On Sun, Oct 14, 2018 at 3:45 AM <ss.k...@pusan.ac.kr> wrote: > Thank you for your prompt reply, David. > > > > I looked at the “assembly.h” in RB example 1 and my code, and I > understood your answer. > > You said inner-product must be parameter-independent. > > That is, dual norm of residual in LibMesh is always “X-norm” > (parameter-independent > norm), right? >
Yes, it uses the parameter-independent inner product and norm that you specify. (I'm not familiar with referring to this as the "X-norm", but if that's what you want to call it then that's fine.) > By the way, if you do not mind, could you please tell me what special > case used the parameter in “compute_residual_dual_norm(N)” code? > You call compute_residual_dual_norm after you do a solve. So the parameter mu that is used inside compute_residual_dual_norm is the parameter that was used for the preceding solve. The idea is that you're getting the dual norm of the residual associated with your previous solve. Best, David > *From:* David Knezevic <david.kneze...@akselos.com> > *Sent:* Friday, October 12, 2018 9:30 PM > *To:* 강신성 <ss.k...@pusan.ac.kr> > *Cc:* libmesh-users <libmesh-users@lists.sourceforge.net> > *Subject:* Re: [Libmesh-users] [RB] Question about a poseteriori error > estimation > > > > On Fri, Oct 12, 2018 at 2:58 AM <ss.k...@pusan.ac.kr> wrote: > > Hello, all. > > > > I have a question about the RB error estimation in LibMesh. > > > > I know that the maximum error bound is computed in the function > "RBConstruction::compute_max_error_bound()." > > Here we should compute the "dual norm of residual" using the function > "compute_residual_dual_norm(N)." > > But I do not know exactly if this "dual norm of residual" is "X-norm" or > "energy-norm," where "X-norm" is parameter-independent and "energy-norm" is > parameter-dependent. > > > > The norm that is used is specified by the user. For example, in > reduced_basis_ex1, we set the inner product in SimpleRBConstruction to be > the "A0" operator (and the inner product is used to generate the norm). So > the inner-product and norm that is used is completely up to you. > > > > Note, though, that the inner product must be parameter independent. This > is necessary since we don't want to change the inner product when we change > parameters. > > > > > > When I looked at the "compute_residual_dual_norm(N)" code, the current > parameter is called by the "const RBParameters & mu = get_parameters();" > code line. > > So I guess the "dual norm of residual" is the "energy-norm," and I would > like to ask if it is correct. > > > > No, the residual is whatever is specified by the user by calling > "set_inner_product_assembly". The parameter is used to evaluate the dual > norm in any specific case, but that is not related to the inner product > that is used. > > > > Best, > David > _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
