Locally Refined Solution of Unsymmetric and Nonlinear Problems

  • Peter Bastian
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


We describe a multigrid method with optimal computational work per cycle on locally refined grids. The method can be interpreted as a multiplicative variant of the BPX preconditioner but it is motivated from the viewpoint of the classical multigrid method. This has several advantages: In the case of quasi-uniform refinement the method is equivalent to the classical multigrid method. All well known smoothing algorithms can be used, including incomplete decompositions. In the nonlinear case the nonlinear multigrid method can be directly transferred to locally refined grids. Since no outer CG iteration is needed the method can also be applied directly to unsymmetric problems. Results will be presented for scalar, linear and nonlinear convection-diffusion equations.


multigrid method unstructured locally refined grids nonlinear p.d.e unsymmetric linear systems 


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Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • Peter Bastian
    • 1
  1. 1.Interdisziplinäres Zentrum für Wissenschaftliches RechnenUniversität HeidelbergHeidelbergDeutschland

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