On Newman's Adiabatic Boundary Problem

[yuluoxiansen]

Hello Lulu,
I am using deepxde, a powerful tool, to solve a heat transfer problem. I have encountered difficulties in defining the adiabatic boundary. To be precise, I don’t know if I can define the adiabatic boundary in this way. Can you help me take a look?

My geometry ：
r = 1
rc = 0.1
vertices=[
(0,0),(0,2r),(r,2r),(r,r+rc/2),(r+2rc,r+rc/2),(r+2rc,2r),
(2r+2rc,2r),(2r+2rc,0),(r+2rc,0),(r+2rc,r-rc/2),(r,r-rc/2),(r,0)
geoms=dde.geometry.Polygon(vertices=vertices)

This is a schematic diagram：

Both sides of the region are Dirichlet conditions, and the remaining boundaries are adiabatic boundaries.but I cannot define the middle boundary as an adiabatic boundary，I looked up some information, but they are all rectangular areas, I don't know what to do.In addition, the adiabatic boundary cannot converge, and the loss value is approximately 1e-2，HELP ME!

pde and func_boundary as follows:

def pde(x, y):
dy_xx = dde.grad.hessian(y, x, i=0, j=0)
dy_yy = dde.grad.hessian(y, x, i=1, j=1)
return dy_xx + dy_yy
def boundary_l(x, on_boundary):
return on_boundary and dde.utils.isclose(x[0], 0)
def boundary_r(x, on_boundary):
return on_boundary and dde.utils.isclose(x[0], 2r+2rc)
def boundary1(x, on_boundary):
return on_boundary and 0 < x[0] <= r
def boundary2(x, on_boundary):
return on_boundary and r+2rc <= x[0] < 2r+2rc
def boundary3(x, on_boundary):
return on_boundary and r <= x[0] < r+2rc
def boundary4(x, on_boundary):
return on_boundary and 0 <= x[1] < r-rc/2 or x[0] == r
def boundary5(x, on_boundary):
return on_boundary and r+rc/2 <= x[1] < 2r or x[0] == r+2rc

bc_left = dde.icbc.DirichletBC(geoms, lambda x: 1, boundary_l)
bc_right = dde.icbc.DirichletBC(geoms, lambda x: 0, boundary_r)
bc_neumann = dde.icbc.NeumannBC(geoms, lambda x: 0, boundary1)
bc_neumann2 = dde.icbc.NeumannBC(geoms, lambda x: 0, boundary2)
bc_neumann3 = dde.icbc.NeumannBC(geoms, lambda x: 0, boundary3)
bc_neumann4 = dde.icbc.NeumannBC(geoms, lambda x: 0, boundary4)
bc_neumann5 = dde.icbc.NeumannBC(geoms, lambda x: 0, boundary5)
data = dde.data.PDE(
geoms,
num_domain=10000,
num_boundary=500,
pde=pde,
bcs=[bc_left, bc_right, bc_neumann,bc_neumann2,bc_neumann3,bc_neumann4,bc_neumann5])
net = dde.nn.FNN([2] + [30] * 5 + [1], "tanh", "Glorot normal")
model = dde.Model(data, net)
model.compile("adam", lr=1e-3, )
losshistory, train_state = model.train(iterations=50000,)
dde.saveplot(losshistory, train_state, issave=True, isplot=True)