Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories

Details Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories Algebraic Multigrid for Disordered Systems and Lattice Gauge Theories

2000-11-30

arxiv.org/abs/hep-lat/0011092v1

Physics

High Energy Physics

High Energy Physics - Lattice

43 pages, 14 figures, revtex4 style

Scientific paper

10.1063/1.1386842

The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the effective coarse-grid operator is obtained as the Schur complement of the original matrix. An optimal approximation to it is found by a numerical optimization procedure akin to Monte Carlo renormalization, resulting in a generalized (gauge-path dependent) stencil that is easily evaluated for a given disorder field. Applications to preconditioning and relaxation methods are investigated.

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