Domain decomposition methods for the neutron diffusion problem

Guérin, Pierre; Baudron, Anne-Marie; Lautard, Jean-Jacques

doi:10.1016/j.matcom.2010.04.009

Cited by 4 publications

(4 citation statements)

References 5 publications

(7 reference statements)

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“…Advance is achieved through the use of decoupling technology: splitting by physical processes (Vabishchevich, 2014)), decomposition of the computational domain into subdomains (Toselli and Widlund, 2005), iterative methods for solving systems of algebraic equations (Saad, 2003). In the case of spectral problems for the neutron diffusion, domain decomposition methods are used, for example, in Guérin et al (2010). Features of solving non-stationary problems on parallel computers are taken into account by constructing special iterative methods such as the parareal in time algorithm (Maday and Turinici, 2005).…”

Section: Introductionmentioning

confidence: 99%

State change modal method for numerical simulation of dynamic processes in a nuclear reactor

Avvakumov

Strizhov

Vabishchevich

et al. 2018

Progress in Nuclear Energy

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Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modeled by a successive change of the reactor states, which are characterized by given coefficients of the equations. In the modal method, the approximate solution is represented as an expansion on the first eigenfunctions of some spectral problem. The numerical-analytical method is based on the use of dominant time-eigenvalues of a multigroup diffusion model taking into account delayed neutrons. Numerical simulations of the dynamic process were performed in the framework of the two-group approximation for the VVER-1000 reactor test model. The last is characterized by the fact that some eigenvalues are complex.

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Section: Introductionmentioning

confidence: 99%

State change modal method for numerical simulation of dynamic processes in a nuclear reactor

Avvakumov

Strizhov

Vabishchevich

et al. 2018

Progress in Nuclear Energy

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“…Many successful works have been done in the parallelization of the neutron model's simulation. For instance [2] studies the static case i.e. eigenvalue problems with space domain decomposition methods, and a very nice strategy [3], [4] uses quasi-stationnary approach to accelerate the simulation.…”

Section: Introductionmentioning

confidence: 99%

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

Baudron

Lautard

Maday

et al. 2014

Journal of Computational Physics

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We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for the space discretization, our implementation provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner (LMW) benchmark [1].

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“…In order to improve computation ability and reduce memory requirements, parallel computing of partial differential equations has become an important subject for studying. The domain decomposition method (DDM) has been proved to be one efficient parallel algorithm and has a wide range of applications in parallel computing platforms [5][6][7]. The basic principle of DDM is that the solution domain can be divided into several sub-domains.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Parallel Computing Method for the Processing of Large Sensed Data

Wang

2013

Automatika

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Original scientific paperIn recent years we witness the advent of the Internet of Things and the wide deployment of sensors in many applications for collecting and aggregating data. Efficient techniques are required to analyze these massive data for supporting intelligent decisions making. Partial differential problems which involve large data are the most common in the engineering and scientific research. For simulations of large-scale three-dimensional partial differential equations, the intensive computation ability and large amounts of memory requirements for modeling are the main research problems. To address the two challenges, this paper provided an effective parallel method for partial differential equations. The proposed approach combines the overlapping domain decomposition strategy and the multi-core cluster technology to achieve parallel simulations of partial differential equations, uses the finite difference method to discretize equations and adopts the hybrid MPI/OpenMP programming model to exploit two-level parallelism on a multi-core cluster. The three-dimensional groundwater flow model with the parallel finite difference overlapping domain decomposition strategy was successfully set up and carried out by the parallel MPI/OpenMP implementation on a multi-core cluster with two nodes. The experimental results show that the proposed parallel approach can efficiently simulate partial differential problems with large amounts of data.Key words: Data processing, Domain decomposition method, Hybrid programming model, Multi-core clusters, Finite difference method Učinkovita metoda paralelnog računanja za obradu velike količine podataka prikupljanih senzorom. Posljednjih godina svjedočimo dolasku tzv. interneta stvari i širokoj uporabi senzora u raznim primjenama prikupljanja i objedinjavanja podataka. Učinkovite metode su potrebne za analizu velike količine podataka u svrhu podrške inteligentnom odlučivanju. Parcijalno diferencijalni problemi koji uključuju veliku količinu podataka su gotovo uobičajeni u inženjerstvu i znanstvenom istraživanju. Za simulaciju masovnih trodimenzionalnih parcijalnih diferencijalnih jednadžbi potrebne su značajne računalne mogućnosti, a potreba za velikom količinom memorije za modeliranje je glavni istraživački problem. Za rješavanje oba problema ovaj rad pruža efektivnu paralelnu metodu za parcijalne diferencijalne jednadžbe. Predloženi pristup kombinira strategiju dekompozicije preklapajućih domena i tehnologiju višejezgrenih klastera za postizanje paralelnih simulacija parcijalnih diferencijalnih jednadžbi, koristi metodu konačnog diferenciranja za diskretizaciju jednadžbi te model MPI/OpenMP hibridnog programiranja za iskorištavanje dvorazinskog paralelizma na višejezgrenom klasteru. Formiran je trodimenzionalan model toka podzemnih voda sa strategijom dekompozicije preklapajućih domena konačnih diferencija. Za izvoîenje je korištena paralelna MPI/OpenMP implementacija na višejezgrenom klasteru s dvačvora. Eksperimentalni rezultati su pokazali kako predloženi paralelni p...

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Domain decomposition methods for the neutron diffusion problem

Cited by 4 publications

References 5 publications

State change modal method for numerical simulation of dynamic processes in a nuclear reactor

State change modal method for numerical simulation of dynamic processes in a nuclear reactor

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

An Efficient Parallel Computing Method for the Processing of Large Sensed Data

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