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Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials

In this paper we construct optimal preconditioners for the discrete mathematical models arising in modeling the elastic responses of lattice block materials. We present extensive numerical experiments to show that the preconditioned system has a uniformly bounded condition number with respect to the size of problem and with respect to the parameter relating the stretching and bending of the beams in a lattice. Using the limiting system of partial differential equations, we show theoretically that for square lattices the proposed preconditioners are efficient by proving a uniform bound on the condition number of the preconditioned system.