Approximate Inverse Preconditioning of FE Systems for Elliptic Operators with non-smooth Coefficients

Mario Bebendorf

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Submission date: 26. Feb. 2004
Pages: 16
published in: SIAM journal on matrix analysis and applications, 27 (2006) 4, p. 909-929 
DOI number (of the published article): 10.1137/S0895479803437621
Bibtex
MSC-Numbers: 65F05, 65F50, 65N30
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Abstract:
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.