Source code for pymordemos.elliptic_oned

#!/usr/bin/env python
# This file is part of the pyMOR project (http://www.pymor.org).

from typer import Argument, Option, run

from pymor.analyticalproblems.domaindescriptions import LineDomain
from pymor.analyticalproblems.elliptic import StationaryProblem
from pymor.analyticalproblems.functions import ExpressionFunction, ConstantFunction, LincombFunction
from pymor.discretizers.builtin import discretize_stationary_cg, discretize_stationary_fv
from pymor.parameters.functionals import ProjectionParameterFunctional

[docs]def main(
problem_number: int = Argument(..., min=0, max=1, help='Selects the problem to solve [0 or 1].'),
n: int = Argument(..., help='Grid interval count.'),

fv: bool = Option(False, help='Use finite volume discretization instead of finite elements.'),
):
"""Solves the Poisson equation in 1D using pyMOR's builtin discreization toolkit."""

rhss = [ExpressionFunction('ones(x.shape[:-1]) * 10', 1, ()),
ExpressionFunction('(x - 0.5)**2 * 1000', 1, ())]
rhs = rhss[problem_number]

d0 = ExpressionFunction('1 - x', 1, ())
d1 = ExpressionFunction('x', 1, ())

f0 = ProjectionParameterFunctional('diffusionl')
f1 = 1.

problem = StationaryProblem(
domain=LineDomain(),
rhs=rhs,
diffusion=LincombFunction([d0, d1], [f0, f1]),
dirichlet_data=ConstantFunction(value=0, dim_domain=1),
name='1DProblem'
)

parameter_space = problem.parameters.space(0.1, 1)

print('Discretize ...')
discretizer = discretize_stationary_fv if fv else discretize_stationary_cg
m, data = discretizer(problem, diameter=1 / n)
print(data['grid'])
print()

print('Solve ...')
U = m.solution_space.empty()
for mu in parameter_space.sample_uniformly(10):
U.append(m.solve(mu))
m.visualize(U, title='Solution for diffusionl in [0.1, 1]')

if __name__ == '__main__':
run(main)