Consider a very simplified 1d wave equation, and with two easy initial conditions u(x,0)=0, u_t(x,0)=0, I read the book, Solving PDEs in Python, but I cannot find the answer for coding this in Fenics, so how to implement these two initial conditions? Any suitable scheme to handle the instability…

Well assuming you have a time discretization then you need to define three functions u and u_n, u_nn. u will be used for time n+2 and u_n for time n and u_nn for n+1. These are to be able to discretize the second order derivative you have in the wave equation. In Fenics given a proper vector spac…

Thank you nami, I have another question, for this 1d wave equation, I also have two mixed boundary conditions, namely u(L,t)=0, where x belongs to 0 to L, u_x(0,t)=f(t), f(t) is a function of t, like exp(t) How to handle these boundary conditions?

BCs like these have to be incorporated in the weak formulation. Namely \int_{\Omega} u_{xx} v dX = \int_{\partial \Omega} \frac{\partial u}{\partial \hat{n}} v dS - \int_{\Omega} u_{x} v_x dX where \hat{n} is the unit outward normal vector at the boundaries (in your 1D case it is 1 or -1 depending…

Yes, I got this. [image] I mean is there an existed 1d mixed boundary conditions code (similar), so I can easily modify it? I really don’t get the syntax of Fenics

Oh sorry. So you are looking for a source term on one side. Then something like this should work: from dolfin import * import numpy as np c =1000 mesh = IntervalMesh(100,0,1.0) V=FunctionSpace(mesh, "Lagrange", 1) class Right(SubDomain): def inside(self,x,on_boundary): return on_bo…

Thank you so much nami, and I have a stupid question when I use paraview to view the results of this code, it has this [image] do I need another reader?

That is strange. I don’t have that problem. Also I edited the code a second time. Make sure you are using my last edit. There were a couple of issues.

What version of ParaView you are using?

I am using 5.4.1 64-bit for windows. But I have an older version on my Linux computer and it works there as well.

Oh I see, [image] Error in opening 3D plots in fenics and .pvd files in Paraview 5.8.0 in Ubuntu 19.04 I/O This is fixed in the development version of FEniCS, with the following commit . You can alternatively use vtkplotter to visualize the data. Could you share how you sa…

Best way for two initial conditions of a wave equation

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Miraboreasu February 14, 2021, 6:34am 12

Oh I see,

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Best way for two initial conditions of a wave equation

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