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arXiv · hep-lat/9204014

Multigrid Methods in Lattice Field Computations

Achi Brandt
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Abstract

The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of freedom in the problem. Current and potential benefits for lattice field computations are outlined. They include: $O(n)$ solution of Dirac equations; just $O(1)$ operations in updating the solution (upon any local change of data, including the gauge field); similar efficiency in gauge fixing and updating; $O(1)$ operations in updating the inverse matrix and in calculating the change in the logarithm of its determinant; $O(n)$ operations per producing each independent configuration in statistical simulations (eliminating CSD), and, more important, effectively just $O(1)$ operations per each independent measurement (eliminating the volume factor as well). These potential capabilities have been demonstrated on simple model problems. Extensions to real life are explored.

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BibTeXRIS

Achi Brandt. 1992-04-27. Multigrid Methods in Lattice Field Computations. https://doi.org/10.1016/0920-5632(92)90234-j

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