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

Advanced computational engineering

This is an author's accepted manuscript of an article published in “International Journal of Computer Mathematics"; Volume 91, Issue 1, 2014; copyright Taylor & Francis; available online at: http://dx.doi.org/10.1080/00207160.2014.880256It is with pleasure that we offer the readers of the International Journal of Computer Mathematics this special issue consisting of some of the most significant contributions to computational and mathematical methods with advanced applications in engineering presented at the International Conference on Mathematical Modelling in Engineering & Human Behaviour 2012, held at the Instituto Universitario de Matemática, Multidisciplinar, Polytechnic City of Innovation in Valencia, Spain, September 4–7, 2012, cf. http://jornadas.imm.upv.es/2012/Ehrhardt, M.; Jódar Sánchez, LA.; Villanueva Micó, RJ. (2014). Advanced computational engineering. International Journal of Computer Mathematics. 91(1):1-3. doi:10.1080/00207160.2014.880256S13911Aznar, F., Pujol, M. J., Sempere, M., & Rizo, R. (2013). A macroscopic model for high intensity radiofrequency signal detection in swarm robotics systems. International Journal of Computer Mathematics, 91(1), 32-41. doi:10.1080/00207160.2013.771180Bernal, A., Abarca, A., Barrachina, T., & Miró, R. (2013). Methodology to resolve the transport equation with the discrete ordinates code TORT into the IPEN/MB-01 reactor. International Journal of Computer Mathematics, 91(1), 113-123. doi:10.1080/00207160.2013.799668Castro, M. A., Rodríguez, F., Cabrera, J., & Martín, J. A. (2013). Difference schemes for time-dependent heat conduction models with delay. International Journal of Computer Mathematics, 91(1), 53-61. doi:10.1080/00207160.2013.779371Cornolti, L., Lucchini, T., Montenegro, G., & D’Errico, G. (2013). A comprehensive Lagrangian flame–kernel model to predict ignition in SI engines. International Journal of Computer Mathematics, 91(1), 157-174. doi:10.1080/00207160.2013.829213García-Oliver, J. M., Novella, R., Pastor, J. M., & Winklinger, J. F. (2013). Evaluation of combustion models based on tabulated chemistry and presumed probability density function approach for diesel spray simulation. International Journal of Computer Mathematics, 91(1), 14-23. doi:10.1080/00207160.2013.770844Gibert, K. (2013). Mixed intelligent-multivariate missing imputation. International Journal of Computer Mathematics, 91(1), 85-96. doi:10.1080/00207160.2013.783209González-Pintor, S., Ginestar, D., & Verdú, G. (2013). Preconditioning the solution of the time-dependent neutron diffusion equation by recycling Krylov subspaces. International Journal of Computer Mathematics, 91(1), 42-52. doi:10.1080/00207160.2013.771181Guardiola, C., Pla, B., Blanco-Rodríguez, D., & Reig, A. (2013). Modelling driving behaviour and its impact on the energy management problem in hybrid electric vehicles. International Journal of Computer Mathematics, 91(1), 147-156. doi:10.1080/00207160.2013.829567Montoliu, C., Ferrando, N., Cerdá, J., & Colom, R. J. (2013). Application of the level set method for the visual representation of continuous cellular automata oriented to anisotropic wet etching. International Journal of Computer Mathematics, 91(1), 124-134. doi:10.1080/00207160.2013.801464Montorfano, A., Piscaglia, F., & Onorati, A. (2013). Wall-adapting subgrid-scale models to apply to large eddy simulation of internal combustion engines. International Journal of Computer Mathematics, 91(1), 62-70. doi:10.1080/00207160.2013.783207Ramos-Martínez, E., Herrera, M., Izquierdo, J., & Pérez-García, R. (2013). Ensemble of naïve Bayesian approaches for the study of biofilm development in drinking water distribution systems. International Journal of Computer Mathematics, 91(1), 135-146. doi:10.1080/00207160.2013.808335Salvador, F. J., Martínez-López, J., Romero, J.-V., & Roselló, M.-D. (2013). Study of the influence of the needle eccentricity on the internal flow in diesel injector nozzles by computational fluid dynamics calculations. International Journal of Computer Mathematics, 91(1), 24-31. doi:10.1080/00207160.2013.770483Sastre, J., Ibáñez, J., Ruiz, P., & Defez, E. (2013). Accurate and efficient matrix exponential computation. International Journal of Computer Mathematics, 91(1), 97-112. doi:10.1080/00207160.2013.791392Serrano, J. R., Arnau, F. J., Piqueras, P., & García-Afonso, O. (2013). Application of the two-step Lax and Wendroff FCT and the CE-SE method to flow transport in wall-flow monoliths. International Journal of Computer Mathematics, 91(1), 71-84. doi:10.1080/00207160.2013.783206Zhyrova, A., & Štys, D. (2013). Construction of the phenomenological model of Belousov–Zhabotinsky reaction state trajectory. International Journal of Computer Mathematics, 91(1), 4-13. doi:10.1080/00207160.2013.76633