42 lines
1.4 KiB
Python
42 lines
1.4 KiB
Python
import torch
|
|
|
|
from pina.problem import SpatialProblem, ParametricProblem
|
|
from pina.operators import nabla
|
|
from pina import Span, Condition
|
|
|
|
|
|
class ParametricPoisson(SpatialProblem, ParametricProblem):
|
|
|
|
spatial_variables = ['x', 'y']
|
|
parameters = ['mu1', 'mu2']
|
|
output_variables = ['u']
|
|
domain = Span({'x': [-1, 1], 'y': [-1, 1]})
|
|
|
|
def laplace_equation(input_, output_):
|
|
force_term = torch.exp(
|
|
- 2*(input_.extract(['x']) - input_.extract(['mu1']))**2
|
|
- 2*(input_.extract(['y']) - input_.extract(['mu2']))**2)
|
|
return nabla(output_.extract(['u']), input_) - force_term
|
|
|
|
def nil_dirichlet(input_, output_):
|
|
value = 0.0
|
|
return output_.extract(['u']) - value
|
|
|
|
conditions = {
|
|
'gamma1': Condition(
|
|
Span({'x': [-1, 1], 'y': 1, 'mu1': [-1, 1], 'mu2': [-1, 1]}),
|
|
nil_dirichlet),
|
|
'gamma2': Condition(
|
|
Span({'x': [-1, 1], 'y': -1, 'mu1': [-1, 1], 'mu2': [-1, 1]}),
|
|
nil_dirichlet),
|
|
'gamma3': Condition(
|
|
Span({'x': 1, 'y': [-1, 1], 'mu1': [-1, 1], 'mu2': [-1, 1]}),
|
|
nil_dirichlet),
|
|
'gamma4': Condition(
|
|
Span({'x': -1, 'y': [-1, 1], 'mu1': [-1, 1], 'mu2': [-1, 1]}),
|
|
nil_dirichlet),
|
|
'D': Condition(
|
|
Span({'x': [-1, 1], 'y': [-1, 1], 'mu1': [-1, 1], 'mu2': [-1, 1]}),
|
|
laplace_equation),
|
|
}
|