[petsc-users] DMPlex tetrahedra facets orientation
Matthew Knepley
knepley at gmail.com
Mon Mar 8 09:27:09 CST 2021
On Mon, Mar 8, 2021 at 10:21 AM Isaac, Tobin G <tisaac at cc.gatech.edu> wrote:
> Right that is what is needed from each side, but taking area and vn and
> scaling them back together is just undoing a computation that happens
> inside of cellgeometryfvm. I'm saying that long term, in the same way that
> for FEM we provide different callbacks that are intended for contraction
> with v and with grad v, we should have callbacks that separate scalar and
> vector fluxes so that unit vs scaled normal is a hidden quadrature detail.
>
Oh, yes I agree. The scaling was just a stopgap.
Matt
> Toby Isaac, Assistant Professor, GTCSE
>
> ------------------------------
> *From:* Matthew Knepley <knepley at gmail.com>
> *Sent:* Monday, March 8, 2021, 10:11
> *To:* Isaac, Tobin G
> *Cc:* Nicolas Barral; PETSc
> *Subject:* Re: [petsc-users] DMPlex tetrahedra facets orientation
>
> On Mon, Mar 8, 2021 at 10:08 AM Isaac, Tobin G <tisaac at cc.gatech.edu>
> wrote:
>
>> What Nicolas wants is pretty common in DG, and the quantity is available
>> as just the cross product of the two vectors of the facet Jacobian.
>> Computing it the way you suggest is kind of a backward reconstruction.
>>
>
> I do not quite understand. The facet Jacobian will not know what the
> orientation with respect to the cell should be, and that is what he wants.
>
> Thanks,
>
> Matt
>
>
>> Toby Isaac, Assistant Professor, GTCSE
>>
>> ------------------------------
>> *From:* petsc-users <petsc-users-bounces at mcs.anl.gov> on behalf of
>> Matthew Knepley <knepley at gmail.com>
>> *Sent:* Monday, March 8, 2021, 09:56
>> *To:* Nicolas Barral
>> *Cc:* PETSc
>> *Subject:* Re: [petsc-users] DMPlex tetrahedra facets orientation
>>
>> On Mon, Mar 8, 2021 at 4:02 AM Nicolas Barral <
>> nicolas.barral at math.u-bordeaux.fr> wrote:
>>
>>> On 07/03/2021 22:56, Matthew Knepley wrote:
>>> > On Sun, Mar 7, 2021 at 4:51 PM Nicolas Barral
>>> > <nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>> wrote:
>>> >
>>> >
>>> > On 07/03/2021 22:30, Matthew Knepley wrote:
>>> > > On Sun, Mar 7, 2021 at 4:13 PM Nicolas Barral
>>> > > <nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>
>>> > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>>> wrote:
>>> > >
>>> > > On 07/03/2021 16:54, Matthew Knepley wrote:
>>> > > > On Sun, Mar 7, 2021 at 8:52 AM Nicolas Barral
>>> > > > <nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>
>>> > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
>>> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>
>>> > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>> wrote:
>>> > > >
>>> > > > Matt,
>>> > > >
>>> > > > Thanks for your answer.
>>> > > >
>>> > > > However, DMPlexComputeCellGeometryFVM does not
>>> compute
>>> > what I
>>> > > need
>>> > > > (normals of height 1 entities). I can't find any
>>> > function doing
>>> > > > that, is
>>> > > > there one ?
>>> > > >
>>> > > >
>>> > > > The normal[] in DMPlexComputeCellGeometryFVM() is
>>> exactly what
>>> > > you want.
>>> > > > What does not look right to you?
>>> > >
>>> > >
>>> > > So it turns out it's not what I want because I need
>>> > non-normalized
>>> > > normals. It doesn't seem like I can easily retrieve the
>>> norm,
>>> > can I?
>>> > >
>>> > >
>>> > > You just want area-weighted normals I think, which means that
>>> you
>>> > just
>>> > > multiply by the area,
>>> > > which comes back in the same function.
>>> > >
>>> >
>>> > Ah by the area times 2, of course, my bad.
>>> > Do you order height-1 elements in a certain way ? I need to access
>>> the
>>> > facet (resp. edge) opposite to a vertex in a tet (resp. triangle).
>>> >
>>> >
>>> > Yes. Now that I have pretty much settled on it, I will put it in the
>>> > manual. It is currently here:
>>> >
>>> >
>>> https://gitlab.com/petsc/petsc/-/blob/main/src/dm/impls/plex/plexinterpolate.c#L56
>>> <https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgitlab.com%2Fpetsc%2Fpetsc%2F-%2Fblob%2Fmain%2Fsrc%2Fdm%2Fimpls%2Fplex%2Fplexinterpolate.c%23L56&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757879503%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=DKiK1w8CS%2F1YPnskkaqsDqemXI8FWmlYsXfKDt3t7HU%3D&reserved=0>
>>> >
>>> > All normals are outward facing, but hopefully the ordering in the
>>> sourse
>>> > file makes sense.
