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From: Rafael Vazquez <vazquez@im...>  20150522 08:08:20

Dear Rahul Yadav, as you said, in GeoPDEs we only provide uniform refinement in the parametric domain. I have never tried to implement anything to improve the refinement in the physical domain. Actually, I do not remember any paper that continues the research in that direction. Regards, Rafa On 22/05/2015 07:53, rahul yadav wrote: > Dear Sir, > > Thanks for the kind reply. I think, I haven't made my question clear > and I apologize for that. > > I want to ask about the uniform meshing in the physical space. > Actually, I am doing the uniform meshing in parametric space but when > I am plotting it in the physical space, it is not uniform. The same > problem has been reported in the first of paper of Isogeometric by > Hughes /et.al <http://et.al>/ [2005] and they have suggested some > improvements in the appendix of that paper. It will be very kind if > you can tell me if there is similar kind of improvements present in > the Geopde. > > I hope to hear from you soon. > > > with best regards, > > Rahul Yadav > 
From: Rafael Vazquez <vazquez@im...>  20150521 12:58:28

Dear Naveed, when you call sp_precompute you are basically computing all the information of the space, that is, for all the elements you compute all the nonvanishing basis functions for every quadrature point. This consumes a lot of memory, especially in the 3D case. Things get worse when you increase the degree. In your particular case for the Greville points, since you are taking the whole domain as one single element, it will get worse whenever you increase the number of degrees of freedom, for instance, if you reduce the regularity. To avoid these memory problems we introduced classes in version 2 of GeoPDEs. The "precompute" functions are left there mostly for didactic purposes, but should not be used in general. Since you are going to use the Greville points to impose the boundary conditions, you can probably use sp_eval_boundary_side, instead of sp_precompute. This should allow you to avoid the problem. Regards, Rafa 
From: Rafael Vazquez <vazquez@im...>  20150521 12:43:42

Dear Rahul Yadav, the function nrbkntplot only plots the geometry with the knot vector, it does not generate any mesh. In all the examples in GeoPDEs, the variable nsub automatically creates a uniform refinement, assuming that the starting mesh is also uniform. Regards, Rafa On 07/05/2015 16:16, rahul yadav wrote: > Hi, > > I am trying to do the analysis of infinite plate with circular hole. I am > trying to mesh it using the function nrbkntplot, but the mesh is not > uniform. It will be very kind if you can help me in making a uniform mesh > of the geometry. > > Thank You > > Rahul Yadav >  > One dashboard for servers and applications across PhysicalVirtualCloud > Widest outofthebox monitoring support with 50+ applications > Performance metrics, stats and reports that give you Actionable Insights > Deep dive visibility with transaction tracing using APM Insight. > http://ad.doubleclick.net/ddm/clk/290420510;117567292;y > _______________________________________________ > Geopdesusers mailing list > Geopdesusers@... > https://lists.sourceforge.net/lists/listinfo/geopdesusers 
From: naveed ahmed <n_ahmed81@ya...>  20150521 11:34:02

