LFA

Practical Fourier analysis for multigrid methods. With CD-ROM. A practical Fourier analysis for multigrid methods is performed. The theoretical framework is necessary for the successful use of multigrid methods for systems of partial differential equations. The local Fourier analysis can be obtained by a simple mouse click, courtesy of accompanying software (LFA) and GUI (xlfa). The studies are for two- and three-dimensioal problems, including Poisson, convection diffusion, biharmonic equation, the Oseen and Stokes equations, a linear shell problem and elasticity systems. The book enables understanding of basic principles of multigrid and local Fourier analysis, allowing investigation of real multigrid effects


References in zbMATH (referenced in 44 articles )

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  1. Arrarás, Andrés; Gaspar, Francisco J.; Portero, Laura; Rodrigo, Carmen: Mixed-dimensional geometric multigrid methods for single-phase flow in fractured porous media (2019)
  2. Brown, Jed; He, Yunhui; Maclachlan, Scott: Local Fourier analysis of balancing domain decomposition by constraints algorithms (2019)
  3. De La Riva, Alvaro Pe; Rodrigo, Carmen; Gaspar, Francisco J.: A robust multigrid solver for isogeometric analysis based on multiplicative Schwarz smoothers (2019)
  4. He, Yunhui; MacLachlan, Scott P.: Local Fourier analysis for mixed finite-element methods for the Stokes equations (2019)
  5. Wu, Jian-Ping; Guo, Pei-Ming; Yin, Fu-Kang; Peng, Jun; Yang, Jin-Hui: A new aggregation algorithm based on coordinates partitioning recursively for algebraic multigrid method (2019)
  6. Bolten, M.; Rittich, H.: Fourier analysis of periodic stencils in multigrid methods (2018)
  7. Franco, Sebastião Romero; Gaspar, Francisco José; Villela Pinto, Marcio Augusto; Rodrigo, Carmen: Multigrid method based on a space-time approach with standard coarsening for parabolic problems (2018)
  8. Franco, S. R.; Rodrigo, C.; Gaspar, F. J.; Pinto, M. A. V.: A multigrid waveform relaxation method for solving the poroelasticity equations (2018)
  9. Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.: Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system (2018)
  10. Gaspar, Francisco J.; Rodrigo, Carmen: Multigrid waveform relaxation for the time-fractional heat equation (2017)
  11. Luo, Peiyao; Rodrigo, Carmen; Gaspar, Francisco J.; Oosterlee, Cornelis W.: Uzawa smoother in multigrid for the coupled porous medium and Stokes flow system (2017)
  12. Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.: On an Uzawa smoother in multigrid for poroelasticity equations. (2017)
  13. Benzi, Michele; Deparis, Simone; Grandperrin, Gwenol; Quarteroni, Alfio: Parameter estimates for the relaxed dimensional factorization preconditioner and application to hemodynamics (2016)
  14. Lu, Peipei; Xu, Xuejun: A robust multilevel method for the time-harmonic Maxwell equation with high wave number (2016)
  15. Moghaderi, Hamid; Dehghan, Mehdi; Hajarian, Masoud: A fast and efficient two-grid method for solving (d)-dimensional Poisson equations (2016)
  16. Pinto, M. A. V.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.: On the robustness of ILU smoothers on triangular grids (2016)
  17. Rodrigo, Carmen: Poroelasticity problem: numerical difficulties and efficient multigrid solution (2016)
  18. Rodrigo, C.; Gaspar, F. J.; Lisbona, F. J.: On a local Fourier analysis for overlapping block smoothers on triangular grids (2016)
  19. Bolten, Matthias; Donatelli, Marco; Huckle, Thomas: Analysis of smoothed aggregation multigrid methods based on Toeplitz matrices (2015)
  20. Bolten, Matthias; Donatelli, Marco; Huckle, Thomas; Kravvaritis, Christos: Generalized grid transfer operators for multigrid methods applied on Toeplitz matrices (2015)

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