Skip to main content

GetILUDP

This routine computes ILUDP preconditioner: incomplete LU factorization with standard droppoing strategy.

Interface​

INTERFACE
  MODULE SUBROUTINE GetILUDP(obj, ALU, JLU, JU, alpha, droptol, &
    & permtol, mbloc, IPERM)
    TYPE(CSRMatrix_), INTENT(INOUT) :: obj
    REAL(DFP), ALLOCATABLE, INTENT(INOUT) :: ALU(:)
    INTEGER(I4B), ALLOCATABLE, INTENT(INOUT) :: JLU(:)
    INTEGER(I4B), ALLOCATABLE, INTENT(INOUT) :: JU(:)
    REAL(DFP), INTENT(IN) :: alpha
    REAL(DFP), INTENT(IN) :: droptol
    REAL(DFP), INTENT(IN) :: permtol
    INTEGER(I4B), INTENT(IN) :: mbloc
    INTEGER(I4B), ALLOCATABLE, INTENT(INOUT) :: IPERM(:)
  END SUBROUTINE GetILUDP
END INTERFACE
  • droptol is the tolerance used for dropping elements in L and U. elements are dropped if they are .lt. norm(row) x droptol row = row being eliminated
  • permtol is the tolerance ratio used for determning whether to permute two columns. Two columns are permuted only when abs(a(i,j))*permtol .gt. abs(a (i,i))
info

permtol = 0 means never permute, and a good values 0.1 to 0.01]

  • mbloc, if desired, permuting can be done only within the diagonal blocks of size mbloc. Useful for PDE problems with several degrees of freedom. If feature not wanted take mbloc=n.

  • iperm contains the permutation arrays, iperm(1:n) old numbers of unknowns, iperm(n+1:2\*n) reverse permutation for new unknowns.

  • abs(a(i,j)) < droptol, that is, average magnitude of elements in row i of A

  • alpha is diagonal compensation parameter, alph * (sum of all dropped out elements in a given row) is added to the diagonal element of U of the factorization

    • alph = 0 means the scheme is ILU with threshold,
    • alph = 1 means the scheme is MILU with threshold.

  • droptol is Threshold parameter for dropping small terms in the factorization. During the elimination, a term a(i,j) is dropped whenever abs (a(i,j)) .lt. droptol

  • obj matrix stored in Compressed Sparse Row format.

  • 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 integer array of length n containing the pointers to the beginning of each row of U in the matrix ALU,JLU.

  • 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.