## Multigrid algorithm with conditional coarsening for the non-aligned sonic flow

Boris Diskin

### Abstract

A multigrid approach using conditional coarsening in constructing solvers for non-elliptic equations on a rectangular grid is presented. Such an approach permits the achievement of a full multigrid efficiency even in the case where the equation characteristics do not align with the grid. The 2D sonic-flow equation linearized over a constant velocity field has been chosen as the model problem. An efficient $FMG$ solver for the problem is demonstrated.

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### Key words

multigrid methods, conditional coarsening, sonic flow, non-alignment.

### AMS subject classifications

65N55, 76H05, 76M20.