Dear Rafael, I have read some of the discussion between you Pavel and Marti and try to implement the idea of the essential boundary in 3D and found some memory issue. The code considers the similar structure as for the 2D case. After creating mesh msh_temp=msh_3d({[0 1], [0 1], [0 1]}, gravpts, {[], [], []}, ... geometry, 'boundary', true, 'der2', false); clear gravpts; msh_temp = msh_precompute (msh_temp); sp_tmp = sp_nurbs_3d (geometry.nurbs, msh_temp); sp_tmp = sp_precompute (sp_tmp, msh_temp); The following error occur's >> Out of memory. Type HELP MEMORY for your options. Error in sp_nurbs_3d/sp_precompute_param (line 156) sp.shape_function_gradients(1,:,:,:) = (Bu  shape_functions .* Du)./D; Another question related to the operator "op_vel_dot_gradu_v_tp", if i am not wrong one can also use this function for the terms occurring in 3D? Actully, I wanted to use or a modification of the function for Saddle point problem. Thank you best regardsnaveed PS: I don't know why i can email to geo_pdes list. On Friday, 24 April 2015, 17:29, naveed ahmed <n_ahmed81@...> wrote:  Dear Rafael, Thanks for the details reply. I will try to implement if or not succeded, will ask you again. Best  From: Rafael Vazquez <vazquez@...>; To: naveed ahmed <n_ahmed81@...>; Cc: <geopdesusers@...>; Subject: Re: GeoPdes help Sent: Fri, Apr 24, 2015 3:14:55 PM  Dear Naveed, for the first part of your message (separating Neumann and Dirichlet conditions), as you may have seen GeoPDEs always works with complete boundary sides. The easiest way to solve this is to create your cube as a multipatch geometry, separating different conditions into different patches, but this would reduce the continuity between patches. Another possibility, but more difficult to implement, is that you create some functions adhoc, in such a way that to impose the Neumann and Dirichlet boundary conditions you only compute the integrals in a given list of boundary elements. For instance, for Neumann conditions you should first decide the elements of the boundary on which you want to compute the integrals, and then call op_f_v_list (sp_side, msh_side, gval, element_list) This function should do the loop only in the elements of the list. Since the mesh is Cartesian it should not be difficult to compute this list of elements, using the function sub2ind. You should do a similar thing for Dirichlet conditions. For the second part of your message, you can implement the boundary function without any loop, using the logical operators in a smart way. For instance, for your condition it should work something like this: value = sin(2*pi) * ((y>=5.0/8.0eps) & (y<=0.75+eps) & (z>= 5.0/8.0eps) & (z<= 0.75 +eps)); Something similar is done in the example of the laplacian in the plate. Notice that I have used the operator & (vectorial) and not && (scalar). I have also removed the condition x==0, since I would check that using the number of the side. I hope this helps, Rafa On 24/04/2015 13:03, naveed ahmed wrote: Dear Rafael, I need some suggestions regarding the inflow boundary conditions and boundary values in cube. What I want to have is as follows: if ((fabs(x1) < eps) && ( y>=3.0/8.0eps) && (y<=0.5+eps) && (z>=0.5eps) && (z<=5.0/8.0+eps)) { cond = NEUMANN; } else cond = DIRICHLET; and then the corresponding boundary values are (eps =1e06) if ((x==0) && (y>=5.0/8.0eps) && (y<=0.75+eps) && (z>= 5.0/8.0eps) && (z<= 0.75 +eps)) { value = sin(2*pi); } else value = 0.0; What I am trying in the function where i define my boundary conditions or boundary values is as follows { value=zeros(size(x)); dir=size(x) for i=1:dir(1) for j=1:dir(2) if (x(i,j) == 0 && y(i,j)>5./8. ....... (the similar if statement above) value(i,j) = sin (2*pi); end end } Could you please help me in this regard as you have the knowledge. Best wishes Naveed  
From: Rafael Vazquez <vazquez@im...>  20150519 12:29:29

Dear Eli, when you plot in Paraview, using sp_to_vtk, you plot the correct results. You don't get the maximum and minimum values of the solution vector because the basis functions are not interpolatory, and less or equal to one. Rafa On 19/05/2015 13:13, John Eli wrote: > Dear Rafa, > > Thanks for your nice guidance for the GeoPDEs. Could you please tell > me the best way of plotting and interpreting the results (important is > the interpretation then). If I compute the errors, i can see the > results which are correct. On the other hand if i plot using > sp_to_vtk(), the results are different then expected. As I also wrote > you in one of my email that the maximum and minimum of the solution > vector is not the similar or nearby which shows in the vtk plots. > > best wishes > Eli > > > >  > Date: Wed, 13 May 2015 11:58:33 +0200 > From: vazquez@... > To: john.eli90@...; geopdesusers@... > Subject: Re: [Geopdesusers] problem in an operator > > Dear Eli, > for 2D examples, and in the case you use the isoparametric approach > (NURBS geometry, NURBS functions), you can create a NURBS geometry > with the third coefficient equal to the solution: > nurbs = geometry.nurbs; > nurbs.coefs(3,:,:) = reshape (u, [1, nurbs.number]) .* nurbs.coefs(4,:,:); > > I multiply by the weight because the NURBS toolboxx works with > homogeneous coordinates. Then you can plot it with nrbctrlplot or > nrbkntplot. > > Rafa > > On 13/05/2015 11:38, John Eli wrote: > > Dear Rafa, > > Thanks for the explanation. Yes, that's everything is fine what > you said. But is there a way to really compare what have been > shown in figure using paraview and the minimum and maximum > obtained from the solution vector itself? > > Best > Eli > >  > Date: Wed, 13 May 2015 09:23:44 +0200 > From: vazquez@... <mailto:vazquez@...> > To: john.eli90@... <mailto:john.eli90@...>; > geopdesusers@... > <mailto:geopdesusers@...> > Subject: Re: [Geopdesusers] problem in an operator > > Dear Eli, > that's not surprising, since Bsplines (and NURBS) basis functions > are not interpolatory, and their values are between 0 and 1. This > difference between the solution vector (the control variables) and > the plotted solution is analogous to the difference between the > control points and the real geometry. > > In any case, for Paraview we are evaluating the solution exactly > at a given set of points. If you use enough points, you will get > an accurate plot of the computed solution. > > Rafa > > 
From: Rafael Vazquez <vazquez@im...>  20150515 10:28:24

