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The paper describes and analyzes an Average Schwarz Method with spectrally enriched coarse space for a reduced Hsieh-Clough-Tocher (RHCT) finite element discretization of a 4th-order elliptic multiscale problem. The derived symmetric preconditioner is applied and the PCG iterative method is used to solve the preconditioned problem. Suppose the enrichments of the coarse space contain sufficiently many specially constructed eigenfunctions. In that case, the convergence rate of the PCG method is weakly dependent on the ratio of the coarse to fine mesh h/H.

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Adaptive Parallel Average Schwarz Preconditioner for Reduced Hsieh-Clouh-Tocher Macro Element

  • 会议论文

  • 发表日期：

    2025年

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  • Leszek Marcinkowski,
  • Talal Rahman

摘要

The paper describes and analyzes an Average Schwarz Method with spectrally enriched coarse space for a reduced Hsieh-Clough-Tocher (RHCT) finite element discretization of a 4th-order elliptic multiscale problem. The derived symmetric preconditioner is applied and the PCG iterative method is used to solve the preconditioned problem. Suppose the enrichments of the coarse space contain sufficiently many specially constructed eigenfunctions. In that case, the convergence rate of the PCG method is weakly dependent on the ratio of the coarse to fine mesh h/H.