ee39b39805
* modify examples/problems * modify tutorials --------- Co-authored-by: Dario Coscia <dariocoscia@dhcp-235.eduroam.sissa.it> Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
52 lines
1.6 KiB
Python
52 lines
1.6 KiB
Python
""" Simple ODE problem. """
|
|
|
|
|
|
# ===================================================== #
|
|
# #
|
|
# This script implements a simple first order ode. #
|
|
# The FirstOrderODE class is defined inheriting from #
|
|
# SpatialProblem. We denote: #
|
|
# y --> field variable #
|
|
# x --> spatial variable #
|
|
# #
|
|
# The equation is: #
|
|
# dy(x)/dx + y(x) = x #
|
|
# #
|
|
# ===================================================== #
|
|
|
|
|
|
from pina.problem import SpatialProblem
|
|
from pina import Condition
|
|
from pina.geometry import CartesianDomain
|
|
from pina.operators import grad
|
|
from pina.equation import Equation, FixedValue
|
|
import torch
|
|
|
|
|
|
class FirstOrderODE(SpatialProblem):
|
|
|
|
# variable domain range
|
|
x_rng = [0., 5.]
|
|
# field variable
|
|
output_variables = ['y']
|
|
# create domain
|
|
spatial_domain = CartesianDomain({'x': x_rng})
|
|
|
|
# define the ode
|
|
def ode(input_, output_):
|
|
y = output_
|
|
x = input_
|
|
return grad(y, x) + y - x
|
|
|
|
# define real solution
|
|
def solution(self, input_):
|
|
x = input_
|
|
return x - 1.0 + 2*torch.exp(-x)
|
|
|
|
# define problem conditions
|
|
conditions = {
|
|
'BC': Condition(location=CartesianDomain({'x': x_rng[0]}), equation=FixedValue(1.)),
|
|
'D': Condition(location=CartesianDomain({'x': x_rng}), equation=Equation(ode)),
|
|
}
|
|
|
|
truth_solution = solution |