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Documentation for v0.1 version (#199)

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* Adding Equations, solving typos
* improve _code.rst
* the team rst and restuctore index.rst
* fixing errors

---------

Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
This commit is contained in:
Dario Coscia
2023-11-08 14:39:00 +01:00
committed by Nicola Demo
parent 3f9305d475
commit 8b7b61b3bd
144 changed files with 2741 additions and 1766 deletions
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21
pina/problem/timedep_problem.py
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@@ -14,14 +14,17 @@ class TimeDependentProblem(AbstractProblem):
:Example:
>>> from pina.problem import SpatialProblem, TimeDependentProblem
>>> from pina.operators import grad, laplacian
>>> from pina import Condition, Span
>>> from pina.equations import Equation, FixedValue
>>> from pina import Condition
>>> from pina.geometry import CartesianDomain
>>> import torch
>>>
>>>
>>> class Wave(TimeDependentSpatialProblem):
>>>
>>> output_variables = ['u']
>>> spatial_domain = Span({'x': [0, 3]})
>>> temporal_domain = Span({'t': [0, 1]})
>>> spatial_domain = CartesianDomain({'x': [0, 3]})
>>> temporal_domain = CartesianDomain({'t': [0, 1]})
>>>
>>> def wave_equation(input_, output_):
>>> u_t = grad(output_, input_, components=['u'], d=['t'])
@@ -29,10 +32,6 @@ class TimeDependentProblem(AbstractProblem):
>>> delta_u = laplacian(output_, input_, components=['u'], d=['x'])
>>> return delta_u - u_tt
>>>
>>> def nil_dirichlet(input_, output_):
>>> value = 0.0
>>> return output_.extract(['u']) - value
>>>
>>> def initial_condition(input_, output_):
>>> u_expected = (-3*torch.sin(2*torch.pi*input_.extract(['x']))
>>> + 5*torch.sin(8/3*torch.pi*input_.extract(['x'])))
@@ -40,10 +39,10 @@ class TimeDependentProblem(AbstractProblem):
>>> return u - u_expected
>>>
>>> conditions = {
>>> 't0': Condition(Span({'x': [0, 3], 't':0}), initial_condition),
>>> 'gamma1': Condition(Span({'x':0, 't':[0, 1]}), nil_dirichlet),
>>> 'gamma2': Condition(Span({'x':3, 't':[0, 1]}), nil_dirichlet),
>>> 'D': Condition(Span({'x': [0, 3], 't':[0, 1]}), wave_equation)}
>>> 't0': Condition(CartesianDomain({'x': [0, 3], 't':0}), Equation(initial_condition)),
>>> 'gamma1': Condition(CartesianDomain({'x':0, 't':[0, 1]}), FixedValue(0.)),
>>> 'gamma2': Condition(CartesianDomain({'x':3, 't':[0, 1]}), FixedValue(0.)),
>>> 'D': Condition(CartesianDomain({'x': [0, 3], 't':[0, 1]}), Equation(wave_equation))}
"""