55 lines
1.7 KiB
Python
55 lines
1.7 KiB
Python
"""Definition of the Poisson problem on a square domain."""
|
|
|
|
from pina.problem import SpatialProblem
|
|
from pina.operator import laplacian
|
|
from pina import Condition
|
|
from pina.domain import CartesianDomain
|
|
from pina.equation.equation import Equation
|
|
from pina.equation.equation_factory import FixedValue
|
|
import torch
|
|
|
|
|
|
def laplace_equation(input_, output_):
|
|
"""
|
|
Implementation of the laplace equation.
|
|
"""
|
|
force_term = torch.sin(input_.extract(["x"]) * torch.pi) * torch.sin(
|
|
input_.extract(["y"]) * torch.pi
|
|
)
|
|
delta_u = laplacian(output_.extract(["u"]), input_)
|
|
return delta_u - force_term
|
|
|
|
|
|
my_laplace = Equation(laplace_equation)
|
|
|
|
|
|
class Poisson2DSquareProblem(SpatialProblem):
|
|
"""
|
|
Implementation of the 2-dimensional Poisson problem on a square domain.
|
|
"""
|
|
|
|
output_variables = ["u"]
|
|
spatial_domain = CartesianDomain({"x": [0, 1], "y": [0, 1]})
|
|
|
|
domains = {
|
|
"D": CartesianDomain({"x": [0, 1], "y": [0, 1]}),
|
|
"g1": CartesianDomain({"x": [0, 1], "y": 1}),
|
|
"g2": CartesianDomain({"x": [0, 1], "y": 0}),
|
|
"g3": CartesianDomain({"x": 1, "y": [0, 1]}),
|
|
"g4": CartesianDomain({"x": 0, "y": [0, 1]}),
|
|
}
|
|
|
|
conditions = {
|
|
"nil_g1": Condition(domain="g1", equation=FixedValue(0.0)),
|
|
"nil_g2": Condition(domain="g2", equation=FixedValue(0.0)),
|
|
"nil_g3": Condition(domain="g3", equation=FixedValue(0.0)),
|
|
"nil_g4": Condition(domain="g4", equation=FixedValue(0.0)),
|
|
"laplace_D": Condition(domain="D", equation=my_laplace),
|
|
}
|
|
|
|
def poisson_sol(self, pts):
|
|
return -(
|
|
torch.sin(pts.extract(["x"]) * torch.pi)
|
|
* torch.sin(pts.extract(["y"]) * torch.pi)
|
|
)
|