Approximate Inverse Preconditioning of Finite Element Discretizations of Elliptic Operators with Nonsmooth Coefficients
Mario Bebendorf · SIAM Journal on Matrix Analysis and Applications · 2006
A new class of approximate inverse preconditioners for large finite element stiffness matrices arising from second order elliptic partial differential operators is introduced which guarantees a bounded, problem-independent condition number. Since the proposed preconditioner is based on hierarchical matrices, it can be generated, stored, and multiplied by a vector with almost linear complexity. This preconditioner may be used as a black-box method, because it is robust with respect to varying coefficients and because it can be applied to arbitrary quasi-uniform grids.