Multiple hard constraints problem setups

[lihangshiwo]

dear lulu，
I am trying to solve a simple problem with two different Dirichlet conditions, on the left boundary E=0 and on the inner circular boundary E=x+y (sum of horizontal and vertical coordinates), the problem is schematically shown below:

Defining these two hard boundaries separately is as simple as the following code：

def output_transform(inputs, outputs):
    x, y= inputs[:, 0:1], inputs[:, 1:2]

    R_square = R ** 2
    dist_square = x ** 2 + y ** 2
    res = dist_square - R_square

    E1 = x + y + res * outputs

    return E1

and

def output_transform(inputs, outputs):
    x, y = inputs[:, 0:1], inputs[:, 1:2]

    E2 = (1 - torch.exp(x-(-1))) * outputs
    return E2

But when I try to satisfy them all at the same time, I don't know how, and here's a failed attempt:

def output_transform(inputs, outputs):
    x, y= inputs[:, 0:1], inputs[:, 1:2]

    R_square = R ** 2
    dist_square = x ** 2 + y ** 2
    res = dist_square - R_square

    E = (x + y + res * outputs)* (1 - torch.exp(x-(-1)))

    return E

The problem doesn't seem to be very complicated, any help from anyone would be appreciated!