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 55 articles , 1 standard article )

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  1. Arrarás, Andrés; Gaspar, Francisco J.; Portero, Laura; Rodrigo, Carmen: Multigrid solvers for multipoint flux approximations of the Darcy problem on rough quadrilateral grids (2021)
  2. Brown, Jed; He, Yunhui; MacLachlan, Scott; Menickelly, Matt; Wild, Stefan M.: Tuning multigrid methods with robust optimization and local Fourier analysis (2021)
  3. He, Yunhui: A generalized and unified framework of local Fourier analysis using matrix-stencils (2021)
  4. Hocking, L. Robert; Greif, Chen: Optimal complex relaxation parameters in multigrid for complex-shifted linear systems (2021)
  5. Sun, Li; Huang, Yu-Mei: A modulus-based multigrid method for image retinex (2021)
  6. Zhang, Li-Li; Ren, Zhi-Ru: A modified modulus-based multigrid method for linear complementarity problems arising from free boundary problems (2021)
  7. Hu, Xiaozhe; Rodrigo, Carmen; Gaspar, Francisco J.: Using hierarchical matrices in the solution of the time-fractional heat equation by multigrid waveform relaxation (2020)
  8. Kahl, Karsten; Kintscher, Nils: Automated local Fourier analysis (aLFA) (2020)
  9. Notay, Yvan: Analysis of two-grid methods: the nonnormal case (2020)
  10. Thompson, Tony; Chen, Ke: An effective diffeomorphic model and its fast multigrid algorithm for registration of lung CT images (2020)
  11. Arrarás, Andrés; Gaspar, Francisco J.; Portero, Laura; Rodrigo, Carmen: Mixed-dimensional geometric multigrid methods for single-phase flow in fractured porous media (2019)
  12. Brown, Jed; He, Yunhui; Maclachlan, Scott: Local Fourier analysis of balancing domain decomposition by constraints algorithms (2019)
  13. De La Riva, Alvaro Pe; Rodrigo, Carmen; Gaspar, Francisco J.: A robust multigrid solver for isogeometric analysis based on multiplicative Schwarz smoothers (2019)
  14. He, Yunhui; MacLachlan, Scott P.: Local Fourier analysis for mixed finite-element methods for the Stokes equations (2019)
  15. 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)
  16. Bolten, M.; Rittich, H.: Fourier analysis of periodic stencils in multigrid methods (2018)
  17. 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)
  18. Franco, S. R.; Rodrigo, C.; Gaspar, F. J.; Pinto, M. A. V.: A multigrid waveform relaxation method for solving the poroelasticity equations (2018)
  19. Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.: Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system (2018)
  20. Gaspar, Francisco J.; Rodrigo, Carmen: Multigrid waveform relaxation for the time-fractional heat equation (2017)

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