def test_energy(self):
tol = 1e-10
L = 2 + rand() # domain length
a = 3 + rand() # amplitude of force
E = 4 + rand() # Young's Mod
for res in [4, 8, 16]:
area_per_pt = L / res
x = np.arange(res) * area_per_pt
force = a * np.cos(2 * np.pi / L * x)
# theoretical FFT of force
Fforce = np.zeros_like(x)
Fforce[1] = Fforce[-1] = res / 2. * a
# theoretical FFT of disp
Fdisp = np.zeros_like(x)
Fdisp[1] = Fdisp[-1] = res / 2. * a / E * L / (np.pi)
# verify consistency
hs = PeriodicFFTElasticHalfSpace(res, E, L)
fforce = rfftn(force.T).T
fdisp = hs.greens_function * fforce
self.assertTrue(
Tools.mean_err(fforce, Fforce, rfft=True) < tol,
"fforce = \n{},\nFforce = \n{}".format(fforce.real, Fforce))
self.assertTrue(
Tools.mean_err(fdisp, Fdisp, rfft=True) < tol,
"fdisp = \n{},\nFdisp = \n{}".format(fdisp.real, Fdisp))
# Fourier energy
E = .5 * np.dot(Fforce / area_per_pt, Fdisp) / res
disp = hs.evaluate_disp(force)
e = hs.evaluate_elastic_energy(force, disp)
kdisp = hs.evaluate_k_disp(force)
self.assertTrue(
abs(disp - irfftn(kdisp.T).T).sum() < tol,
("disp = {}\n"
"ikdisp = {}").format(disp,
irfftn(kdisp.T).T))
ee = hs.evaluate_elastic_energy_k_space(fforce, kdisp)
self.assertTrue(
abs(e - ee) < tol,
"violate Parseval: e = {}, ee = {}, ee/e = {}".format(
e, ee, ee / e))
self.assertTrue(
abs(E - e) < tol,
"theoretical E = {}, computed e = {}, diff(tol) = {}({})".
format(E, e, E - e, tol))
def test_parabolic_shape_disp(self):
""" test whether the Elastic energy is a quadratic function of the
applied displacement"""
hs = PeriodicFFTElasticHalfSpace(self.res, self.young,
self.physical_sizes)
disp = random(self.res)
disp -= disp.mean()
nb_tests = 4
El = np.zeros(nb_tests)
for i in range(nb_tests):
force = hs.evaluate_force(i * disp)
El[i] = hs.evaluate_elastic_energy(i * force, disp)
tol = 1e-10
error = norm(El / El[1] - np.arange(nb_tests)**2)
self.assertTrue(error < tol)