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Adding new problems to problem.zoo (#484)

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* adding problems
* add tests
* update doc + formatting

---------

Co-authored-by: Dario Coscia <dariocos99@gmail.com>
This commit is contained in:
Giovanni Canali
2025-03-12 10:42:16 +01:00
committed by Nicola Demo
parent 2ae4a94e49
commit f67467e5bd
21 changed files with 570 additions and 168 deletions
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61
pina/problem/zoo/poisson_2d_square.py
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@@ -1,31 +1,35 @@
"""Definition of the Poisson problem on a square domain."""
"""Formulation of the Poisson problem in a square domain."""
import torch
from ..spatial_problem import SpatialProblem
from ...operator import laplacian
from ... import Condition
from ...operator import laplacian
from ...problem import SpatialProblem
from ...domain import CartesianDomain
from ...equation.equation import Equation
from ...equation.equation_factory import FixedValue
from ...equation import Equation, FixedValue
def laplace_equation(input_, output_):
"""
Implementation of the laplace equation.
:param LabelTensor input_: Input data of the problem.
:param LabelTensor output_: Output data of the problem.
:return: The residual of the laplace equation.
:rtype: LabelTensor
"""
force_term = torch.sin(input_.extract(["x"]) * torch.pi) * torch.sin(
input_.extract(["y"]) * torch.pi
force_term = (
torch.sin(input_.extract(["x"]) * torch.pi)
* torch.sin(input_.extract(["y"]) * torch.pi)
* (2 * torch.pi**2)
)
delta_u = laplacian(output_.extract(["u"]), input_)
delta_u = laplacian(output_, input_, components=["u"], d=["x", "y"])
return delta_u - force_term
my_laplace = Equation(laplace_equation)
class Poisson2DSquareProblem(SpatialProblem):
"""
Implementation of the 2-dimensional Poisson problem on a square domain.
r"""
Implementation of the 2-dimensional Poisson problem in the square domain
:math:`[0, 1] \times [0, 1]`.
"""
output_variables = ["u"]
@@ -33,24 +37,31 @@ class Poisson2DSquareProblem(SpatialProblem):
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]}),
"g1": CartesianDomain({"x": [0, 1], "y": 1.0}),
"g2": CartesianDomain({"x": [0, 1], "y": 0.0}),
"g3": CartesianDomain({"x": 1.0, "y": [0, 1]}),
"g4": CartesianDomain({"x": 0.0, "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),
"g1": Condition(domain="g1", equation=FixedValue(0.0)),
"g2": Condition(domain="g2", equation=FixedValue(0.0)),
"g3": Condition(domain="g3", equation=FixedValue(0.0)),
"g4": Condition(domain="g4", equation=FixedValue(0.0)),
"D": Condition(domain="D", equation=Equation(laplace_equation)),
}
def poisson_sol(self, pts):
"""TODO"""
def solution(self, pts):
"""
Implementation of the analytical solution of the Poisson problem.
return -(
:param LabelTensor pts: Points where the solution is evaluated.
:return: The analytical solution of the Poisson problem.
:rtype: LabelTensor
"""
sol = -(
torch.sin(pts.extract(["x"]) * torch.pi)
* torch.sin(pts.extract(["y"]) * torch.pi)
)
sol.labels = self.output_variables
return sol