2D Poisson equation with variable coefficient about deepxde HOT 13 CLOSED

Could you change x1=x[:,0] and x2=x[:,1] to x1=x[:, 0:1] and x2=x[:, 1:], so that x1 and x2 are column vectors?

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Thanks a lot! That appears to be the bug.

Do you happen to have a 3D case or a time-dependent 2D example by any chance, or have you ever tried it?

-Qi

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Yes, we have time-dependent 2D example, but the code is not online.

from deepxde.

Great! Looking forward to it. Thanks again for the help.

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Hi Lu, is there any chance to share a simple 2D time dependent case, like the one in the arxiv paper for us to try? Thanks, -Qi

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I will upload these days. 2D time case should be very similar to 1D case.

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Thank you! That would be great!

from deepxde.

Hello Lulu!

Please where can I find an example of a time dependent 2D domain.

best regards,

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Hello Lulu!

Please is this the right syntax to fix the time-periodicity condition for a PDE problem in 2D in space?

Spatial_domain = dde.geometry.Rectangle(xmin=[-1, -1], xmax=[1, 1])
Temporal_domain = dde.geometry.TimeDomain(0, 2*np.pi)
Spatio_temporal_domain = dde.geometry.GeometryXTime(Spatial_domain, Temporal_domain)
boundary_condition_u = dde.DirichletBC(Spatio_temporal_domain, u_func, lambda _, on_boundary: on_boundary, component=0)
boundary_condition_v = dde.DirichletBC(Spatio_temporal_domain, v_func, lambda _, on_boundary: on_boundary, component=1)

periodic_condition_u = dde.PeriodicBC(Spatio_temporal_domain, 1, lambda _, on_boundary: on_boundary, component=0)???
periodic_condition_v = dde.PeriodicBC(Spatio_temporal_domain, 1, lambda _, on_boundary: on_boundary, component=1)???

I only want to check the two last line for: u(x, y, 0) = u(x, y, 2pi); v(x, y, 0) = v(x, y, 2pi)

thank you very much!

best,

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Or should I instead use this syntax for the time-periodicity for a problem in 2D in space ?

periodic_condition_u = dde.PeriodicBC(Spatio_temporal_domain, 1, lambda _, on_periodic: on_periodic, component=0)???
periodic_condition_v = dde.PeriodicBC(Spatio_temporal_domain, 1, lambda _, on_periodic: on_periodic, component=1)???

Thank you very much!

best,

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For the periodic in x and y, why "u(x, y, 0) = u(x, y, 2pi); v(x, y, 0) = v(x, y, 2pi)"? Should it be

• u(-1, y, t) = u(1, y, t), v(-1, y, t) = v(1, y, t)
• u(x, -1, 0) = u(x, 1, t), v(x, -1, 0) = v(x, 1, t)
  ?

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Hello Professor!

Thank you for replying. I want to enforce the periodic in time. So, my problem is in 2 dimension in space and the third dimension is the time as: (x, y, t). I actually want to write:

u(x, y, 0) = u(x, y, 2pi); v(x, y, 0) = v(x, y, 2pi) for all (x, y).

best regards!

Fayaud!

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For more precision, I am solving the following time-dependent Navier-Stokes equation:

File.pdf

best,

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