Dear Eli, if you already know the position in the parametric domain, you can compute the value of the solution with sp_eval, it will automatically find the cell using findspan. If you only know the position in the physical domain you can compute the pullback to the parametric domain by solving a nonlinear problem. There was a discussion with Pavel about this some months ago, check the archives. Regards, Rafa On 15/05/2015 12:03, John Eli wrote: > Actually I want to compute some values at the some point and for that > i have to find some particular points on each cell and if the points > lies within that cell, i have to compute the basis function > corresponding to that point and multiply by the vector. In > mathematical sense u_h(x_p,y_p). > > best > eli > >  > Date: Fri, 15 May 2015 11:59:05 +0200 > From: vazquez@... > To: john.eli90@...; geopdesusers@... > Subject: Re: points in cell > > Dear Eli, > I am not sure to understand what you want. Can you be more precise? > > Rafa > > On 15/05/2015 11:48, John Eli wrote: > > Dear Rafa, > > Could you please guide me how to get cells and find some > particular points on that? > > best regards > Eli > > 
From: John Eli <john.eli90@ho...>  20150515 10:03:40

Actually I want to compute some values at the some point and for that i have to find some particular points on each cell and if the points lies within that cell, i have to compute the basis function corresponding to that point and multiply by the vector. In mathematical sense u_h(x_p,y_p). best eli Date: Fri, 15 May 2015 11:59:05 +0200 From: vazquez@... To: john.eli90@...; geopdesusers@... Subject: Re: points in cell Dear Eli, I am not sure to understand what you want. Can you be more precise? Rafa On 15/05/2015 11:48, John Eli wrote: Dear Rafa, Could you please guide me how to get cells and find some particular points on that? best regards Eli 
From: Rafael Vazquez <vazquez@im...>  20150515 09:59:14

Dear Eli, I am not sure to understand what you want. Can you be more precise? Rafa On 15/05/2015 11:48, John Eli wrote: > Dear Rafa, > > Could you please guide me how to get cells and find some particular > points on that? > > best regards > Eli 
From: John Eli <john.eli90@ho...>  20150515 09:48:57

Dear Rafa, Could you please guide me how to get cells and find some particular points on that? best regards Eli 
From: Rafael Vazquez <vazquez@im...>  20150513 09:58:42

Dear Eli, for 2D examples, and in the case you use the isoparametric approach (NURBS geometry, NURBS functions), you can create a NURBS geometry with the third coefficient equal to the solution: nurbs = geometry.nurbs; nurbs.coefs(3,:,:) = reshape (u, [1, nurbs.number]) .* nurbs.coefs(4,:,:); I multiply by the weight because the NURBS toolboxx works with homogeneous coordinates. Then you can plot it with nrbctrlplot or nrbkntplot. Rafa On 13/05/2015 11:38, John Eli wrote: > Dear Rafa, > > Thanks for the explanation. Yes, that's everything is fine what you > said. But is there a way to really compare what have been shown in > figure using paraview and the minimum and maximum obtained from the > solution vector itself? > > Best > Eli > >  > Date: Wed, 13 May 2015 09:23:44 +0200 > From: vazquez@... > To: john.eli90@...; geopdesusers@... > Subject: Re: [Geopdesusers] problem in an operator > > Dear Eli, > that's not surprising, since Bsplines (and NURBS) basis functions are > not interpolatory, and their values are between 0 and 1. This > difference between the solution vector (the control variables) and the > plotted solution is analogous to the difference between the control > points and the real geometry. > > In any case, for Paraview we are evaluating the solution exactly at a > given set of points. If you use enough points, you will get an > accurate plot of the computed solution. > > Rafa 
From: Rafael Vazquez <vazquez@im...>  20150513 07:23:54

