Source code for pymordemos.elliptic_unstructured

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

import numpy as np
from typer import Argument, run

from pymor.analyticalproblems.domaindescriptions import CircularSectorDomain
from pymor.analyticalproblems.elliptic import StationaryProblem
from pymor.analyticalproblems.functions import ConstantFunction, ExpressionFunction
from pymor.discretizers.builtin import discretize_stationary_cg

[docs]def main( angle: float = Argument(..., help='The angle of the circular sector.'), num_points: int = Argument(..., help='The number of points that form the arc of the circular sector.'), clscale: float = Argument(..., help='Mesh element size scaling factor.'), ): """Solves the Poisson equation in 2D on a circular sector domain of radius 1 using an unstructured mesh. Note that Gmsh ( is required for meshing. """ problem = StationaryProblem( domain=CircularSectorDomain(angle, radius=1, num_points=num_points), diffusion=ConstantFunction(1, dim_domain=2), rhs=ConstantFunction(np.array(0.), dim_domain=2, name='rhs'), dirichlet_data=ExpressionFunction('sin(polar(x)[1] * pi/angle)', 2, (), {}, {'angle': angle}, name='dirichlet') ) print('Discretize ...') m, data = discretize_stationary_cg(analytical_problem=problem, diameter=clscale) grid = data['grid'] print(grid) print() print('Solve ...') U = m.solve() solution = ExpressionFunction('(lambda r, phi: r**(pi/angle) * sin(phi * pi/angle))(*polar(x))', 2, (), {}, {'angle': angle}) U_ref = m.visualize((U, U_ref, U-U_ref), legend=('Solution', 'Analytical solution (circular boundary)', 'Error'), separate_colorbars=True)
if __name__ == '__main__': run(main)