On Fri, Mar 15, 2019 at 3:07 AM <ss...@pu...> wrote:
> Hello, David.
>
>
>
> I have a question about the inner product assembly in RB example 5.
>
>
>
> According to equations about the RB method, the inner product assembly
> (•,•)_{V} in the RB method is constructed in the same equation as A
> assembly a(•,•;mu), with the constant parameter mu’.
>
> In other words, the inner product assembly should be computed as
> (•,•)_{V} = a(•,•;mu’), but the inner product assembly in the RB example 5
> is not.
>
>
>
> Why does not the inner product assembly of the RB example 5 code include
> coefficient matrix C_{ijkl}, which is used in A assembly?
>
>
>
> I look forward to hearing from you.
>
In practice the exact choice of inner product doesn't matter too much
unless you're really trying to compute a rigorous error bound, since then
you need to be careful about the way the inner product is defined in order
to make sure your error bound is rigorous. In the libMesh examples we're
not trying to generate a rigorous error bound since that involves extra
complications (e.g. SCM in some cases), and so instead we just compute an
approximate bound which is usually sufficient in practice anyway. With that
goal in mind, the simpler inner product defined in the example is
sufficient. But of course if you can define the inner product however you
like for your own cases.
Best,
David
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