The Hierarchical LU node () is an attribute node that handles parameters for boundary element method (BEM) solvers that use hierarchical LU factorization. Right-click an Iterative, Krylov Preconditioner, Presmoother, Postsmoother, or Coarse Solver attribute node to add an Hierarchical LU node.

This node can only be used together with the boundary element method. The Hierarchical LU algorithm approximately factorizes a matrix stored in the BEM Far field approximation format. It is useful when other preconditioners for BEM fails to converge because it usually converges quickly. You can control the numerical accuracy of the approximate LU factorization with the Drop tolerance and Elimination tolerance settings.

Use the Drop tolerance field to tune the maximum allowed sizes of dropped (neglected) elements (default: 0.001). 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.

Use the Elimination tolerance field to specify the tolerance (default: 1) for the computation of the eliminated Jacobian (multiplies with Drop tolerance value).

Use the Number of iterations field to specify how many iterations to perform (default: 2). The relaxation factor ω is similar to the one used by, for example, the SOR node. Specify such a factor in the Relaxation factor field (default: 1). See also About the Relaxation Factor.

Use the settings in the Hybridization section to set up a hybrid preconditioner where the direct preconditioner is active for some dependent variables. See Hybrid Preconditioners for more information.