Source code for tests.msepy.div_grad._2d_outer

# -*- coding: utf-8 -*-
r"""
"""

import sys


[docs] def div_grad_2d_general_bc_manufactured_test(degree, K, c=0.): r""" Parameters ---------- degree : int The degree of the mimetic spectral elements. K : int In total we will use :math:`4 * K * K` elements. c : float, default=0 The deformation factor of the :ref:`GALLERY-msepy-domains-and-meshes=crazy`. Returns ------- phi_error: float The :math:`L^2`-error of solution :math:`\varphi_h^2`. u_error: float The :math:`L^2`-error of solution :math:`u_h^1`. """ ph_dir = '../../' # customize it to your own dir containing phyem if ph_dir not in sys.path: sys.path.append(ph_dir) import phyem as ph import numpy as np n = 2 ls, mp = ph.samples.wf_div_grad(n=n, degree=degree, orientation='outer', periodic=False) msepy, obj = ph.fem.apply('msepy', locals()) manifold = msepy.base['manifolds'][r"\mathcal{M}"] boundary_manifold = msepy.base['manifolds'][r"\partial\mathcal{M}"] Gamma_phi = msepy.base['manifolds'][r"\Gamma_\phi"] Gamma_u = msepy.base['manifolds'][r"\Gamma_u"] msepy.config(manifold)( 'crazy', c=c, bounds=[[0., 1.] for _ in range(n)], periodic=False, ) msepy.config(Gamma_u)( manifold, {0: [1, 1, 0, 0]} ) # manifold.visualize() # boundary_manifold.visualize() # Gamma_phi.visualize() # Gamma_u.visualize() mesh = msepy.base['meshes'][r'\mathfrak{M}'] msepy.config(mesh)([K, K]) # for mesh_repr in msepy.base['meshes']: # mesh = msepy.base['meshes'][mesh_repr] # mesh.visualize() phi = msepy.base['forms']['potential'] u = msepy.base['forms']['velocity'] f = msepy.base['forms']['source'] ls = obj['ls'].apply() def phi_func(t, x, y): """""" return - np.cos(2 * np.pi * x) * np.cos(2 * np.pi * y) + t * 0 phi_scalar = ph.vc.scalar(phi_func) phi.cf = phi_scalar u.cf = - phi.cf.codifferential() f.cf = - u.cf.exterior_derivative() # u.cf = phi_scalar.gradient # f.cf = - phi_scalar.gradient.divergence ls.bc.config(Gamma_phi)(phi_scalar) ls.bc.config(Gamma_u)(phi_scalar.gradient) f[0].reduce() # phi[0].reduce() # f[0].visualize() ls0 = ls(0) als = ls0.assemble() results = als.solve() ls0.x.update(results[0]) # phi[0].visualize() # u[0].visualize() return phi[0].error(), u[0].error()
if __name__ == '__main__': # python tests/msepy/div_grad/_2d_outer.py ph_dir = '../' if ph_dir not in sys.path: sys.path.append(ph_dir) import doctest doctest.testmod() errors = div_grad_2d_general_bc_manufactured_test(2, 4) print(errors)