Matrix-dependent prolongations and restrictions in a blackbox multigrid solver. (English) Zbl 0717.65099

If one applies standard multigrid methods to solve linear systems resulting from the 9-point discretization of a linear second-order elliptic partial differential equation with discontinuous coefficients or dominating first-order terms, the rate of convergence often deteriorates. To improve the convergence behaviour of the multigrid methods in these cases the author develops a special multigrid code, in which matrix- dependent prolongations and restrictions are used.
By hard numerical examples it is shown that this code is more robust and more efficient (for these hard problems) than a standard multigrid code based on the usual prolongation and restriction obtained by linear interpolation.
Reviewer: M.Jung


65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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