>>>
>>> Thanks Matt, but I'm not sure I understand well. What I do so far is:
>>>
>>> ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
>>> for (i=0; i<dim+1; ++i) {
>>> f = cone[i];
>>> ierr = DMPlexComputeCellGeometryFVM(dm, f, &area, NULL,
>>> &vn[i*dim]);CHKERRQ(ierr);
>>> if (dim == 3) { area *= 2; }
>>> for (j=0; j<dim; ++j) { vn[i*dim+j] *= area; }
>>>
>>> So in 3D, it seems that:
>>> (vn[9],vn[10],vn[11]) is the inward normal to the facet opposing vertex0
>>> (vn[6],vn[7],vn[8]) " " 1
>>> (vn[3],vn[4],vn[5]) " " 2
>>> (vn[0],vn[1],vn[2]) " " 3
>>>
>>> in 2D:
>>> (vn[2],vn[3]) is a normal to the edge opposing vertex 0
>>> (vn[4],vn[5]) " " 1
>>> (vn[0],vn[1]) " " 2
>>> Yet in 2D, whether the normals are inward or outward does not seem
>>> consistent across elements.
>>>
>>> What am I wrongly assuming ?
>>>
>>
>> Ah, I see the problem. I probably need another function. You can tell
>> that not many people use Plex this way yet.
>> The logic for what you want is embedded my traversal, but it simple:
>>
>> ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
>> ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
>> ierr = DMPlexGetConeOrientation(dm, c, &ornt);CHKERRQ(ierr);
>> for (i=0; i<coneSize; ++i) {
>> f = cone[i];
>> flip = ornt[i] >= 0 ? 1 : -1;
>> ierr = DMPlexComputeCellGeometryFVM(dm, f, &area, NULL,
>> &vn[i*dim]);CHKERRQ(ierr);
>> if (dim == 3) { area *= 2; }
>> for (j=0; j<dim; ++j) { vn[i*dim+j] *= area * flip; }
>>
>> I could make a function that returns all normals, properly oriented. It
>> would just do this.
>>
>> Thanks,
>>
>> Matt
>>
>> Thanks,
>>>
>>> --
>>> Nicolas
>>>
>>> >
>>> > Thanks,
>>> >
>>> > Matt
>>> >
>>> > Thanks
>>> >
>>> > --
>>> > Nicolas
>>> >
>>> >
>>> > > Thanks,
>>> > >
>>> > > Matt
>>> > >
>>> > > If not, I'll fallback to computing them by hand for now. Is
>>> the
>>> > > following assumption safe or do I have to use
>>> > DMPlexGetOrientedFace?
>>> > > > if I call P0P1P2P3 a tet and note x the cross product,
>>> > > > P3P2xP3P1 is the outward normal to face P1P2P3
>>> > > > P0P2xP0P3 " P0P2P3
>>> > > > P3P1xP3P0 " P0P1P3
>>> > > > P0P1xP0P2 " P0P1P2
>>> > >
>>> > > Thanks
>>> > >
>>> > > --
>>> > > Nicolas
>>> > > >
>>> > > > Thanks,
>>> > > >
>>> > > > Matt
>>> > > >
>>> > > > So far I've been doing it by hand, and after a lot of
>>> > > experimenting the
>>> > > > past weeks, it seems that if I call P0P1P2P3 a
>>> tetrahedron
>>> > > and note x
>>> > > > the cross product,
>>> > > > P3P2xP3P1 is the outward normal to face P1P2P3
>>> > > > P0P2xP0P3 " P0P2P3
>>> > > > P3P1xP3P0 " P0P1P3
>>> > > > P0P1xP0P2 " P0P1P2
>>> > > > Have I been lucky but can't expect it to be true ?
>>> > > >
>>> > > > (Alternatively, there is a link between the normals
>>> > and the
>>> > > element
>>> > > > Jacobian, but I don't know the formula and can find
>>> them)
>>> > > >
>>> > > >
>>> > > > Thanks,
>>> > > >
>>> > > > --
>>> > > > Nicolas
>>> > > >
>>> > > > On 08/02/2021 15:19, Matthew Knepley wrote:
>>> > > > > On Mon, Feb 8, 2021 at 6:01 AM Nicolas Barral
>>> > > > > <nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>
>>> > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
>>> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>
>>> > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>
>>> > > > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>
>>> > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
>>> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>
>>> > > <mailto:nicolas.barral at math.u-bordeaux.fr
>>> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>>> wrote:
>>> > > > >
>>> > > > > Hi all,
>>> > > > >
>>> > > > > Can I make any assumption on the orientation
>>> of
>>> > triangular
>>> > > > facets in a
>>> > > > > tetrahedral plex ? I need the inward facet
>>> > normals. Do
>>> > > I need
>>> > > > to use
>>> > > > > DMPlexGetOrientedFace or can I rely on either
>>> > the tet
>>> > > vertices
>>> > > > > ordering,
>>> > > > > or the faces ordering ? Could
>>> > > DMPlexGetRawFaces_Internal be
>>> > > > enough ?
