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
- if ( (i,j)S ) and ( (r,j)S ) then
- end (j-loop)
- e := dai,r;
- end if
- end (i-loop)
- d := 1/ arr
- 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"
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