[Nek5000-users] weak derivative, dssum and binvm1 in cvode_driver

Thu Jun 5 10:11:12 CDT 2014

I guess you want to solve for species and temperature using detailed
chemistry and transport. Right?

Von:  <nek5000-users at lists.mcs.anl.gov>
Antworten an:  <nek5000-users at lists.mcs.anl.gov>
Datum:  Thursday, June 5, 2014 at 5:06 PM
An:  "nek5000-users at lists.mcs.anl.gov" <nek5000-users at lists.mcs.anl.gov>
Betreff:  Re: [Nek5000-users] weak derivative, dssum and binvm1 in
cvode_driver

Hi Paul and Stefan,

Thank you for the explanations, things are going gradually more clear in my
mind.

So for a practical application, still in the context of cvode, I would like
to add a new term to the RHS of the temperature equation. This new term is
roughly

(vdiff * grad (Y)) grad (T)
where Y is a passive scalar, vdiff the diffusion coefficient of this passive
scalar and T the temperature.

Basically in the routine makeq.f the implementation should looks like to

call wgradm1(Y_x, Y_y, Y_z, t(1,1,1,1,ifield+1), nelv)
call dssum(grad_Y, Y_x, Y_y, Y_z)
call col2(grad_Y,bintm1,ntot)

call col2(grad_Y, vdiff(1,1,1,1,ifield+2) ,ntot )

call wgradm1(T_x, T_y, T_z, t(1,1,1,1,ifield), nelv)
call dssum(grad_T, T_x, T_y, T_z)

call col2(grad_T,grad_Y,ntot)

call add2(bq(1,1,1,1,ifield), grad_T,ntot)

and then convab and wlaplacian routines will add the other terms, and it
will finish with 
call dssum(bq,nx1,ny1,nz1)
 call col2(bq,bintm1,ntot)
 call col2(bq,bm1,ntot)

Am I right??
Thank you for your help !

Best regards,
Emmanuel

On 5 Jun 2014, at 19:25, <nek5000-users at lists.mcs.anl.gov>
<nek5000-users at lists.mcs.anl.gov> wrote:

> 
> Hi Emmanuel, 
> 
> Note that bintm1 and bm1 are not precise inverses of one another.
> bm1 is the unassembled mass matrix - i.e., it is the collection of local
> (to each element) mass matrices, each of which is diagonal.
> 
> Conceptually, we denote the local mass matrix as B_L, for local.
> Then, the assembled mass matrix is:
> 
>      B := Q^T B_L Q
> 
> where Q is the Boolean matrix that copies global degrees of freedom
> to their shared counterparts (i.e., copies a values to shared faces,
> edges, vertices, etc.).   For the SEM, B_L is diagonal, as is B, so
> Binv := B^-1 is easily computed.   Once the entries of this diagonal
> matrix are known, we can copy them to their element-based locations,
> so that we can generate B^-1 * r very easily.
> 
> Often, products with these matrices, in conjunction with dssum, are used
> to generate continuous fields and that appears to be what is happening in
> this case.   An example would be if you want to find a the continuous
> counterpart to a discontinuous function g.  The usual projection approach
> is:  Find gc \in H1 such that  \int v gc dV = \int v g dV for all v in H1,
> which
> ends up looking like:
> 
> Find gc \in H1 such that:
> 
> 
>          (v,gc) = (v,g)  for all g \in H1
> 
> or
> 
>          v B gc = v Q^T B_L g_L
> 
>                gc = B^-1 Q^T B_L g_L
> 
>                gc_L = Q B^-1 Q^T B_L g_L
> 
> In Nek, the last statement is expressed as:
> 
>               call col2(g,bm1,n)
>               call dssum(g,nx1,ny1,nz1)
>               call col2(g,bintm1,n)
> 
> In your cvode case, these statements are permuted because of the
> initial state of the data and the desired output (which is to be B*q --
> which is why the variable is labeled bq).
> 
> Paul
> 
> 
> 
> 
> 
> From: nek5000-users-bounces at lists.mcs.anl.gov
> [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of
> nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov]
> Sent: Thursday, June 05, 2014 2:38 AM
> To: nek5000-users at lists.mcs.anl.gov
> Subject: Re: [Nek5000-users] weak derivative, dssum and binvm1 in cvode_driver
> 
> Hi Emmanuel
> 
> From what I recall:
> CVODE solves the governing non-linear eqns in the strong form. That¹s why we
> have to project every term of the RHS onto H2 (dssum and collocate with
> bintm1). The sum is projected again onto H2 because it gets devided by vtrans.
> Hope this helps.
> 
> Cheers,
> Stefan
> 
> Von: <nek5000-users at lists.mcs.anl.gov>
> Antworten an: <nek5000-users at lists.mcs.anl.gov>
> Datum: Thursday, June 5, 2014 at 9:20 AM
> An: "nek5000-users at lists.mcs.anl.gov" <nek5000-users at lists.mcs.anl.gov>
> Betreff: Re: [Nek5000-users] weak derivative, dssum and binvm1 in cvode_driver
> 
> I¹m adding another quick question:
> 
> why in the routine makeq, under the cvode statement, there are these following
> 2 lines:
>              call col2(bq,bintm1,ntot)
>              call col2(bq,bm1,ntot)
> 
> I¹m not sure to understand why we are multiplying bq by the inverse of the
> mass matrix (bintm1) and just after multiplying it back by the mass matrix
> (bm1). Moreover, after leaving the makeq routine, fctfun will multiplying
> again ydot=bq/vtrans by the inverse of the mass matrix.
> 
> Why all of these operations? Thank you for your help !
> 
> 
> 
> Best regards,
> Emmanuel
> 
> 
> 
> On 5 Jun 2014, at 12:14, <nek5000-users at lists.mcs.anl.gov>
> <nek5000-users at lists.mcs.anl.gov> wrote:
> 
>> Dear Nek team, 
>> 
>> I have a quick question: in cvode_driver.f, in the routine fcvfun, do all the
>> derivatives must be in weak formulation (using wgradm1) when constructing the
>> right hand side term ydot?
>> Because at the end of the routine fcvfun,  dssum and multiplication by binvm1
>> are applied to the right hand side term ydot.
>> 
>> It¹s also not clear to me if I need to apply dssum and binvm1 for each
>> derivative term appearing in my equation (in other terms, each time after
>> calling wgradm1), or if I need to apply dssum and binvm1 only to the whole
>> RHS term ydot ?
>> 
>> I¹m afraid of inconsistency if apply twice dssum and binvm1: one during the
>> construction of operators and one on the final ydot term.
>> 
>> Thank you for you help !
>> 
>> Best regards,
>> Emmanuel
>> 
>> 
>> 
>> _______________________________________________
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>> Nek5000-users at lists.mcs.anl.gov
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> 
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