Dear Eli, that's not surprising, since Bsplines (and NURBS) basis functions are not interpolatory, and their values are between 0 and 1. This difference between the solution vector (the control variables) and the plotted solution is analogous to the difference between the control points and the real geometry. In any case, for Paraview we are evaluating the solution exactly at a given set of points. If you use enough points, you will get an accurate plot of the computed solution. Rafa On 12/05/2015 23:49, John Eli wrote: > Dear all, > > Thanks for the nice suggestions. I have a question related the plot in > paraview. If one uses the function sp_to_vtk() for plotting, then in > the color menu of paraview one can see the upper and lower limit of > the solution vector e.g., u,. On the other hand if one find the > maximum and minimum of the solution vector itself, then one can see > that are too much different then what is shown in the vtk resolution. > I agree that it must not be equal as we evaluate the solution on > different points (vtkpnts) but it some how close to it? Is there a way > to compare what have been plotted by vtk and the solution or some > reasoning for that? For example I have some results where in the plot > I have the minimum = 0.0006 and maximum = 3.026 but if i find the > maximum and minimum of solution vector then it becomes 0.01273 and > maximum=3.4937. > > best wishes > Eli > >  > Date: Mon, 11 May 2015 17:19:47 +0200 > From: vazquez@... > To: john.eli90@...; geopdesusers@... > Subject: Re: [Geopdesusers] problem in an operator > > Dear Eli, > I am moving the discussion in the mailing list. > > What do you mean by having different test and ansatz functions? The > operators in general should work for any kind of test and trial function. > > The advection term was implemented directly in version 2. I don't know > if any other user has it, but if not you can implement it yourself as > an exercise. > > And yes, mesh.element_size(iel) should be the right quantity for the > scaling. > > Rafa > > On 11/05/2015 17:11, John Eli wrote: > > Dear Rafael, > > Thanks for your nice answer. I have got the three different types > of implementations for initial data from Martin, thanks to him. I > guess I will implement by myself now for the boundary terms. In my > operator actually the test and ansatz functions are different from > what have implemented in op_vel_dot_gradu_v and aditionally i have > to scale them by h_K (msh.element_size(iel) i guess is the right > field?). I will try to read the older version of the code and try > to understand. If you still have the older version of > op_vel_gradu_v. then kindly send me that or refer me from where i > should get. Thanks > > best > Eli > > 
From: John Eli <john.eli90@ho...>  20150512 21:49:29

Dear all, Thanks for the nice suggestions. I have a question related the plot in paraview. If one uses the function sp_to_vtk() for plotting, then in the color menu of paraview one can see the upper and lower limit of the solution vector e.g., u,. On the other hand if one find the maximum and minimum of the solution vector itself, then one can see that are too much different then what is shown in the vtk resolution. I agree that it must not be equal as we evaluate the solution on different points (vtkpnts) but it some how close to it? Is there a way to compare what have been plotted by vtk and the solution or some reasoning for that? For example I have some results where in the plot I have the minimum = 0.0006 and maximum = 3.026 but if i find the maximum and minimum of solution vector then it becomes 0.01273 and maximum=3.4937. best wishes Eli Date: Mon, 11 May 2015 17:19:47 +0200 From: vazquez@... To: john.eli90@...; geopdesusers@... Subject: Re: [Geopdesusers] problem in an operator Dear Eli, I am moving the discussion in the mailing list. What do you mean by having different test and ansatz functions? The operators in general should work for any kind of test and trial function. The advection term was implemented directly in version 2. I don't know if any other user has it, but if not you can implement it yourself as an exercise. And yes, mesh.element_size(iel) should be the right quantity for the scaling. Rafa On 11/05/2015 17:11, John Eli wrote: Dear Rafael, Thanks for your nice answer. I have got the three different types of implementations for initial data from Martin, thanks to him. I guess I will implement by myself now for the boundary terms. In my operator actually the test and ansatz functions are different from what have implemented in op_vel_dot_gradu_v and aditionally i have to scale them by h_K (msh.element_size(iel) i guess is the right field?). I will try to read the older version of the code and try to understand. If you still have the older version of op_vel_gradu_v. then kindly send me that or refer me from where i should get. Thanks best Eli 
From: Rafael Vazquez <vazquez@im...>  20150511 15:19:58

