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Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems

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Abstract

We describe tensor product type techniques to derive robust solvers for anisotropic elliptic model problems on rectangular domains in ℝd. Our analysis is based on the theory of additive subspace correction methods and applies to finite element and prewavelet schemes. We present multilevel- and prewavelet-based methods that are robust for anisotropic diffusion operators with additional Helmholtz term. Furthermore, the resulting convergence rates are independent of the discretization level. Beside their theoretical foundation, we also report on the results of various numerical experiments to compare the different methods.

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Authors and Affiliations

  1. Institut für Informatik, TU München, D-80290, München, Germany

    M. Griebel

  2. Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA

    P. Oswald

Authors
  1. M. Griebel
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  2. P. Oswald
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Griebel, M., Oswald, P. Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems. Adv Comput Math 4, 171–206 (1995). https://doi.org/10.1007/BF02123478

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