Dear all, To complete this topic for both MappingQGeneric and MappingFEField, I am wondering if it is possible to extract the quadrature in the reference element in the function maybe_update_Jacobians and maybe_compute_q_points? These are needed to ensure that the normals are consistent at each surface quadrature node with the metric terms that satisfy GCL. I was able to get the reference quadrature nodes in maybe_update_q_points_Jacobians_and_grads_tensor in fe/mapping_q_generic.cc by using data.shape_info.data[0].quadrature, but when it is not a tensor product basis (in the 2 functions listed above for mapping_q_generic.cc) I noticed that data.shape_info is empty (and there is no data.shape_info in mapping_fe_field.cc). Ideally, is it possible to fill data.shape_info in mapping_q_generic.cc or are there any other suggestions on how to extract the quadrature on the reference element for both mapping_q_generic.cc and mapping_fe_field.cc (just the 1D representation is sufficient)? Thank you, Alex
On Friday, July 10, 2020 at 12:37:21 PM UTC-4 alexande...@gmail.com wrote: > Dear Martin or whom it may concern, > > I have solved the previous problem and am confirming that the conservative > curl form has now been implemented and passes 2 complicated tests for GCL > on symmetric and non-symmetric curvilinear grids for different polynomial > degrees. Turns out that we did not need to use the "evaluate" call. The > changes are found in: > > https://github.com/AlexanderCicchino/dealii/blob/master/source/fe/mapping_q_generic.cc > lines 1599 - 1697 (line 1602 to switch it on or off) > and the 2 tests are /tests/mappings/mapping_q_generic_GCL_curvilinear.cc > for symmetric curv. grid and > /tests/mappings/mapping_q_generic_GCL_curvilinear_nonsym.cc for non-sym. > curv grid. > How should I proceed with the pull request? > > Also, for additional work, are there any suggestions on how to proceed > with 2D. Additionally, are there any suggestions for templating the mapping > for ease automatically differentiating the metric terms? > > Thank you for all the help, > Alex > > > On Thursday, July 9, 2020 at 11:54:12 AM UTC-4, Alexander Cicchino wrote: >> >> Dear Martin, >> >> As an update, I figured out a way to have it work in 3D without needing >> to use another Evaluate call. The only issue is that I need the quadrature >> in the reference element since I construct an FE_DQGArbitraryNodes to >> evaluate the derivative (I do this since the metric Jacobian is in a sense >> "collocated" on the quadrature points so the gradient needed is just the >> derivative of the basis functions). >> I have it passing collocated and uncollocated curvilinear test cases in >> 3D now perfectly, but I currently construct the FE_DGQArbitraryNodes in >> mapping_q_generic.cc by explicitly constructing a Quadrature like the >> testcase (example QGauss if the testcase uses QGauss). >> >> I couldn't find a way to extract the reference element quadrature from >> the MappingQGeneric InternalData, do you have any suggestions? >> >> Thank you, >> Alex >> >> On Friday, July 3, 2020 at 6:11:28 PM UTC-4, Alexander Cicchino wrote: >>> >>> Dear Martin, >>> >>> I would like to start by thanking you for all of your help. Here is a >>> link to my fork: https://github.com/AlexanderCicchino/dealii >>> It is not fully working yet, I need your help for the "evaluate" as you >>> mentioned earlier. I have been trying multiple different ways but cannot >>> seem to get it to work properly. >>> First, I have a test setup in: >>> tests/mappings/mapping_q_generic_GCL_curvilinear.cc >>> where currently I am outputting everything, this will change in the >>> future and I will later on add a more complicated curvilinear mesh to test. >>> But, importantly, the current implementation fails the test. >>> Also, I made changes to source/fe/mapping_q_generic.cc as you suggested >>> in the function mentioned above. The last part, which is including the >>> evaluate is in: >>> >>> >>> https://github.com/AlexanderCicchino/dealii/blob/master/source/fe/mapping_q_generic.cc >>> >>> line 1622. We have X_l*grad(X_m) evaluated at each quadrature point, now >>> we need to somehow have the gradient of that evaluated at the quadrature >>> points. I assumed after line 1622 that that