GetILUT

This routine builds the ILUT precondition.

ILUT: Incomplete LU factorization with dual truncation strategy.

caution

The diagonal elements of the input matrix must be nonzero (at least 'structurally').

Dual drop strategy works as follows:

Theresholding in L and U as set by droptol. Any element whose MAGNITUDE is less than some tolerance (relative to the abs value of diagonal element in U) is dropped, that is

\vert a_{ij} \vert < \text{ tol } \times \vert a_{ii} \vert

note

you can use droptol between $0.001$ and $0.005$

Keeping only the largest lfil elements in the ith row of L and the largest lfil elements in the ith row of U (excluding diagonal elements).

note

You can use lfil between 5 ans 10. Higher value of lfil is more reliable.

Flexibility: one can use droptol=0 to get a strategy based on keeping the largest elements in each row of L and U.
Taking droptol .ne. 0 but lfil=n will give the usual threshold strategy (however, fill-in is then not predictible).

Sparse matrix in modified sparse row storage format:

Interface

܀ Interface 1
܀ Interface 2
↢

INTERFACE
  MODULE SUBROUTINE GetILUT(obj, ALU, JLU, JU, lfil, droptol)
    TYPE(CSRMatrix_), INTENT(INOUT) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: ALU(:)
    INTEGER(I4B), ALLOCATABLE, INTENT(INOUT) :: JLU(:)
    INTEGER(I4B), ALLOCATABLE, INTENT(INOUT) :: JU(:)
    INTEGER(I4B), INTENT(IN) :: lfil
    REAL(DFP), INTENT(IN) :: droptol
  END SUBROUTINE GetILUT
END INTERFACE

obj matrix stored in Compressed Sparse Row format.
lfil is a fill-in parameter. Each row of L and each row of U will have a maximum of lfil elements (excluding the diagonal element). lfil must be .ge. 0.
droptol sets the threshold for dropping small terms in the factorization. See below for details on dropping strategy.
ALU,JLU, matrix stored in Modified Sparse Row (MSR) Format containing the L and U factors together. The diagonal (stored in ALU(1:n) ) is inverted. Each ith row of the ALU,JLU matrix contains the ith row of L (excluding the diagonal entry=1) followed by the ith row of U.
JU is an integer array of length n containing the pointers to the beginning of each row of U in the matrix ALU,JLU.

Dual drop strategy works as follows:

Theresholding in L and U as set by droptol. Any element whose MAGNITUDE is less than some tolerance (relative to the abs value of diagonal element in U) is dropped.
Keeping only the largest lfil elements in the ith row of L and the largest lfil elements in the ith row of U (excluding diagonal elements).
Flexibility: one can use droptol=0 to get a strategy based on keeping the largest elements in each row of L and U.
Taking droptol .ne. 0 but lfil=n will give the usual threshold strategy (however, fill-in is then mpredictible).

INTERFACE
  MODULE SUBROUTINE GetILUT(obj, Pmat, lfil, droptol)
    TYPE(CSRMatrix_), INTENT(INOUT) :: obj
    TYPE(CSRMatrix_), INTENT(INOUT) :: Pmat
    INTEGER(I4B), INTENT(IN) :: lfil
    REAL(DFP), INTENT(IN) :: droptol
  END SUBROUTINE GetILUT
END INTERFACE

This method is similar to interface 1, but in this case we return ILU factorization in CSRMatrix_ form.

Interface​

Interface