Incomplete LU

The node (

) is an attribute node that handles parameters for linear system solvers/preconditioners that use incomplete LU factorization. Right-click an Iterative, Krylov Preconditioner, Presmoother, Postsmoother, or Coarse Solver attribute node to add an node. Also see About Incomplete LU.

In this section you specify the properties of the incomplete LU preconditioner.

Select a . Select:

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to use the ILUT solver (preconditioner) from Intel® MKL (Intel® Math Kernel Library). Unlike ILU0, ILUT preserves some resulting fill-in in the preconditioner matrix (see Ref. 26).

The ILUT (MKL) and ILUT0 (MKL) preconditioners can perform better than ILU when solving large systems but are not multithreaded.

	ILUT (MKL) and ILU0 (MKL) are not applicable to complex-valued problems.

For , select an option from the list to specify a drop rule. See Selecting a Drop Rule. Select:

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(the default) to let the solver drop (neglect) elements that have small enough absolute values. Tune the sizes of the neglected elements either in the field or using the accompanying slide bar. A larger tolerance neglects more elements.

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to let the solver keep a certain fraction of the elements. The elements with largest absolute values are kept. Tune the number of nonzero elements in the incomplete factorization using either the field or the accompanying field. A smaller fill ratio neglects more elements.

For , you can specify both a drop tolerance and a fill ratio.

For , , and , use the field or the accompanying slide bar to tune the maximum allowed sizes of dropped (neglected) elements (default: 0.01). A smaller drop tolerance means that the preconditioner drops fewer elements and so the preconditioner becomes more accurate. This leads to fewer iterations in the iterative solver, but memory requirements and preconditioning time increase. A larger drop tolerance means that the preconditioner drops more elements and so memory use and preconditioning time decrease. In this case, however, the preconditioner becomes less accurate, which leads to more iterations in the iterative solver, or, if the drop tolerance is too high, to no convergence at all. Often it is most efficient to use as high a drop tolerance as possible; that is, choose it so that the iterative solver barely converges.

For , by default the solver never drops elements in positions where the original matrix is nonzero. Clear the check box to allow the solver to also drop such elements.

For both and , use the field to enter a number between 0 and 1 that acts as pivot threshold (default: 1). This means that in any given column, the algorithm accepts an entry as a pivot element if its absolute value is greater than or equal to the specified pivot threshold times the largest absolute value in the column. The solver permutes rows for stability. In any given column, if the absolute value of the diagonal element is less than the pivot threshold times the largest absolute value in the column, it permutes rows such that the largest element is on the diagonal. Thus the default value 1 means that it uses partial pivoting.

For , , and — once the approximate factors L and U have been computed — you can use the incomplete LU factorization as an iterative preconditioner/smoother. Here, M = (LU)/ω, where ω is a relaxation factor, and L and U are the approximate factors. Use the field to specify how many iterations to perform (default: 1). The relaxation factor ω is similar to the one used by, for example, the node. Specify such a factor in the field (default: 1). See also About the Relaxation Factor.