Sunday, November 23, 2008

Rates of convergence. Using DD preconditioning


Convergence of different methods solving system of linear equations for finite element method on grids of different sizes.

  • The asterisk means that not the actual number of iterations is presented. The actual number is multiplied by some constant, so that the iterations in subdomains would also be taken into consideration.
  • The number of iterations for Gauss method assumed to be equal to size of the matrix.
  • Jacobi converges too slow, that's why here it is shown for accuracy 1e-5; 1e-8 for all the rest
  • CG - stands for Conjugate Gradient method
  • Additive Schwartz can be accelerated, by performing the iterations in subdomains parallel (my implementation accelerated it in nearly 1.3 times)

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