On Wed, Sep 7, 2016 at 11:54 AM, Salazar De Troya, Miguel < salazardet...@llnl.gov> wrote:
> In the case I used the Adjoint Residual Error Estimator as an error > indicator to adaptively refine my mesh, will I obtain a more accurate goal > functional with less refinement than if I used a primal solution based > error indicator? Even if the error estimate of the goal functional is not > reliable. > > Yes, one would expect to achieve a better estimate of the goal functional (QoI) with the Adjoint Residual Estimator. The reliability of the error indicator depends on the estimators you use for the primal and dual weight calculations. Patch recovery tends to work well, and there is some theory behind this, which I can point to if there is interest. > With regards to the weighted error estimator, the implementation is for > the patch based recovery estimators, could I do something similar for other > error estimators, for instance, the Kelly error? > I believe extending the weighted indicator support to the Kelly error estimator should not be a problem. All the weights really do is scale contributions from each individual error component. > > Thanks > Miguel > From: <simulation...@gmail.com> on behalf of Vikram Garg < > vikram.v.g...@gmail.com> > Date: Tuesday, September 6, 2016 at 7:19 PM > To: Miguel Salazar <salazardet...@llnl.gov> > Cc: "libmesh-users@lists.sourceforge.net" <libmesh-users@lists. > sourceforge.net> > Subject: Re: [Libmesh-users] Dual weighted residual error estimator in > libMesh > > Hello Salazar, > > On Tue, Sep 6, 2016 at 5:46 PM, Salazar De Troya, Miguel < > salazardet...@llnl.gov> wrote: > >> Hello >> >> I started learning about the dual weighted residual error estimator. From >> what I read here: http://cadmus.usc.edu/UQ-SummerSchool-2013/bauman.pdf >> there are two approaches in libMesh: One, calculate the adjoint solution in >> an enriched space; two, use a classic error estimator for both the primal >> and the adjoint solutions. I have two questions with regards to this >> approach: >> >> * What is the error incurred by choosing the second option? >> > > The second option (called Adjoint Residual Error Estimator) is suitable > for use as an *error indicator*, i.e. the calculation of an element wise > metric > to decide whether they should be refined. For obtaining reliable error > estimates, the first option (Adjoint Refinement Estimator) is the way to go. > > A combined strategy can also be used, where one does a few mesh refinement > steps using the Adjoint Residual approach, and then does a step with the > Adjoint Refinement Estimator to check whether error tolerances have been > met. > > >> * In the case of elasticity, how do we apply the constitutive tensor? >> In both error estimators or just the primal? Basically, in the above >> presentation, slide 66, the application of R_k >> > > If you use the Adjoint Refinement Error Estimator, the constitutive tensor > is automatically included via the definition of the residual one provides > in element_time_deriative. > > If you use the Adjoint Residual Indicator, and wish to include the effect > of the constitutive tensor, you will need to build a weights matrix. See > *Adjoints > example 3*. > > If your constitutive tensor is nonlinear, then you will need to use the > weighted patch recovery estimator (see src/error_estimation/ > weighted_patch_recovery_estimator.C), specify the weight functions and > provide function pointers to them. *Adjoints example 3* covers this as > well. > > >> >> Thanks >> Miguel >> >> ------------------------------------------------------------ >> ------------------ >> _______________________________________________ >> Libmesh-users mailing list >> Libmesh-users@lists.sourceforge.net >> https://lists.sourceforge.net/lists/listinfo/libmesh-users >> > > Thanks. > -- > Vikram Garg > Postdoctoral Associate > The University of Texas at Austin > > http://vikramvgarg.wordpress.com/ > http://www.runforindia.org/runners/vikramg > -- Vikram Garg Postdoctoral Associate The University of Texas at Austin http://vikramvgarg.wordpress.com/ http://www.runforindia.org/runners/vikramg ------------------------------------------------------------------------------ _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
