Timeline for System of pde with Neumann boundary conditions
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2020 at 20:06 | answer | added | Alex Trounev | timeline score: 3 | |
| Feb 8, 2020 at 17:24 | comment | added | smj | @Alex Trounev I am not sure how to implement the BC equations without explicitly stating the z dependence on the u variable. | |
| Feb 8, 2020 at 15:59 | comment | added | Alex Trounev |
@smj The equations do not contain $\partial_z$, condition NeumannValue[0, z == 0.45 || z == 0.5] mean that there is no dependence on z.
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| Feb 8, 2020 at 15:22 | comment | added | smj | @Alex Trounev in the article the superconductor on which the equations have to be solved is placed in the xy plane and the magnetic field is applied along the z-axis. To properly implement the Neumann BC and take into account the width of the superconductor I suppose one has to solve the equations in 3D. | |
| Feb 8, 2020 at 13:11 | comment | added | Alex Trounev | @smj In the article that you quoted they solve the equation in 2D. | |
| Feb 8, 2020 at 9:06 | comment | added | smj | @user21 the documentation for FEM shows the solution of the heat equation and the wave equation, so I thought it should be sufficient. Nevertheless I tried: Method -> {"PDEDiscretization" -> {"MethodOfLines", "SpatialDiscretization" -> "FiniteElement"}}, but I am still getting the same error. I suspect the problem is in the proper implementation of the BC. | |
| Feb 8, 2020 at 9:02 | comment | added | smj | @ Alex Trounev I tried some of your suggestions but I still get the same error, moreover u1 and u2 do not satisfy any Dirichlet BC as shown in the equations I wrote above. | |
| Feb 8, 2020 at 5:35 | comment | added | user21 | Using Method->"FiniteElement" is not ging to work for time dependent PDEs. Usw Method->{"MethodOfLines", .... } instead. You can find exampls on this site. | |
| Feb 7, 2020 at 22:14 | comment | added | Alex Trounev |
Now delete all [t_, x_, y_, z_] from u, delgma, f, f1, f2,f3,f4,dudt,put f={f1,f2,f3,f4} and eqns = dA.dudt + delgma - f;. Add u1[0, x, y, z] == 0, u2[0, x, y, z] == 0, DirichletCondition[{u1[t, x, y, z] == 0, u2[t, x, y, z] == 0}, True], In NDSolve put eqns=={0,0,0,0}.
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| Feb 7, 2020 at 18:47 | comment | added | smj | I've edited the question, I still get the same error after changing the BC. | |
| Feb 7, 2020 at 18:46 | history | edited | smj | CC BY-SA 4.0 |
added 54 characters in body
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| Feb 7, 2020 at 14:20 | comment | added | Alex Trounev |
Parameter dudt is not defined. Typo in boundary conditions: should be NeumannValue[0, z == 0.45 || z == 0.5]. Use {u1, u2, u3, u4} instead of u in NDSolve[].
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| Feb 7, 2020 at 12:25 | history | asked | smj | CC BY-SA 4.0 |