Overview on ILUPACK

OBJECTIVE OF ILUPACK

Numerical solution of large sparse linear systems Ax=b by

• iterative methods, in particular preconditioned Krylov subspace methods
• preconditioner constructed from incomplete LU decomposition

PRECONDITIONED KRYLOV SUBSPACE METHODS

• General case. As iterative solver preconditioned restarted GMRES is used.
• Symmetric positive definite case. Use preconditioned CG.

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

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.

4. Template 4. Iterative solver
   After the incomplete LU decomposition is computed, the linear system is solved iteratively.