Dear Eli, I am moving the discussion in the mailing list. What do you mean by having different test and ansatz functions? The operators in general should work for any kind of test and trial function. The advection term was implemented directly in version 2. I don't know if any other user has it, but if not you can implement it yourself as an exercise. And yes, mesh.element_size(iel) should be the right quantity for the scaling. Rafa On 11/05/2015 17:11, John Eli wrote: > Dear Rafael, > > Thanks for your nice answer. I have got the three different types of > implementations for initial data from Martin, thanks to him. I guess I > will implement by myself now for the boundary terms. In my operator > actually the test and ansatz functions are different from what have > implemented in op_vel_dot_gradu_v and aditionally i have to scale them > by h_K (msh.element_size(iel) i guess is the right field?). I will try > to read the older version of the code and try to understand. If you > still have the older version of op_vel_gradu_v. then kindly send me > that or refer me from where i should get. Thanks > > best > Eli 
From: Rafael Vazquez <vazquez@im...>  20150511 14:01:04

Dear Eli, the advection term is already implemented in geopdes, in the file op_vel_dot_gradu_v. If that is not exactly what you need, you can try to create your function from this one. The functions to compute the matrices in version 2 are not easy to read, but in some of them (op_gradu_gradv, for instance) we have left, at the bottom of the file, an older version which should be much easier to understand. In general, plotting on the mesh lines does not make sense, because you will only get a piecewise linear function in a very coarse mesh. If you really want to do it, you can define the variable vtk_pts using the knot vector. For now, the best way we have to plot the solution is the one you can find in the examples. For the implementation of initial and boundary conditions you should ask if other users want to share what they have done. For smooth functions, an L2 projection should work fine. Regards, Rafa On 11/05/2015 12:29, John Eli wrote: > Dear All and Rafael, > > I am facing a problem to create a matrix for one of the form in my equation i.e., sum_K h_K (u, b.grad v)_K . Somehow this term looks similar as in the supg stabilization methods for convectiondiffusionreaction problem. I have found there some users is doing transient case. Can he help me with the initial and boundary data approximation. Another question is about the plotting. Is there a way to plot solution on the mesh? Or what is the better way to plot the solution? My file is attached here with. I will be very thankful for the nice suggestions and help. > > best > Eli > > > >  > One dashboard for servers and applications across PhysicalVirtualCloud > Widest outofthebox monitoring support with 50+ applications > Performance metrics, stats and reports that give you Actionable Insights > Deep dive visibility with transaction tracing using APM Insight. > http://ad.doubleclick.net/ddm/clk/290420510;117567292;y > > > _______________________________________________ > Geopdesusers mailing list > Geopdesusers@... > https://lists.sourceforge.net/lists/listinfo/geopdesusers 
From: John Eli <john.eli90@ho...>  20150511 10:29:44

Dear All and Rafael, I am facing a problem to create a matrix for one of the form in my equation i.e., sum_K h_K (u, b.grad v)_K . Somehow this term looks similar as in the supg stabilization methods for convectiondiffusionreaction problem. I have found there some users is doing transient case. Can he help me with the initial and boundary data approximation. Another question is about the plotting. Is there a way to plot solution on the mesh? Or what is the better way to plot the solution? My file is attached here with. I will be very thankful for the nice suggestions and help. best Eli 
From: Rafael Vazquez <vazquez@im...>  20150508 08:26:27

Create a qn with one single element in each direction, and then create the msh. As far as I remember this is already what Pavel was using, not only for the boundary but for the whole domain. Rafa On 08/05/2015 10:24, Martin Ebert wrote: > Right, then how this will work for the all other element which are not > on the boundary using GeoPDEs? Could you give me a hint? Do I also > need to use as a qn in the whole domain? > > thanks > Martin > > On Fri, May 8, 2015 at 10:18 AM, Rafael Vazquez <vazquez@... > <mailto:vazquez@...>> wrote: > > Dear Martin, > yes, when computing the Greville points for the boundary in the > parametric domain, you only need to compute the averages for the > corresponding knot vector(s). In a 2D domain, it is the second for > x=0 and x=1, and the first for y=0 and y=1. > > Notice that there is not a nice correspondence between the number > of Greville points and the number of knots/elements. Pavel solved > this creating one single element with all the Greville points, but > he was giving the qn as a row vector (1 x nqn) instead of a column > vector (nqn x 1), which is the one we use in GeoPDEs. > > Regards, > Rafa > > > > >  > Martin Ebert 
From: Martin Ebert <ebert.marti@gm...>  20150508 08:24:57

