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/ a_rr

for i := (r+1) step 1 until n do

if (i,r)S then

e := da_i,r;

a_i,r := e ;

for j := (r+1) step 1 until n do

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

a_i,j := a_i,j - e a_r,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