>>> > > > >
>>> > > > >
>>> > > > > You can do it by hand, but you have to account for
>>> > the face
>>> > > > orientation
>>> > > > > relative to the cell. That is what
>>> > > > > DMPlexGetOrientedFace() does. I think it would be
>>> > easier
>>> > > to use the
>>> > > > > function below.
>>> > > > >
>>> > > > > Alternatively, is there a function that
>>> > computes the
>>> > > normals
>>> > > > - without
>>> > > > > bringing out the big guns ?
>>> > > > >
>>> > > > >
>>> > > > > This will compute the normals
>>> > > > >
>>> > > > >
>>> > > >
>>> > >
>>> >
>>> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DMPLEX/DMPlexComputeCellGeometryFVM.html
>>> <https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.mcs.anl.gov%2Fpetsc%2Fpetsc-current%2Fdocs%2Fmanualpages%2FDMPLEX%2FDMPlexComputeCellGeometryFVM.html&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757889499%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=4rVG%2Bm1CaS99h4rupjL9oHsk15xAg8Or%2BYClMPyCqBg%3D&reserved=0>
>>> > > > > Should not be too heavy weight.
>>> > > > >
>>> > > > > THanks,
>>> > > > >
>>> > > > > Matt
>>> > > > >
>>> > > > > Thanks
>>> > > > >
>>> > > > > --
>>> > > > > Nicolas
>>> > > > >
>>> > > > >
>>> > > > >
>>> > > > > --
>>> > > > > What most experimenters take for granted before
>>> > they begin
>>> > > their
>>> > > > > experiments is infinitely more interesting than
>>> any
>>> > > results to which
>>> > > > > their experiments lead.
>>> > > > > -- Norbert Wiener
>>> > > > >
>>> > > > > https://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=https:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757889499%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=5878nejeDkupEZ1eD7piCcBIFxC%2FG6Qp%2FFa3vFIhC2c%3D&reserved=0>
>>> > > > <http://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757899493%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=mROjnXpduNPj7pAmTFDncuWuqM2XyfTbAfSVtVogHao%3D&reserved=0>
>>> >
>>> > > >
>>> > > >
>>> > > >
>>> > > > --
>>> > > > What most experimenters take for granted before they
>>> begin
>>> > their
>>> > > > experiments is infinitely more interesting than any
>>> > results to which
>>> > > > their experiments lead.
>>> > > > -- Norbert Wiener
>>> > > >
>>> > > > https://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=https:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757899493%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=4lQB0CcXHxiJiyeKHOVrLrlq1UEfETGdKgpGy9ET%2BNc%3D&reserved=0>
>>> > > <http://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757909490%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=u2ikuRDA2cpWRufgL3%2BR71WsMZTw6yhQ6mhSTK1Cr9c%3D&reserved=0>
>>> >
>>> > >
>>> > >
>>> > >
>>> > > --
>>> > > What most experimenters take for granted before they begin their
>>> > > experiments is infinitely more interesting than any results to
>>> which
>>> > > their experiments lead.
>>> > > -- Norbert Wiener
>>> > >
>>> > > https://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=https:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757909490%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=XnFyaUANJ2irZpE8wsciKyrrW3Kg4KCYY7e%2FJHdcJKg%3D&reserved=0>
>>> > <http://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757919485%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=D9P%2FJfJHvCVO0OdAC2zS%2BpfEroNRn71D6ZaLuykcwzE%3D&reserved=0>
>>> >
>>> >
>>> >
>>> >
>>> > --
>>> > What most experimenters take for granted before they begin their
>>> > experiments is infinitely more interesting than any results to which
>>> > their experiments lead.
>>> > -- Norbert Wiener
>>> >
>>> > https://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=https:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757929476%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=ney5wRVAAaP%2Bz6dTbPjoyJjy%2BCLJG2q1K4%2Bd62VG2dQ%3D&reserved=0>
>>> <http://www.cse.buffalo.edu/~knepley/
>>> <https://nam12.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757929476%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=2tuCY%2BWGmUPq3rm1hEoi9VGqEXICotvj1sZ1URUgTm0%3D&reserved=0>
>>> >
>>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <https://nam12.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757939476%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=IH94mX1hggpYxZTiLRSiz8p0%2F1CPaLEfp485ZStn1WU%3D&reserved=0>
>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <https://nam12.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=04%7C01%7Ctisaac%40cc.gatech.edu%7C2ac1bf606bd3461e087a08d8e2446a6b%7C482198bbae7b4b258b7a6d7f32faa083%7C0%7C0%7C637508130757939476%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=IH94mX1hggpYxZTiLRSiz8p0%2F1CPaLEfp485ZStn1WU%3D&reserved=0>
>
>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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