@article {20.500.11767_83906, title = {deal2lkit: A toolkit library for high performance programming in deal.II}, journal = {SOFTWAREX}, volume = {7}, year = {2018}, pages = {318{\textendash}327}, doi = {10.1016/j.softx.2018.09.004}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {11966, title = {A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel}, journal = {Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208}, volume = {87}, number = {Annals of Nuclear Energy;87}, year = {2016}, pages = {208}, publisher = {Elsevier}, chapter = {198}, abstract = {In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well.}, doi = {doi:10.1016/j.anucene.2015.09.002}, url = {http://urania.sissa.it/xmlui/handle/1963/35191}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {11967, title = {A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods}, journal = {NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019}, volume = {2}, number = {Journal of Nuclear Engineering and Radiation Science;2}, year = {2016}, note = {8 pages}, month = {02/2016}, pages = {8}, publisher = {ASME}, abstract = {This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a {\textquotedblleft}classical{\textquotedblright} a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.}, doi = {10.1115/1.4031945}, url = {http://urania.sissa.it/xmlui/handle/1963/35192}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2015, title = {Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods}, journal = {Communications in Computational Physics}, year = {2016}, month = {2016}, publisher = {SISSA}, abstract = {

In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a {\textquotedblleft}staircase{\textquotedblright} strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as {\textquotedblleft}truth{\textquotedblright} solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine {\textquotedblleft}truth{\textquotedblright} finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34963}, author = {Alberto Sartori and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @article {2015, title = {Deal2lkit: a Toolkit Library for High Performance Programming in deal.II}, year = {2015}, publisher = {SISSA}, abstract = {We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit.}, url = {http://urania.sissa.it/xmlui/handle/1963/35006}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {2014, title = {Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics}, journal = {Annals of Nuclear Energy}, volume = {71}, number = {Annals of Nuclear Energy;volume 71; pages 217-229;}, year = {2014}, month = {09/2014}, pages = {229}, publisher = {Elsevier}, chapter = {217}, abstract = {

In this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

}, doi = {10.1016/j.anucene.2014.03.043}, url = {http://urania.sissa.it/xmlui/handle/1963/35039}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Davide Chiesa and Lelio Luzzi and Roberto R. Ponciroli and Ezio Previtali and Marco E. Ricotti and Gianluigi Rozza and Monica Sisti} } @proceedings {2014, title = {A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics}, number = {International Conference on Nuclear Engineering, Proceedings, ICONE;volume 5;}, year = {2014}, note = {2014 22nd International Conference on Nuclear Engineering, ICONE 2014; Prague; Czech Republic; 7 July 2014 through 11 July 2014; Code 109131;}, month = {07/2014}, pages = {V005T17A048-V005T17A048}, publisher = {American Society of Mechanical Engineers (ASME)}, edition = {American Society Mechanical Engineering}, address = {Prague, Czech Republic}, abstract = {

In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

}, isbn = {978-079184595-0}, doi = {10.1115/ICONE22-30707}, url = {http://urania.sissa.it/xmlui/handle/1963/35123}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} }