Right, then how this will work for the all other element which are not on the boundary using GeoPDEs? Could you give me a hint? Do I also need to use as a qn in the whole domain? thanks Martin On Fri, May 8, 2015 at 10:18 AM, Rafael Vazquez <vazquez@...> wrote: > Dear Martin, > yes, when computing the Greville points for the boundary in the parametric > domain, you only need to compute the averages for the corresponding knot > vector(s). In a 2D domain, it is the second for x=0 and x=1, and the first > for y=0 and y=1. > > Notice that there is not a nice correspondence between the number of > Greville points and the number of knots/elements. Pavel solved this > creating one single element with all the Greville points, but he was giving > the qn as a row vector (1 x nqn) instead of a column vector (nqn x 1), > which is the one we use in GeoPDEs. > > Regards, > Rafa > >  Martin Ebert 
From: Rafael Vazquez <vazquez@im...>  20150508 08:18:27

Dear Martin, yes, when computing the Greville points for the boundary in the parametric domain, you only need to compute the averages for the corresponding knot vector(s). In a 2D domain, it is the second for x=0 and x=1, and the first for y=0 and y=1. Notice that there is not a nice correspondence between the number of Greville points and the number of knots/elements. Pavel solved this creating one single element with all the Greville points, but he was giving the qn as a row vector (1 x nqn) instead of a column vector (nqn x 1), which is the one we use in GeoPDEs. Regards, Rafa 
From: Martin Ebert <ebert.marti@gm...>  20150507 20:46:21

As you wrote in one of your reply for Pavel "Notice that you are using it (Greville points) as qn, which must have size (for direction j) equal to nqn_dir(j) x nel_dir(j). In your case you have only one element, so it should be a column vector, and not a row vector. " In the case if one uses not on the boundary or for more elements, and the formula for Greville points (x_i) are defined through x_i = (t_i + t_{i+1} + ... + t_{k+p1})/(p1) , i=1,2,...,n (where n denotes the number of basis function). To my understanding, these points will stays same for nqn_dir(2)xnel_dir(2) ? because the loop starts from i=1:n and the knots t's are same. Or there is some thing I am totally missing? Best Martin  Martin Ebert 
From: Rafael Vazquez <vazquez@im...>  20150507 14:29:42

Dear Pavel and Martin, to explain what I had in mind, you can take a look at this paper by Costantini et al. Please read it carefully, at least to be sure that you understand the notation. http://www.sciencedirect.com/science/article/pii/S0167839610000762# In Section 5 they mention three different possibilities to impose boundary conditions, that is, to compute the coefficients of the boundary functions. The same arguments work if you want to compute the coefficients for the initial solution.  Type I: apply your boundary function to the Greville points. In this case you don't need to compute the mesh and space objects.  Type II: solve the interpolation problem. I think this is the same that at the beginning of Ch. XII in de Boor's book, and the one that Pavel was implementing. In this case, you will need the mesh and space objects. Martin, I am not sure that this will eliminate the oscillations in your problem.  Type III: apply a quasiinterpolant, as the one in the paper by Lee, Lyche and Morken. Martin has already implemented a particular case of this. Type I is probably the easiest to compute, and it should remove the oscillations, but I'm not sure about its robustness. By the way, I realized that before I was calling all of them quasiinterpolants, which is probably wrong. Regards, Rafa On 07/05/2015 13:21, Martin Ebert wrote: > Dear Rafa and Pavel, > > I think to avoid extra mesh and space structure, one can replace qn = > greville points after creating mesh and then can use the same space > and mesh constructed before? Is that be the case or I am mixing some > thing? > > Best > Martin > > > >  > Martin Ebert 
From: rahul yadav <rahulyadav1002@gm...>  20150507 14:16:26

Hi, I am trying to do the analysis of infinite plate with circular hole. I am trying to mesh it using the function nrbkntplot, but the mesh is not uniform. It will be very kind if you can help me in making a uniform mesh of the geometry. Thank You Rahul Yadav 
From: Martin Ebert <ebert.marti@gm...>  20150507 11:21:53

Dear Rafa and Pavel, I think to avoid extra mesh and space structure, one can replace qn = greville points after creating mesh and then can use the same space and mesh constructed before? Is that be the case or I am mixing some thing? Best Martin  Martin Ebert 
From: Rafael Vazquez <vazquez@im...>  20150506 14:29:24

