Reference documentation for deal.II version GIT d8dacc551e 2022-08-19 06:50:03+00:00

#include <deal.II/lac/trilinos_precondition.h>

## Public Member Functions

AdditionalData (const double ilut_drop=0., const unsigned int ilut_fill=0, const double ilut_atol=0., const double ilut_rtol=1., const unsigned int overlap=0)

## Public Attributes

double ilut_drop

unsigned int ilut_fill

double ilut_atol

double ilut_rtol

unsigned int overlap

## Detailed Description

Standardized data struct to pipe additional parameters to the preconditioner. The Trilinos ILU-T decomposition allows for some fill- in, so it actually is a threshold incomplete LU factorization. The amount of fill-in, and hence, the amount of memory used by this preconditioner, is controlled by the parameters ilut_drop and ilut_fill, which specifies a threshold about which values should form the incomplete factorization and the level of additional fill-in. When forming the preconditioner, for certain problems bad conditioning (or just bad luck) can cause the preconditioner to be very poorly conditioned. Hence it can help to add diagonal perturbations to the original matrix and form the preconditioner for this slightly better matrix. ilut_atol is an absolute perturbation that is added to the diagonal before forming the prec, and ilu_rtol is a scaling factor $$rtol \geq 1$$. The last parameter specifies the overlap of the partitions when the preconditioner runs in parallel.

Definition at line 1100 of file trilinos_precondition.h.

## Constructor & Destructor Documentation

 TrilinosWrappers::PreconditionILUT::AdditionalData::AdditionalData ( const double ilut_drop = 0., const unsigned int ilut_fill = 0, const double ilut_atol = 0., const double ilut_rtol = 1., const unsigned int overlap = 0 )

Constructor. By default, no element will be dropped, the level of extra fill-ins is set to be zero (just use the matrix structure, do not generate any additional fill-in except the one that results from non-dropping large elements), the tolerance level are 0 and 1, respectively, and the overlap in case of a parallel execution is zero. This overlap in a block-application of the ILU in the parallel case makes the preconditioner a so-called additive Schwarz preconditioner.

Definition at line 553 of file trilinos_precondition.cc.

## ◆ ilut_drop

This specifies the relative size of elements which should be dropped when forming an incomplete LU decomposition with threshold.

Definition at line 1122 of file trilinos_precondition.h.

## ◆ ilut_fill

This specifies the amount of additional fill-in elements besides the sparse matrix structure. When ilu_fill is large, this means that many fill-ins will be added, so that the ILU preconditioner comes closer to a (direct) sparse LU decomposition. Note, however, that this will drastically increase the memory requirement, especially when the preconditioner is used in 3D.

Definition at line 1132 of file trilinos_precondition.h.

## ◆ ilut_atol

This specifies the amount of an absolute perturbation that will be added to the diagonal of the matrix, which sometimes can help to get better preconditioners.

Definition at line 1139 of file trilinos_precondition.h.

## ◆ ilut_rtol

This specifies the factor by which the diagonal of the matrix will be scaled, which sometimes can help to get better preconditioners.

Definition at line 1145 of file trilinos_precondition.h.