Overview on ILUPACK

OBJECTIVE OF ILUPACK

Numerical solution of large sparse linear systems Ax=b by



PRECONDITIONED KRYLOV SUBSPACE METHODS



INCOMPLETE LU DECOMPOSITION

Incomplete LU decomposition methods



INVERSE-BASED APPROACH

Prescribe a bound and apply diagonal pivoting such that at any step k, and .

Strategy ensures that the

is kept bounded.



TEMPLATES THAT FORM ILUPACK

  1. Template 1. Static reordering schemes.
    Given system is reordered and scaled.
      -->  
    Initial system reordered and scaled system

  2. Template 2. Inverse-based ILU with diagonal pivoting
    After preordering and scaling the initial system, an inverse-based ILU with diagonal pivoting is applied.

    controlled by diagonal pivoting         

  3. Template 3. Multilevel framework
    For the reduced matrix that is left over from the second template, a recursive multilevel strategy is applied that repeatedly applies Templates 1 and 2.

    west2021_org west2021_lev1start west2021_lev1end
    west2021_lev2org west2021_lev2start west2021_lev2end
  4. Template 4. Iterative solver
    After the incomplete LU decomposition is computed, the linear system is solved iteratively.



m.bollhoefer@tu-bs.de

Last modified: Tuesday, 11-Oct-2011 17:45:55 CEST