU factorization for preconditioning as long as the linear system to be solved is large enough, as it occurs for three-dimensional problems. They also outperform classical diagonal Jacobi preconditioners, as long as the number of systems to be solved is large enough in such a way that the overhead of building the pre-conditioner is less than the improvement in the convergence rate. (C) 2016 Elsevier B.V. All rights reserved.The work has been partially supported by the spanish Ministerio de Economía y Competitividad under projects ENE 2014-59442-P and MTM2014-58159-P, the Generalitat Valenciana under the project PROMETEO II/2014/008 and the Universitat Politècnica de València under the project FPI-2013. The work has also been supported partially by the Swedish Research Council (VR-Vetenskapsrådet) within a framework grant called DREAM4SAFER, research contract C0467701.Vidal-Ferràndiz, A.; González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ.; Demazière, C. (2017). Schwarz type preconditioners for the neutron diffusion equation. Journal of Computational and Applied Mathematics. 309:563-574. https://doi.org/10.1016/j.cam.2016.02.056S56357430

Does the development of new medicinal products in the European Union address global and regional health concerns?

<p>Abstract</p> <p>Background</p> <p>Since 1995, approval for many new medicinal products has been obtained through a centralized procedure in the European Union. In recent years, the use of summary measures of population health has become widespread. We investigated whether efforts to develop innovative medicines are focusing on the most relevant conditions from a global public health perspective.</p> <p>Methods</p> <p>We reviewed the information on new medicinal products approved by centralized procedure from 1995 to 2009, information that is available to the public in the European Commission Register of medicinal products and the European Public Assessment Reports from the European Medicines Agency. Morbidity and mortality data were included for each disease group, according to the Global Burden of Disease project. We evaluated the association between authorized medicinal products and burden of disease measures based on disability-adjusted life years (DALYs) in the European Union and worldwide.</p> <p>Results</p> <p>We considered 520 marketing authorizations for medicinal products and 338 active ingredients. New authorizations were seen to increase over the period analyzed. There was a positive, high correlation between DALYs and new medicinal product development (ρ = 0.619, p = 0.005) in the European Union, and a moderate correlation for middle-low-income countries (ρ = 0.497, p = 0.030) and worldwide (ρ = 0.490, p = 0.033). The most neglected conditions at the European level (based on their attributable health losses) were neuropsychiatric diseases, cardiovascular diseases, respiratory diseases, sense organ conditions, and digestive diseases, while globally, they were perinatal conditions, respiratory infections, sense organ conditions, respiratory diseases, and digestive diseases.</p> <p>Conclusions</p> <p>We find that the development of new medicinal products is higher for some diseases than others. Pharmaceutical industry leaders and policymakers are invited to consider the implications of this imbalance by establishing work plans that allow for the setting of future priorities from a public health perspective.</p

The burden of premature mortality in Spain using standard expected years of life lost: a population-based study

<p>Abstract</p> <p>Background</p> <p>Measures of premature mortality have been used to guide debates on future health priorities and to monitor the population health status. Standard expected years of life lost (SEYLL) is one of the methods used to assess the time lost due to premature death. This article affords an overview of premature mortality in Spain for the year 2008.</p> <p>Methods</p> <p>A population-based study was conducted estimating SEYLL by sex and age groups. SEYLL, a key component of the disability-adjusted life years measure of disease burden, was calculated using Princeton West standard life tables with life expectancy at birth fixed at 80 years for males and 82.5 years for females. Population data and specific death records were obtained from the official registers of the National Institute of Statistics. All data were analysed and prepared in GesMor and Epidat software packages.</p> <p>Results</p> <p>The burden of premature mortality was estimated at 2.1 million SEYLL when age at death is taken into account. Males lost 60.9% and females lost 39.1% of total SEYLL. Malignant tumors (34.5%) and cardiovascular diseases (24.0%) were the leading categories in terms of SEYLL. Ischaemic heart disease (8.5%) and lung cancers (8.0%) were the most common specific causes of SEYLL followed by cerebrovascular diseases (5.9%), colorectal cancer (4.1%), road traffic accidents (3.5%), Alzheimer and other dementias (2.9%), chronic obstructive pulmonary disease (2.8%), breast cancer (2.8%) and suicides (2.6%).</p> <p>Conclusions</p> <p>In Spain, premature mortality was essentially due to chronic non-communicable diseases. Data provided in this study are relevant for a more balanced health agenda aimed at reducing the burden of premature mortality. This study also represents a first step in estimating the overall burden of disease in terms of premature death and disability.</p