## Re: [Libmesh-users] hanging nodes and triangular elements

 Re: [Libmesh-users] hanging nodes and triangular elements From: Roy Stogner - 2005-02-16 18:24:43 ```On Wed, 16 Feb 2005, Michael Povolotskyi wrote: > We have tested both triangular and rectangular finite elements, both first > and second approximation order. > > The "problems" start to appear when we use the adaptive mesh refinement. > Detailed study shows that the same problems occur BOTH with triangular and > rectangular elements (in contrast to what I informed yesterday). > > We send a solution visualised by GMV program in files example_fullview.pdf > and example_magnified.pdf. One can see in Fig. example_magnified.pdf that > the solution at some points (indicated by red circles) is not continuous. > We tried different solvers. The solution changes very slightly, but the > problem persists. Are you sure you see this problem with linear and bilinear elements? With quadratic and biquadratic elements, you may be encountering a known problem with GMV output of solutions on higher order elements. libMesh outputs the same linear or bilinear elements, regardless of what your solution degree is. For uniform meshes this isn't as obvious since the result is still continuous; for adaptive meshes, however, a hanging node's value will be plotted on fine element neighbors but not coarse element neighbors, and unless the hanging node's value is precisely the (bi)linear interpolant between the other nodes on its edge/face, the resulting plot will be discontinuous. --- Roy ```

