def energy(self):
ans = 0
for e in range(self.Ne):
model = Corotated(self.config.mu, self.config.lambd,
self.F[e, :, :])
ans += self.vol[e] * model.psi()
return ans
def Df(self):
"""Df = grad(f_int) = -Hessian(e)"""
d, num_inside_pts = self.config.d, self.num_inside_pts
df_dphi = np.zeros((d * num_inside_pts, d * num_inside_pts))
mu, lambd = self.config.mu, self.config.lambd
for e in range(self.Ne):
model = Corotated(mu, lambd, self.F[e, :, :])
dPdF = model.dPdF()
for p in range(d + 1):
mesh_i = (d + 1) * e + p
i = self.mesh[mesh_i]
for q in range(d + 1):
mesh_j = (d + 1) * e + q
# for mesh_j in self.incident_element[i]:
j = self.mesh[mesh_j]
vectori, vectorj = self.i_to_vectori[i], self.i_to_vectori[
j]
if vectori != None and vectorj != None:
for beta in range(d):
for gamma in range(d):
for alpha in range(d):
for epsilon in range(d):
df_dphi[vectori*d+beta, vectorj*d+alpha] -= \
self.vol[e]*dPdF[beta*d+gamma, alpha*d+epsilon]*self.grad_N[mesh_j,epsilon]*self.grad_N[mesh_i,gamma]
return df_dphi
def del_f(self):
"""Blackbox function for CG"""
d = self.config.d
dP_function_list = []
for e in range(self.Ne):
model = Corotated(self.config.mu, self.config.lambd,
self.F[e, :, :])
dP_function_list.append(model.dP)
def calculate_del_f(del_phi):
ans = np.zeros(self.num_inside_pts * d)
del_F_vector = self.del_F(del_phi)
for e in range(self.Ne):
dP = dP_function_list[e](del_F_vector[e])
for p in range(d + 1):
i = self.mesh[(d + 1) * e + p]
vectori = self.i_to_vectori[i]
if vectori != None:
for beta in range(d):
for gamma in range(d):
ans[d * vectori + beta] -= self.vol[e] * dP[
beta, gamma] * self.grad_N[(d + 1) * e + p,
gamma]
return ans
df = LinearOperator((self.num_inside_pts * d, self.num_inside_pts * d),
matvec=calculate_del_f)
return df
def internal_force(self):
"""assembly external force vector based on current deformed_grid, Ds, F"""
"""f_int = -grad(e)"""
d, num_inside_pts = self.config.d, self.num_inside_pts
f = np.zeros(d * num_inside_pts)
mu, lambd = self.config.mu, self.config.lambd
for e in range(self.Ne):
model = Corotated(mu, lambd, self.F[e, :, :])
P = model.P()
for p in range(d + 1):
i = self.mesh[(d+1)*e+p]
vectori = self.i_to_vectori[i]
if vectori != None:
for beta in range(d):
for gamma in range(d):
f[d*vectori+beta] -= self.vol[e]*P[beta,gamma]*self.grad_N[(d+1)*e+p, gamma]
# Add gravity
f += self.gravity_force
return f