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- W2073529350 abstract "A survey of two approaches for stabilizing the hierarchical basis (HB) multilevel preconditioners, both additive and multiplicative, is presented. The first approach is based on the algebraic extension of the two-level methods, exploiting recursive calls to coarser discretization levels. These recursive calls can be viewed as inner iterations (at a given discretization level), exploiting the already defined preconditioner at coarser levels in a polynomially-based inner iteration method. The latter gives rise to hybrid-type multilevel cycles. This is the so-called (hybrid) algebraic multilevel iteration (AMLI) method. The second approach is based on a different direct multilevel splitting of the finite element discretization space. This gives rise to the so-called wavelet multilevel decomposition based on $L^2$-projections, which in practice must be approximated. Both approaches---the AMLI one and the one based on approximate wavelet decompositions---lead to optimal relative condition numbers of the multilevel preconditioners." @default.
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- W2073529350 date "1997-01-01" @default.
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- W2073529350 title "On Two Ways of Stabilizing the Hierarchical Basis Multilevel Methods" @default.
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- W2073529350 doi "https://doi.org/10.1137/s0036144595282211" @default.
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