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1 results

  • 6 - Fast Solvers

  • from Part I - The Sobolev Space Setting
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book:
    Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
    Published online:
    10 October 2019
    Print publication:
    24 October 2019, pp 90-102

  • Summary

    By representing the operator as independent, sparse, well-conditioned linear systems, theoperator-adapted wavelet (gamblet) transform of the previous chapter naturally leads to a scalable linear solver with some degree of universality. The near-linear complexity of the solver and the Fast Gamblet Transform are based on the nesting, exponential localization, and Riesz stability of the underlying wavelets. The representation of the Green's function in the basis formed by these wavelets is sparse and rank-revealing.The algorithm isillustrated through a numerical application toa second-order divergence form elliptic operator with rough coefficients.