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1 results

  • An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

  • Part of
  • Xiaoqiang Yue, Shi Shu, Xiao wen Xu, Zhiyang Zhou
  • Journal:
    Communications in Computational Physics / Volume 18 / Issue 5 / November 2015
    Published online by Cambridge University Press:
    23 November 2015, pp. 1313-1335
    Print publication:
    November 2015

  • The paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.