, Volume 18, Issue 8, pp 813-843

An introduction to the multi-grid method for numerical relativists

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Abstract

The multi-grid method, which has made a considerable impact on both theoretical and applied numerical analysis in the past decade, is reviewed within the context of the solution of boundary value problems in 3 + 1 numerical relativity. The basic principles of operation of a multi-grid algorithm are discussed and, with the aid of numerical experiments on exactly soluble model problems, the method is compared to more traditional techniques such as SOR. The results of application of the method to a set of axisymmetric problems for black hole initial data, previously determined by relaxation techniques, are presented.