from pygmsh import generate_mesh
from pygmsh.built_in import Geometry
geom = Geometry()
circle = geom.add_circle([0.] * 3, 1., .5**3)
geom.add_physical(circle.line_loop.lines, 'circle')
geom.add_physical(circle.plane_surface, 'disk')
m = from_meshio(generate_mesh(geom, dim=2))
basis = InteriorBasis(m, ElementTriP2())
A = asm(laplace, basis)
b = asm(unit_load, basis)
x = solve(*condense(A, b, D=basis.find_dofs()))
area = sum(b)
k = b @ x / area**2
k1, = basis.interpolator(x)(np.zeros((2, 1))) / area
if __name__ == '__main__':
from skfem.visuals.matplotlib import plot3, show
print('area = {:.4f} (exact = {:.4f})'.format(area, np.pi))
print('k = {:.5f} (exact = 1/8/pi = {:.5f})'.format(k, 1/np.pi/8))
print("k' = {:.5f} (exact = 1/4/pi = {:.5f})".format(k1, 1/np.pi/4))
plot3(basis, x)
show()
@LinearForm
def rhs(v, p):
w = p['prev']
return dot(grad(w), grad(v)) / np.sqrt(1 + dot(grad(w), grad(w)))
basis = Basis(m, ElementTriP1())
x = basis.zeros()
D = m.boundary_nodes()
x[D] = np.sin(np.pi * m.p[0, D])
for itr in range(100):
w = basis.interpolate(x)
J = asm(jacobian, basis, prev=w)
F = asm(rhs, basis, prev=w)
x_prev = x.copy()
x += 0.7 * solve(*condense(J, -F, D=D))
if np.linalg.norm(x - x_prev) < 1e-8:
break
if __name__ == "__main__":
print(np.linalg.norm(x - x_prev))
if __name__ == "__main__":
from skfem.visuals.matplotlib import plot3, show
plot3(m, x)
show()
def runTest(self):
m = self.mesh_type()
plot3(m, m.p[0])