Re: [Libmesh-users] [RB] Question about a poseteriori error estimation

[David K. <dav...@ak...>]

On Sun, Oct 14, 2018 at 3:45 AM <ss...@pu...> 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 <dav...@ak...>
> *Sent:* Friday, October 12, 2018 9:30 PM
> *To:* 강신성 <ss...@pu...>
> *Cc:* libmesh-users <lib...@li...>
> *Subject:* Re: [Libmesh-users] [RB] Question about a poseteriori error
> estimation
>
>
>
> On Fri, Oct 12, 2018 at 2:58 AM <ss...@pu...> 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
>