Pavel, the error you get in line 14 is due to the size of the array containing the Greville points. Notice that you are using it as qn, which must have size (for direction j) equal to nqn_dir(j) x nel_dir(j). In your case you have only one element, so it should be a column vector, and not a row vector. I will add a comment in the help about that. For both, I don't think you really need to compute msh and space structures with the Greville points. The quasiinterpolant for a given function g should be: Q(g) = \sum_i g(P_i) B_i, where P_i is the Greville point, and B_i the corresponding basis function. Once you have the Greville points, it should be enough to evaluate the function g at those points, and take those values as the coefficients associated to your basis functions. Rafa On 06/05/2015 13:43, Pavel Jan wrote: > Dear Colleagues, > I wish to help, but all I have is a simple function to calculate > Greville abscissae and a sketch of example which should work but > actually it does not (I get error at Line 14). I attach these files, > but I think they will be useless. > Pavel > *Sent:* Wednesday, May 06, 2015 at 10:16 AM > *From:* "Rafael Vazquez" <vazquez@...> > *To:* "Pavel Jan" <pavel.j@...> > *Cc:* "Martin Ebert" <ebert.marti@...>, > geopdesusers@... > *Subject:* quasiinterpolant using Greville points > Dear Pavel, > Martin Ebert, another user of GeoPDEs, would like to use the > quasiinterpolation on Greville points to set up initial data of an > unsteady problem. This means that the computations should be done in the > whole domain, and not only on the boundary, but I think everything > should work in a very similar way. > > Is it possible for you to share your code for quasiinterpolation on > Greville points? > > Best regards, > Rafa 
From: Rafael Vazquez <vazquez@im...>  20150506 08:16:36

Dear Pavel, Martin Ebert, another user of GeoPDEs, would like to use the quasiinterpolation on Greville points to set up initial data of an unsteady problem. This means that the computations should be done in the whole domain, and not only on the boundary, but I think everything should work in a very similar way. Is it possible for you to share your code for quasiinterpolation on Greville points? Best regards, Rafa 
From: Rafael Vazquez <vazquez@im...>  20150504 08:11:56

