Auxiliary space preconditioners of the form ∇*B_div∇ are shown to be uniformly spectrally equivalent to the negative-order fractional Laplacian; the required fractional H(div) preconditioner is built by additive multigrid but depends on an unproven two-level estimate.
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An Auxiliary Space Preconditioner for Fractional Laplacian of Negative Order
Auxiliary space preconditioners of the form ∇*B_div∇ are shown to be uniformly spectrally equivalent to the negative-order fractional Laplacian; the required fractional H(div) preconditioner is built by additive multigrid but depends on an unproven two-level estimate.