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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
∣aij∣< tol ×∣aii∣\vert a_{ij} \vert < \text{ tol } \times \vert a_{ii} \vert
note

you can use droptol between 0.0010.001 and 0.0050.005

  • 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
  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).