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Approximate Inverse Preconditioning of FE Systems for Elliptic Operators with non-smooth Coefficients
A new class of approximate inverse preconditioners for large finite element stiffness matrices arising from elliptic partial differential operators is introduced which guarantees a bounded number of iterations of the conjugate gradients method. This preconditioner can be generated, stored and multiplied by a vector with almost linear complexity. Since the proposed preconditioner is robust with respect to varying coefficients and does not need a grid hierarchy it may be used as a black-box method.