Incomplete LU factorization - ILU

From CFD-Wiki

Algorithm ILU

Algorithm for computing ILU for a n by n matrix A is given by

  for r:= 1 step 1 until n-1 do
      d := 1/ arr 

      for i := (r+1) step 1 until n do 

         if (i,r)S then 

            e := dai,r; 

            ai,r := e ; 

            for j := (r+1) step 1 until n do 

              if ( (i,j)S ) and ( (r,j)S ) then 

                  ai,j := ai,j - e ar,j 

              end if 

            end (j-loop) 

         end if 

      end (i-loop) 

  end (r-loop) 

Here S represents the set of elements of matrix A. The same algorithm could be applied to full matrix A.

Reference

Tony F. Chan and Hank A. Van Der Vorst , Approaximate and Incomplete Factorizations