Source code for pymordemos.elliptic_oned

#!/usr/bin/env python
# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2020 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

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


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)