Multigrid in general relativity. I. Schwarzschild spacetime

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Abstract
The multigrid method is applied for numerically solving the stationary axisymmetric Einstein equations in vacuum. Numerical results are presented for the model problem where the equations are specialised to the Schwarzschild metric. Special attention has been paid to the effect of singularities (which are a typical feature of such problems) on the multigrid procedures. This is the first test problem of a series, aiming at the treatment of self-gravitating tori rotating around rapidly rotating black holes.