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GetILUD

This routine computes the ILU factorization with standard threshold dropping: at ith step of elimination, an element a(i,j) in row i is dropped if it satisfies the following criterion:

∣a(i,j)∣< tol ×a~i,\vert a(i,j) \vert < \text{ tol } \times \tilde{a}_{i},

where a~i\tilde{a}_{i} is average magnitude of elements in row i of A, which is given by:

a~i=1nnzi∑jnnzi∣a(i,j)∣\tilde{a}_{i} = \frac{1}{{nnz}_{i}}\sum_{j}^{nnz_{i}}{\vert a(i,j) \vert}

where, nnzi{nnz}_{i} is the number of nonzeros in ith row.

  • There is no control on memory size required for the factors as is done in ILUT.
  • This routine computes also various diagonal compensation ILU's such, MILU. These are defined through the parameter alpha.
caution

All diagonal elements of the input matrix must be nonzero.

Interface​

INTERFACE
MODULE SUBROUTINE GetILUD(obj, ALU, JLU, JU, alpha, droptol)
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
END SUBROUTINE GetILUD
END INTERFACE

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

    • alph = 0 means the scheme is ILU with threshold, that is, no compensation
    • alph = 1 means the scheme is MILU with threshold.

  • droptol = 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. tol

  • nnz the number of NNZ elements in the row.

  • 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.

  • droptol it governs the theresholding in L and U. Any element whose MAGNITUDE is less than some tolerance (relative to the abs value of diagonal element in U) is dropped.