gradient is written in >>> "grad_Xl_grad_Xm" which is gradient( X_l * gradient(X_m) ) then I loop >>> cyclically through it for the conservative curl form. >>> >>> Please let me know how you suggest I should proceed/setup the evaluate >>> call at line 1624. >>> Also, I noticed that the conservative curl form from Kopriva is not well >>> posed for 2D. In the past, for 2D we would extend the grid by unit 1 in the >>> z direction to properly evaluate the metric terms since, for example we >>> need: d/(d \zeta) ( z* dy / (d\eta) ). Any suggestions on how to implement >>> the 2D version in mapping Q generic? >>> >>> Thank you, >>> Alex >>> >>> On Wednesday, June 24, 2020 at 9:40:55 AM UTC-4, Martin Kronbichler >>> wrote: >>>> >>>> Dear Alex, >>>> >>>> Great! I would suggest to start by simply adding new code to the >>>> maybe_update_q_points_Jacobians_... function with the option to turn it >>>> off >>>> or on. Depending on how the final implementation will look like we might >>>> want to move that to a separate place, but I think it will be less >>>> repetitive if we use a single place. >>>> >>>> Best, >>>> Martin >>>> On 22.06.20 19:59, Alexander Cicchino wrote: >>>> >>>> Dear Martin, >>>> >>>> Thank you very much! I have been working on making the test case not >>>> depend on our in house flowsolver's functions. >>>> I think that implementing Eq. 36 the "conservative curl" form would be >>>> sufficient. >>>> Yes this procedure sounds perfect to me, and I agree with the dimension >>>> of the object described. I have been going through the source code that >>>> you >>>> sent to familiarize myself with the objects. Should I be adding to the >>>> function maybe_update_q_points_Jacobians_and_grads_tensor or should I >>>> create a new function for it? >>>> >>>> Thank you, >>>> Alex >>>> >>>> On Friday, June 19, 2020 at 5:09:14 AM UTC-4, Martin Kronbichler wrote: >>>>> >>>>> Dear Alex, >>>>> >>>>> Great! The first thing we need to know is the equation. I had a quick >>>>> look in the paper by Kopriva and I think we want to use either equation >>>>> (36) or (37), depending on whether we consider the conservative or >>>>> invariant curl form, respectively. In either case, it appears that we >>>>> need >>>>> to do this in a two-step procedure. The first step is to compute X_l and >>>>> \nabla_\xi X_m, which in deal.II speak are the "q_points" and >>>>> "Jacobians". >>>>> The implementation in mapping_q_generic.cc is a bit involved because we >>>>> have a slow algorithm (working for arbitrary quadrature rules) and a fast >>>>> one for tensor product quadrature rules. Let us consider the fast one >>>>> because I think we have most ingredients available, whereas we would need >>>>> to fill additional fields for the slow algorithm. The source code for >>>>> those >>>>> parts is here: >>>>> >>>>> >>>>> https://github.com/dealii/dealii/blob/9e05a87db802ecd073bf7567d77f3491170d84b4/source/fe/mapping_q_generic.cc#L1463-L1592 >>>>> >>>>> I skipped the part on the Hessians (second derivative of >>>>> transformation) because we won't need them. The important parts here are >>>>> the extractions of the positions in line 1554 and the extraction of the >>>>> gradients (contravariant transformations) in line 1575. Those two parts >>>>> will be the starting point for the second phase we need to do in >>>>> addition: >>>>> According to the algorithm by Kopriva, we need to define this as the curl >>>>> of the discrete interpolation of X_l \nabla_\xi X_m. To get the curl, we >>>>> need another round through the SelectEvaluator::evaluate() call in that >>>>> function to get the reference-cell gradient of that object, from which we >>>>> can then collect the entries of the curl. To call into evaluate one more >>>>> time, we also need a new data.shape_info object that does the collocation >>>>> evaluation of derivatives. That should only be two lines that I can show >>>>> you how and where to add, so let us not worry about that part now. What >>>>> is >>>>> important to understand first (in terms of index notation vs tensor >>>>> notation) is the dimension of the object. I believe that X_l \nabla_\xi >>>>> X_m >>>>> is a rank-two tensor, so it has dim*dim components, and we compute the >>>>> gradient that gives us a dim * dim * dim