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version 0.0.1

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2022-02-11 16:44:37 +01:00
parent fa8ffd5042
commit 1483746b45
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examples/problems/parametric_poisson.py
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@@ -1,43 +1,41 @@
import numpy as np
import torch
from pina.segment import Segment
from pina.cube import Cube
from pina.problem2d import Problem2D
from pina.problem import Problem
from pina.problem import SpatialProblem, ParametricProblem
from pina.operators import nabla
from pina import Span, Condition
class ParametricPoisson2DProblem(Problem2D):
class ParametricPoisson(SpatialProblem, ParametricProblem):
def __init__(self):
spatial_variables = ['x', 'y']
parameters = ['mu1', 'mu2']
output_variables = ['u']
domain = Span({'x': [-1, 1], 'y': [-1, 1]})
def laplace_equation(input_, param_, output_):
grad_u = self.grad(output_['u'], input_)
gradgrad_u_x = self.grad(grad_u['x'], input_)
gradgrad_u_y = self.grad(grad_u['y'], input_)
force_term = torch.exp(
- 2*(input_['x'] - input_['mu1'])**2 -
2*(input_['y'] - input_['mu2'])**2
)
return gradgrad_u_x['x'] + gradgrad_u_y['y'] - force_term
def laplace_equation(input_, output_):
force_term = torch.exp(
- 2*(input_['x'] - input_['mu1'])**2 - 2*(input_['y'] -
input_['mu2'])**2)
return nabla(output_['u'], input_) - force_term
def nil_dirichlet(input_, param_, output_):
value = 0.0
return output_['u'] - value
def nil_dirichlet(input_, output_):
value = 0.0
return output_['u'] - value
self.conditions = {
'gamma1': {'location': Segment((-1, -1), ( 1, -1)),'func': nil_dirichlet},
'gamma2': {'location': Segment(( 1, -1), ( 1, 1)),'func': nil_dirichlet},
'gamma3': {'location': Segment(( 1, 1), (-1, 1)),'func': nil_dirichlet},
'gamma4': {'location': Segment((-1, 1), (-1, -1)),'func': nil_dirichlet},
'D': {'location': Cube([[-1, 1], [-1, 1]]), 'func': laplace_equation}
}
self.input_variables = ['x', 'y']
self.output_variables = ['u']
self.parameters = ['mu1', 'mu2']
#self.truth_solution = poisson_sol
self.spatial_domain = Cube([[0, 1], [0, 1]])
self.parameter_domain = np.array([[-1, 1], [-1, 1]])
#self.check() # Check the problem is correctly set
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),
}