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R. Wienands and W. Joppich, Practical Fourier Analysis for Multigrid Methods, Chapman & Hall/CRC Press, Boca Raton, FL, USA, 2005.

Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions. This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the details of the subject. The book is published at Chapman & Hall/CRC-Press.

Reviews:
Irad Yavneh in SIAM Review, Volume 48, Number 2, pp. 433-435, 2006
Justin Wan in Mathematics of Computation, Volume 76, Number 258, pp. 1089-1091, 2007


Journal papers, Proceedings

1. R. Wienands and H. Köstler, A practical framework for the construction of prolongation operators for multigrid based on canonical basis functions. Comput. Visual. Sci. 13, 207-220 (2010).


2. R. Wienands and I. Yavneh, Collocation Coarse Approximation (CCA) in Multigrid, SIAM J. Sci. Comput. 31, 3643-3660 (2009).


3. H. Köstler, K. Ruhnau, and R. Wienands, Multigrid solution of the optical flow system using a combined diffusion and curvature-based regularizer. Numer. Linear Algebra Appl. 15, 201-218 (2008).


4. H. bin Zubair, C. W. Oosterlee, and R. Wienands, Multigrid for high dimensional elliptic partial differential equations on nonequidistant grids. SIAM J. Sci. Comput. 29, 1613-1636 (2007).


5. R. Wienands, Coarse grid approximation governed by Local Fourier Analysis. In: P. Wesseling, E. Onate and J. Periaux (eds.), European Conference on Computational Fluid Dynamics (ECCOMAS), TU Delft, Egmond an Zee, September 5th-8th 2006.


6. R. Wienands and O. Bröker, Weighted Relaxations as Smoothers for Multigrid. In: P. Wesseling, C.W. Oosterlee and P. Hemker (eds), 8th European Multigrid Conference, TU Delft, Scheveningen, September 27th-30th 2005.


7. R. Wienands, Selecting coarse grid operators within a multigrid algorithm by local Fourier analysis. Mathematisches Forschungsinstitut Oberwolfach, Report No. 20/2005, 1171-1174 (2005).


8. F. J. Gaspar, F. J. Lisbona, C. W. Oosterlee, and R. Wienands, A Systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system. Numer. Linear Algebra Appl. 11, 93-113 (2004).


9. M. Mohr and R. Wienands, Cell-Centred multigrid revisited. Comput. Visual. Sci. 7, 129-140 (2004).


10. R. Wienands, F. J. Gaspar, F. J. Lisbona, and C. W. Oosterlee, An efficient multigrid solver based on distributive smoothing for poroelasticity equations. Computing 73, 99-119 (2004).


11. R. Wienands, F.J. Gaspar, F.J. Lisbona and C.W. Oosterlee, Analysis of a Pointwise Smoother in Multigrid for Poroelasticity. In: K.J. Bathe (ed.), 2nd MIT Conf. on Comp. Fluid and Solid Mechanics 2003, 2178-2181, Elsevier (2003).


12. C. W. Oosterlee and R. Wienands, A genetic search for optimal multigrid components within a Fourier analysis setting. SIAM J. Sci. Comput. 24, 924-944 (2002).


13. R. Wienands and C. W. Oosterlee, On three-grid Fourier analysis for multigrid. SIAM J. Sci. Comput., 23, 651-671 (2001).


14. R. Wienands, C. W. Oosterlee, and T. Washio, Fourier analysis of GMRES(m) preconditioned by multigrid. SIAM J. Sci. Comput., 22, 582-603 (2000).


15. R. Wienands and C. W. Oosterlee, Fourier analysis for Krylov subspace acceleration of multigrid with application to 3D anisotropic problems. In: E. Dick, K. Riemslagh, J. Vierendeels (eds.), Multigrid Methods VI, Lecture Notes in Computational Science and Engineering 14, 278-284, Springer, Berlin (2000).


16. C. W. Oosterlee, R. Wienands, T. Washio and F. J. Gaspar, The acceleration of multigrid convergence by recombination techniques. In: E. Dick, K. Riemslagh, J. Vierendeels (eds.), Multigrid Methods VI, Lecture Notes in Computational Science and Engineering 14, 34-43, Springer, Berlin (2000).


17. C.W. Oosterlee, F.J. Gaspar, T. Washio, and R. Wienands, New smoothers for higher order upwind discretizations of convection-dominated problems like the Euler equations. In: A. Schüller (ed.), Portable Parallelization of Industrial Aerodynamic Applications (POPINDA), Results of a BMBF Project, Notes on Num. Fluid Mech. 71, Section 3.5, Vieweg Braunschweig (1999)


18. C. W. Oosterlee, F. J. Gaspar, T. Washio, and R. Wienands, Multigrid line smoothers for higher order upwind discretizations of convection-dominated problems. Journ. Comp. Physics 139, 274-307 (1998).


19. C. W. Oosterlee, F. J. Gaspar, T. Washio, and R. Wienands, Fast multigrid solvers for higher order upwind discretizations of convection-dominated problems. In: W. Hackbusch, G. Wittum (eds.), Multigrid Methods V, Lecture Notes in Computational Science and Engineering 3, Springer Berlin, 212-224 (1998).