tensor. Taking the curl in the >>>>> derivative and inner tensor dimension space, we get rid of one component >>>>> and up with a dim * dim tensor as expected. The final step we need to do >>>>> is >>>>> to divide by the determinant of the Jacobian (contravariant vectors), >>>>> because the inverse Jacobian in deal.II does not yet pre-multiply with >>>>> the >>>>> determinant. >>>>> >>>>> Does that procedure sound reasonable to you? If yes, we could start >>>>> putting together the ingredients. It would be good to have a mesh (the >>>>> curvilinear case you were mentioning) where we can test those formulas. >>>>> >>>>> Best, >>>>> Martin >>>>> On 17.06.20 18:37, Alexander Cicchino wrote: >>>>> >>>>> Dear Martin, >>>>> >>>>> Thank you for your response. Yes I agree that only some local >>>>> computations are necessary to implement the identities. >>>>> Yes I would be interested in this feature and trying to implement it. >>>>> Do you have any suggestions on where I should start and overall practices >>>>> I >>>>> should follow? >>>>> >>>>> Thank you, >>>>> Alex >>>>> >>>>> On Wednesday, June 17, 2020 at 1:19:29 AM UTC-4, Martin Kronbichler >>>>> wrote: >>>>>> >>>>>> Dear Alex, >>>>>> >>>>>> This has been on my list of things to implement and verify with >>>>>> deal.II over a range of examples for quite a while, so I'm glad you >>>>>> bringing the topic up. It is definitely true that our way to define >>>>>> Jacobians does not take those identities into account, but I believe we >>>>>> should add support for them. The nice thing is that only some local >>>>>> computations are necessary, so having the option to use it in the >>>>>> polynomial mapping classes would be great. If you would be interested in >>>>>> this feature and trying to implement things, I'd be happy to guide you >>>>>> to >>>>>> the right places in the code. >>>>>> >>>>>> Best, >>>>>> Martin >>>>>> On 17.06.20 06:02, Alexander Cicchino wrote: >>>>>> >>>>>> Thank you for responding Wolfgang Bangerth. >>>>>> >>>>>> The GCL condition comes from the discretized scheme satisfying >>>>>> free-stream preservation. I will demonstrate this for 2D below, (can be >>>>>> interpreted for spectral, DG, finite difference, finite volume etc): >>>>>> Consider the conservation law: \frac{\partial W}{\partial t} + >>>>>> \frac{\partial F}{\partial x} +\frac{\partial G}{\partial y} =0 >>>>>> Transforming this to the reference computational space (x,y)->(\xi, >>>>>> \eta): >>>>>> J*\frac{\partial W}{\partial t} + J*\frac{ \partial \xi}{\partial x} >>>>>> * \frac{\partial F}{\partial \xi} + J * \frac{ \partial \eta}{\partial >>>>>> x}* >>>>>> \frac{\partial F}{\partial \eta} + J * \frac{ \partial \xi}{\partial y} >>>>>> * >>>>>> \frac{\partial G}{\partial \xi} + J*\frac{ \partial \eta}{\partial >>>>>> y}*\frac{\partial G}{\partial \eta} >>>>>> Putting this in conservative form results in: >>>>>> J\frac{\partial W}{\partial t} + \frac{\partial}{\partial \xi} ( >>>>>> J*F*\frac{\partial \xi}{\partial x} +J*G*\frac{\partial \xi}{\partial y} >>>>>> ) >>>>>> + \frac{\partial}{\partial \eta} ( J*F*\frac{\partial \eta}{\partial x} >>>>>> +J*G*\frac{\partial \eta}{\partial y} ) - F*( GCL in x) - G*(GCL in y) =0 >>>>>> >>>>>> where GCL in x = \frac{\partial }{\partial \xi} ( det(J)* >>>>>> \frac{\partial \xi >>>>>> }{\partial x}) + \frac{\partial }{\partial \eta}( det(J)* >>>>>> \frac{\partial >>>>>> \eta}{\partial x} ) >>>>>> similarly for y. >>>>>> >>>>>> So for the conservative numerical scheme to satisfy free stream >>>>>> preservation, the GCL conditions must go to zero. >>>>>> For linear grids, there are no issues with the classical definition >>>>>> for the inverse of the Jacobian, but what Kopriva had shown (before him >>>>>> Thomas and Lombard), was that the metric Jacobian has to be calculated >>>>>> in >>>>>> either a "conservative curl form" or an "invariant curl form" since it >>>>>> reduces the GCL condition to the divergence of a curl, which is always >>>>>> discretely satisfied. In the paper by Kopriva, he shows this, an example >>>>>> in >>>>>> 3D: >>>>>> Analytically >>>>>> J*\frac{\partial \xi}{\partial x} = \frac{\partial z}{\partial \zeta} >>>>>> * \frac{\partial y}{\partial \eta} - \frac{\partial z}{\partial \eta} * >>>>>> \frac{\partial y}{\partial \zeta} >>>>>> >>>>>> but the primer doesn't satisfy free-stream preservation while the >>>>>> latter ("conservative curl form") does. >>>>>> >>>>>> I will put together a unit test for a curvilinear grid. >>>>>> >>>>>> Thank you, >>>>>> Alex >>>>>> >>>>>> On Tuesday, June 16, 2020 at 10:24:59 PM UTC-4, Wolfgang Bangerth >>>>>> wrote: >>>>>>> >>>>>>> >>>>>>> Alexander, >>>>>>> >>>>>>> > I am wondering if anybody has also found that the inverse of the >>>>>>> Jacobian from >>>>>>> > FE Values, with MappingQGeneric does not satisfy the Geometric >>>>>>> Conservation >>>>>>> > Law (GCL), in the sense of: >>>>>>> > >>>>>>> > Kopriva, David A. "Metric identities and the discontinuous >>>>>>> spectral element >>>>>>> > method on curvilinear meshes." /Journal of Scientific Computing/ >>>>>>> 26.3 (2006): 301. >>>>>>> > >>>>>>> > on curvilinear elements/manifolds in 3D. >>>>>>> > That is: >>>>>>> > \frac{\partial }{\partial \hat{x}_1} *det(J)* \frac{\partial >>>>>>> \hat{x}_1 >>>>>>> > }{\partial x_1} + \frac{\partial }{\partial \hat{x}_2} *det(J)* >>>>>>> \frac{\partial >>>>>>> > \hat{x}_2}{\partial x} + \frac{\partial }{\partial \hat{x}_3} * >>>>>>> > det(J)*\frac{\partial \hat{x}_3 }{\partial x_1} != 0 (GCL says it >>>>>>> should =0, >>>>>>> > similarly for x_2 and x_3) >>>>>>> > >>>>>>> > If so or if not, also, has anybody found a remedy to have the >>>>>>> inverse of the >>>>>>> > Jacobian from FE Values with MappingQGeneric to satisfy the GCL. >>>>>>> >>>>>>> I'm not sure any of us have ever thought about it. (I haven't -- but >>>>>>> I really >>>>>>> shouldn't speak for anyone else.) Can you explain what this equality >>>>>>> represents? Why should it hold? >>>>>>> >>>>>>> I'm also unsure whether we've ever checked whether it holds (exactly >>>>>>> or >>>>>>> approximately). Can you create a small test program that illustrates >>>>>>> the >>>>>>> behavior you are seeing? >>>>>>> >>>>>>> Best >>>>>>> W. >>>>>>> >>>>>>> -- >>>>>>> ------------------------------------------------------------------------ >>>>>>> >>>>>>> >>>>>>> Wolfgang Bangerth email: >>>>>>> bang...@colostate.edu >>>>>>> www: >>>>>>> http://www.math.colostate.edu/~bangerth/ >>>>>>> >>>>>>> -- >>>>>> The deal.II project is located at http://www.dealii.org/ >>>>>> For mailing list/forum options, see >>>>>> https://groups.google.com/d/forum/dealii?hl=en >>>>>> --- >>>>>> You received this message because you are subscribed to the Google >>>>>> Groups "deal.II User Group" group. >>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>> send an email to dea...@googlegroups.com. >>>>>> To view this discussion on the web visit >>>>>> https://groups.google.com/d/msgid/dealii/4f313231-dbb3-445f-923c-9eaff17ab783o%40googlegroups.com >>>>>> >>>>>> <https://groups.google.com/d/msgid/dealii/4f313231-dbb3-445f-923c-9eaff17ab783o%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>>> . >>>>>> >>>>>> -- >>>>> The deal.II project is located at http://www.dealii.org/ >>>>> For mailing list/forum options, see >>>>> https://groups.google.com/d/forum/dealii?hl=en >>>>> --- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "deal.II User Group" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to dea...@googlegroups.com. >>>>> To view this discussion on the web visit >>>>> https://groups.google.com/d/msgid/dealii/b764b4b7-02d2-4139-95d9-68c30ad4f2a9o%40googlegroups.com >>>>> >>>>> <https://groups.google.com/d/msgid/dealii/b764b4b7-02d2-4139-95d9-68c30ad4f2a9o%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>> . >>>>> >>>>> -- >>>> The deal.II project is located at http://www.dealii.org/ >>>> For mailing list/forum options, see >>>> https://groups.google.com/d/forum/dealii?hl=en >>>> --- >>>> You received this message because you are subscribed to the Google >>>> Groups "deal.II User Group" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to dea...@googlegroups.com. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/dealii/cf020345-b304-45d2-a228-4081da2d4effo%40googlegroups.com >>>> >>>> <https://groups.google.com/d/msgid/dealii/cf020345-b304-45d2-a228-4081da2d4effo%40googlegroups.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>>> -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. 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