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 RE: [Libmesh-users] hanging nodes and triangular elements From: KIRK, BENJAMIN (JSC-EG) (NASA) - 2005-02-15 18:29:39 ```Are you using CG as the iterative solver? I just realized that the constraints are inserted into the system matrix in such a way that the solution vector automatically satisfies the constraints, but this is not symmetric. Try running your problem when CG and then with GMRES or BiCG. If the latter two work then the aforementioned problem is probably the source of your difficulty. Let me know & I'll get a patch together. -Ben -----Original Message----- From: libmesh-users-admin@... [mailto:libmesh-users-admin@...] On Behalf Of Roy Stogner Sent: Tuesday, February 15, 2005 12:18 PM To: Michael Povolotskyi Cc: libmesh-users@... Subject: Re: [Libmesh-users] hanging nodes and triangular elements On Tue, 15 Feb 2005, Michael Povolotskyi wrote: > Yes, the code works correctly with uniformly refined triangular > elements. > > Could you, please, tell how can I check if the nodes are in a correct > order? If you're getting good results with uniform refinement, there's likely nothing wrong with your coarse mesh - the distorted triangle problem was just the only thing I'd ever seen that would give you problems with a triangular mesh but not a quadrilateral mesh. Could you specify exactly what problems you're getting with adaptive triangles that you aren't seeing with uniform triangles or adaptive quads? Is it a bad convergence rate, a crash, or something else? --- Roy Stogner ------------------------------------------------------- SF email is sponsored by - The IT Product Guide Read honest & candid reviews on hundreds of IT Products from real users. Discover which products truly live up to the hype. Start reading now. http://ads.osdn.com/?ad_id=6595&alloc_id=14396&op=click _______________________________________________ Libmesh-users mailing list Libmesh-users@... https://lists.sourceforge.net/lists/listinfo/libmesh-users ```
 RE: [Libmesh-users] hanging nodes and triangular elements From: KIRK, BENJAMIN (JSC-EG) (NASA) - 2005-02-17 02:33:49 ```I will look through this in detail as soon as I can. We are in the middle of a simulated mission right now, so I can't even breathe until Friday. Sorry, but I'm sure we can straighten this out in relatively short order. -Ben -----Original Message----- From: Michael Povolotskyi [mailto:povolotskyi@...] Sent: Wednesday, February 16, 2005 11:18 AM To: KIRK, BENJAMIN (JSC-EG) (NASA) Cc: 'Roy Stogner'; libmesh-users@... Subject: Re: [Libmesh-users] hanging nodes and triangular elements Today we performed a set of tests in order to understand where the problem is (if any). We are solving the equation -\nabla^2 u = exp(-(x^2 + y^2)) on a square -1.0<= x <= 1.0, -1.0<= y <= 1.0 The boundary conditions are as follows: u = 1.0 if -1.0<=x<=0.8, y = 1.0 u = 1.0 if 0.8<=x<=1.0, y = 1.0 u = 0.0 if -0.4<=x<=0.4, y = 1.0 For the rest of the boundary we assume natural boundary conditions (von Neumann). In order to implement the Dirichlet boundary conditions we DON'T use the penalty function method shown in the examples. Instead we assign boundary values to the nodes that lie on the boundary. We found that the code produces a reasonable solution if: a) there is no mesh refinement; b) if there is uniform mesh refinement; We have tested both triangular and rectangular finite elements, both first and second approximation order. The "problems" start to appear when we use the adaptive mesh refinement. Detailed study shows that the same problems occur BOTH with triangular and rectangular elements (in contrast to what I informed yesterday). We send a solution visualised by GMV program in files example_fullview.pdf and example_magnified.pdf. One can see in Fig. example_magnified.pdf that the solution at some points (indicated by red circles) is not continuous. We tried different solvers. The solution changes very slightly, but the problem persists. In order to be more specific we attach our code (Poisson.C) and the input file Poisson.in that the program reads. We don't understand if we are using libmesh in a wrong way or if there is a problem in libmesh itself. Thank you for your time, Michael. KIRK, BENJAMIN (JSC-EG) (NASA) wrote: > Are you using CG as the iterative solver? I just realized that the > constraints are inserted into the system matrix in such a way that the > solution vector automatically satisfies the constraints, but this is > not symmetric. > > Try running your problem when CG and then with GMRES or BiCG. If the > latter two work then the aforementioned problem is probably the source > of your difficulty. Let me know & I'll get a patch together. > > -Ben > > > > -----Original Message----- > From: libmesh-users-admin@... > [mailto:libmesh-users-admin@...] On Behalf Of Roy > Stogner > Sent: Tuesday, February 15, 2005 12:18 PM > To: Michael Povolotskyi > Cc: libmesh-users@... > Subject: Re: [Libmesh-users] hanging nodes and triangular elements > > > On Tue, 15 Feb 2005, Michael Povolotskyi wrote: > > >>Yes, the code works correctly with uniformly refined triangular >>elements. >> >>Could you, please, tell how can I check if the nodes are in a correct >>order? > > > If you're getting good results with uniform refinement, there's likely > nothing wrong with your coarse mesh - the distorted triangle problem > was just the only thing I'd ever seen that would give you problems > with a triangular mesh but not a quadrilateral mesh. > > Could you specify exactly what problems you're getting with adaptive > triangles that you aren't seeing with uniform triangles or adaptive > quads? Is it a bad convergence rate, a crash, or something else? > --- > Roy Stogner > > > ------------------------------------------------------- > SF email is sponsored by - The IT Product Guide > Read honest & candid reviews on hundreds of IT Products from real > users. Discover which products truly live up to the hype. Start > reading now. http://ads.osdn.com/?ad_id=6595&alloc_id=14396&op=click > _______________________________________________ > Libmesh-users mailing list Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users > -- ------------------------------------------------------------ Michael Povolotskyi, Ph.D. University of Rome "Tor Vergata" Department of Electronic Engineering Viale Politecnico, 1 - 00133 Rome - Italy Phone + 39 06 72597367 Fax + 39 06 2020519 http://www.optolab.uniroma2.it/pages/moshe/moshe.html ------------------------------------------------------------- ```
 Re: [Libmesh-users] hanging nodes and triangular elements From: Roy Stogner - 2005-02-16 18:24:43 ```On Wed, 16 Feb 2005, Michael Povolotskyi wrote: > We have tested both triangular and rectangular finite elements, both first > and second approximation order. > > The "problems" start to appear when we use the adaptive mesh refinement. > Detailed study shows that the same problems occur BOTH with triangular and > rectangular elements (in contrast to what I informed yesterday). > > We send a solution visualised by GMV program in files example_fullview.pdf > and example_magnified.pdf. One can see in Fig. example_magnified.pdf that > the solution at some points (indicated by red circles) is not continuous. > We tried different solvers. The solution changes very slightly, but the > problem persists. Are you sure you see this problem with linear and bilinear elements? With quadratic and biquadratic elements, you may be encountering a known problem with GMV output of solutions on higher order elements. libMesh outputs the same linear or bilinear elements, regardless of what your solution degree is. For uniform meshes this isn't as obvious since the result is still continuous; for adaptive meshes, however, a hanging node's value will be plotted on fine element neighbors but not coarse element neighbors, and unless the hanging node's value is precisely the (bi)linear interpolant between the other nodes on its edge/face, the resulting plot will be discontinuous. --- Roy ```

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