Locally Refined Solution of Unsymmetric and Nonlinear Problems
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.
Keywordsmultigrid method unstructured locally refined grids nonlinear p.d.e unsymmetric linear systems
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