Block hybrid multilevel method to compute the dominant lambda-modes of the neutron diffusion equation

[EN] The dominant lambda-modes associated with a nuclear reactor configuration describe the neutron steady-state distribution and its criticality. Furthermore, they are useful to develop modal methods to study reactor instabilities. Different eigenvalues solvers have been successfully used to obtain such modes, most of them are implemented reducing the original generalized eigenvalue problem to an ordinary one. Thus, it is necessary to solve many linear systems making these methods not very efficient, especially for large problems. In this work, the original generalized eigenvalue problem is considered and two block iterative methods to solve it are studied: the block inverse-free preconditioned Arnoldi method and the modified block Newton method. All of these iterative solvers are initialized using a block multilevel technique. A hybrid multilevel method is also proposed based on the combination of the methods proposed. Two benchmark problems are studied illustrating the convergence and the competitiveness of the methods proposed. A comparison with the Krylov-Schur method and the Generalized Davidson is also included.This work has been partially supported by Spanish Ministerio de Economia y Competitividad under projects ENE2017-89029-P, MTM2017-85669-P and BES-2015-072901.Carreño, A.; Vidal-Ferràndiz, A.; Ginestar Peiro, D.; Verdú Martín, GJ. (2018). Block hybrid multilevel method to compute the dominant lambda-modes of the neutron diffusion equation. Annals of Nuclear Energy. 121:513-524. https://doi.org/10.1016/j.anucene.2018.08.010S51352412

Efficient p-multigrid spectral element model for water waves and marine offshore structures

In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave-body interaction with high computational efficiency within a single modellingapproach. We design and propose an efficientO(n)-scalable computational procedure based on geometric p-multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high-order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p-multigrid spectralelement model can take advantage of the high-order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h-multigrid approaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of the iterative geometric p-multigrid solver. Results of numerical experiments are presented for wave propagation and for wave-body interaction in an advanced case for focusing design waves interacting with a FPSO. Our study shows, that the use of iterative geometric p-multigrid methods for theLaplace problem can significantly improve run-time efficiency of FNPF simulators.Comment: Submitted to an international journal for peer revie