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On smoothness of numerically convergent solutions
Posted 30.12.2015, 10:21 GMT-5 Version 5.0 4 Replies
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Dear all,
I am using the latest Multiphysics coefficient PDE solver to address the problem of finding lattice solutions of a 2D system in cartesian coordinates.
For this problem the COMSOL solver is really well suited, it allows one to specify periodic boundary conditions which extends the solution of a single unit cell to the whole cartesian domain and it includes the option of imposing pointwise constraints such as boundary conditions at the corners of the cell etc.
I find converging solutions to the problem which look like the solutions I would expect (see attached sol1), however when I zoom in to these solutions I find that there seems to be a point where the solution is not smooth (see attached sol2). This is worrying since if the solution found is truly non-smooth then it doesn't correspond to a physical solution, if instead it is just a numerical artifact then I can safely proceed with it.
My question is therefore, how can I make sure I can safely interpret the solution to be smooth? Or on the contrary, how can I know for sure the solution is not everywhere smooth?
Many thanks.
I am using the latest Multiphysics coefficient PDE solver to address the problem of finding lattice solutions of a 2D system in cartesian coordinates.
For this problem the COMSOL solver is really well suited, it allows one to specify periodic boundary conditions which extends the solution of a single unit cell to the whole cartesian domain and it includes the option of imposing pointwise constraints such as boundary conditions at the corners of the cell etc.
I find converging solutions to the problem which look like the solutions I would expect (see attached sol1), however when I zoom in to these solutions I find that there seems to be a point where the solution is not smooth (see attached sol2). This is worrying since if the solution found is truly non-smooth then it doesn't correspond to a physical solution, if instead it is just a numerical artifact then I can safely proceed with it.
My question is therefore, how can I make sure I can safely interpret the solution to be smooth? Or on the contrary, how can I know for sure the solution is not everywhere smooth?
Many thanks.
4 Replies Last Post 02.03.2016, 19:27 GMT-5
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Posted:
9 years ago
Gianni,
Seems this is mesh-related effect. Try to refine the mesh and observe change in curve smoothness.
Regards,
Sergei
Seems this is mesh-related effect. Try to refine the mesh and observe change in curve smoothness.
Regards,
Sergei
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Posted:
9 years ago
Hi, Tallarita, are you using v5.2? Do the periodic conditions work well in PDE modes? I find that it doesnot work in v5.0. Thank you.
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Posted:
9 years ago
Dear Jack,
yes I am using the latest version 5.2. However I am not that sure on the result of pde solving in COMSOL. Especially solutions with pointwise constraints seem really non-smooth. Something is suspicious.
Best
yes I am using the latest version 5.2. However I am not that sure on the result of pde solving in COMSOL. Especially solutions with pointwise constraints seem really non-smooth. Something is suspicious.
Best
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Posted:
9 years ago
Thanks for your timely reply. I guess your solution is mesh convergence related.