Dear Pavel, to impose the boundary condition you only need to impose the values for the functions on the boundary, therefore you only need to use the Greville abscissae corresponding to boundary functions. To avoid misunderstanding, please note that there is nothing like "usual" control points and control points corresponding to the Greville abscissae. The control points define the geometry, and since the geometry is fixed, they do not need to be changed/replaced. The Greville abscissae ARE NOT control points, they are a particular choice of points in the parametric domain, that you can map to the physical domain. For plotting, you can plot the control points with the command nrbctrlplot of the NURBS toolbox. For plotting the Greville abscissae, you can compute the position in the physical domain with nrbeval, and then rearrange the output to make a plot with the standard surf command. Regards, Rafa On 03/05/2015 08:35, Pavel Jan wrote: > Dear Rafael, > > When imposing essential boundary condition using interpolation at Greville abscissae, should I use control points corresponding to Greville abscissae only for interpolation on the boundary, or do I need to replace the interior control points by them also? > > Is there any easy way to plot both the usual control points and the control points corresponding to Greville abscissae on the physical domain? > > Thank you in advance! > > Pavel > > > Sent: Wednesday, April 15, 2015 at 3:24 PM > From: "Rafael Vazquez" <vazquez@...> > To: geopdesusers@... > Subject: Re: [Geopdesusers] Imposition of essential boundary conditions using interpolation > Dear Pavel, > what I was suggesting is to impose the boundary conditions using spline > interpolation as in De Boor's book, Ch. XIII. Actually, this is also > used in the paper by Wang and Xuan, cited in the geodpes paper, and is > equivalent to solve a collocation problem on the boundary. > > Once you have the Greville points (\tau) and the basis functions (B) > evaluated on them, you should assemble the spline collocation matrix > A_{ij} = B_j (\tau_i) > and the right hand side > g(\tau_i) > where "g" is the function on the boundary condition. Once you have > those, solving the system should give you the values to impose for the > boundary degrees of freedom. After that, everything goes like for the > L^2 projection. > > Regards, > Rafa > > On 11/04/2015 17:25, Pavel Jan wrote: >> Dear Rafael, >> >> Regarding to my previous question on imposing essential boundary condition, I have calculated Greville abscissae, mapped them on the physical domain etc. >> >> I attach my simplified code below and I would like to ask whether I am on the right way? I have no idea what to do next. >> >> I appreciate your educational work which you patiently do on this mailing list. >> >> Pavel >> >>  >> geometry = geo_load ('ring.mat'); >> knots = geometry.nurbs.knots; >> >> ndim = numel (knots); >> n = geometry.nurbs.number; >> p = geometry.nurbs.order  1; >> >> % Calculating Greville abscissae >> grv_abs = cell(1, ndim); >> for idir = 1:ndim >> for i = 1:n(idir) >> grv_abs{idir}(i) = sum(knots{idir}(i+1:i+p(idir)))/p(idir); >> end >> grv_abs{idir} = grv_abs{idir}'; # Need for msh_precompute (?) >> end >> >> msh_grv = msh_2d ({[0 1], [0 1]}, grv_abs, [], geometry, 'boundary', false, 'der2', false); >> msh_grv = msh_precompute (msh_grv) >> % Mapping Greville abscissae to the physical domain >> [x, y] = deal (squeeze (msh_grv.geo_map(1,:,:)), squeeze (msh_grv.geo_map(2,:,:)) ); >> >> sp_grv = space.constructor (msh_grv); >> sp_grv = sp_precompute (sp_grv, msh_grv); >> sph_grv = sp_grv.shape_functions; >>  >> >> >> Sent: Tuesday, April 07, 2015 at 10:27 AM >> From: "Rafael Vazquez" <vazquez@...> >> To: geopdesusers@... >> Subject: Re: [Geopdesusers] Imposition of essential boundary conditions using interpolation >> >> Dear Pavel, >> interpolation on control points is not a good idea, since they are not >> on the physical geometry. I suggest you to use Greville points instead >> (you can see the definition in De Boor's book, or in the papers about >> collocation). You can construct them easily as knot averages, and map >> them to the physical domain using the parametrization in geometry.map. >> >> Once you have the Greville points, you will need to evaluate the basis >> functions on them. For this you can construct an auxiliary "mesh" >> structure, with one point per element, similar to what is done for >> visualization in sp_eval. >> >> I hope this helps, >> Rafa >> >> On 06/04/2015 21:33, pavel.j@... wrote: >>> Dear Colleagues, >>> >>> I am trying to impose inhomogenous essential boundary condition using interpolation on control points. Can anybody give any advise on how this can be done in the most easiest way? How to calculate the values of basis functions on boundary points? In GeoPDEs I can found only examples of essential boundary conditions imposed using L^2projection. >>> >>> Thank you >>> >>> Pavel >>> >>  >> BPM Camp  Free Virtual Workshop May 6th at 10am PDT/1PM EDT >> Develop your own process in accordance with the BPMN 2 standard >> Learn Process modeling best practices with Bonita BPM through live exercises >> http://www.bonitasoft.com/bepartofit/events/bpmcampvirtual event?utm_ >> source=Sourceforge_BPM_Camp_5_6_15&utm_medium=email&utm_campaign=VA_SF >> _______________________________________________ >> Geopdesusers mailing list >> Geopdesusers@... >> https://lists.sourceforge.net/lists/listinfo/geopdesusers[https://lists.sourceforge.net/lists/listinfo/geopdesusers] > >  > BPM Camp  Free Virtual Workshop May 6th at 10am PDT/1PM EDT > Develop your own process in accordance with the BPMN 2 standard > Learn Process modeling best practices with Bonita BPM through live exercises > http://www.bonitasoft.com/bepartofit/events/bpmcampvirtual[http://www.bonitasoft.com/bepartofit/events/bpmcampvirtual] event?utm_ > source=Sourceforge_BPM_Camp_5_6_15&utm_medium=email&utm_campaign=VA_SF > _______________________________________________ > Geopdesusers mailing list > Geopdesusers@... > https://lists.sourceforge.net/lists/listinfo/geopdesusers[https://lists.sourceforge.net/lists/listinfo/geopdesusers] > >  > One dashboard for servers and applications across PhysicalVirtualCloud > Widest outofthebox monitoring support with 50+ applications > Performance metrics, stats and reports that give you Actionable Insights > Deep dive visibility with transaction tracing using APM Insight. > http://ad.doubleclick.net/ddm/clk/290420510;117567292;y > _______________________________________________ > Geopdesusers mailing list > Geopdesusers@... > https://lists.sourceforge.net/lists/listinfo/geopdesusers 