def sdc_regression_test(self):
M = 2
P = 5
tstart = 0.0
tend = 0.25
nsteps = 5
dt = (tend - tstart) / float(nsteps)
prob = problem_model(a=1.0, nu=1.0, alpha=2.0, v0=0.25)
K_iter = 12
u0 = [2.0, 0.0, 0.0, 0.0, 0.0]
for n in range(nsteps):
tstart = float(n) * dt
tend = float(n + 1) * dt
sdc = sdc_step(M, P, tstart, tend, prob)
# reset buffers to zero
u = np.zeros((M, prob.dim))
usub = np.zeros((M, P, prob.dim))
fu = np.zeros((M, prob.dim))
fu_sub = np.zeros((M, P, prob.dim))
sdc.predict(u0, u, usub, fu, fu_sub)
for k in range(K_iter):
sdc.sweep(u0, u, usub, fu, fu_sub)
u0 = u[M - 1]
###
file = open('sdc-model-regression.txt')
val = []
for line in file:
val = np.append(val, float(line))
defect = np.linalg.norm(val - u0, np.inf)
assert defect < 1e-15, (
"Regression test failed, different from previous version. Defect: %5.3e"
% defect)
def sdc_regression_test(self):
M = 2
P = 5
tstart = 0.0
tend = 0.25
nsteps = 5
dt = (tend - tstart)/float(nsteps)
prob = problem_model(a=1.0, nu=1.0, alpha=2.0, v0=0.25)
K_iter = 12
u0 = [2.0, 0.0, 0.0, 0.0, 0.0]
for n in range(nsteps):
tstart = float(n)*dt
tend = float(n+1)*dt
sdc = sdc_step(M, P, tstart, tend, prob)
# reset buffers to zero
u = np.zeros((M,prob.dim))
usub = np.zeros((M,P,prob.dim))
fu = np.zeros((M,prob.dim))
fu_sub = np.zeros((M,P,prob.dim))
sdc.predict(u0, u, usub, fu, fu_sub)
for k in range(K_iter):
sdc.sweep(u0, u, usub, fu, fu_sub)
u0 = u[M-1]
###
file = open('sdc-model-regression.txt')
val = []
for line in file:
val = np.append(val, float(line))
defect = np.linalg.norm(val - u0, np.inf)
assert defect < 1e-15, ("Regression test failed, different from previous version. Defect: %5.3e" % defect)
def test_converge_to_fixpoint(self):
self.prob = problem_model(a=-0.1, nu=-1.0, alpha=1.0, v0=1.0)
self.M = 3
self.P = 4
tstart = 0.0
tend = 0.2
self.sdc = sdc_step(self.M, self.P, tstart, tend, self.prob)
u0 = np.reshape([2.0, 1.0, 0.0, 1.0, 0.0], (self.prob.dim, ))
u = np.zeros((self.M, self.prob.dim))
usub = np.zeros((self.M, self.P, self.prob.dim))
fu = np.zeros((self.M, self.prob.dim))
fu_sub = np.zeros((self.M, self.P, self.prob.dim))
# run predictor
self.sdc.predict(u0, u, usub, fu, fu_sub)
for k in range(25):
u_ = copy.deepcopy(u)
usub_ = copy.deepcopy(usub)
# run standard node sweep...
self.sdc.sweep(u0, u, usub, fu, fu_sub)
update_standard = np.linalg.norm((u - u_).flatten(), np.inf)
update_embedded = np.linalg.norm((usub - usub_).flatten(), np.inf)
res_standard = self.sdc.residual(u0, u)
res_embedded = self.sdc.sub_residual(u0, usub)
fu_sub_ = copy.deepcopy(fu_sub)
assert update_standard < 1e-12, (
"Standard update failed to converge to zero. Value: %5.3e" %
update_standard)
assert update_embedded < 1e-12, (
"Embedded update failed to converge to zero. Value: %5.3e" %
update_embedded)
assert res_standard < 1e-12, (
"Standard residual failed to converge to zero. Value: %5.3e" %
res_standard)
assert res_embedded < 1e-12, (
"Embedded residual failed to converge to zero. Value: %5.3e" %
res_embedded)
# Continue test to validate collocation update formula
u0_sub = u0
for m in range(self.M):
u0_coll = self.sdc.collocation_update(u0_sub, u, usub, m)
u0_sub = usub[m, -1]
err = np.linalg.norm(u0_coll - u0_sub)
assert err < 1e-12, (
"For collocation solution, update formula failed to reproduce last stage. Error: %5.3e"
% err)
def test_converge_to_fixpoint(self):
self.prob = problem_model(a = -0.1, nu = -1.0, alpha = 1.0, v0 = 1.0)
self.M = 3
self.P = 4
tstart = 0.0
tend = 0.2
self.sdc = sdc_step(self.M, self.P, tstart, tend, self.prob)
u0 = np.reshape([2.0, 1.0, 0.0, 1.0, 0.0], (self.prob.dim,))
u = np.zeros((self.M,self.prob.dim))
usub = np.zeros((self.M,self.P,self.prob.dim))
fu = np.zeros((self.M,self.prob.dim))
fu_sub = np.zeros((self.M,self.P,self.prob.dim))
# run predictor
self.sdc.predict(u0, u, usub, fu, fu_sub)
for k in range(25):
u_ = copy.deepcopy(u)
usub_ = copy.deepcopy(usub)
# run standard node sweep...
self.sdc.sweep(u0, u, usub, fu, fu_sub)
update_standard = np.linalg.norm( (u-u_).flatten(), np.inf)
update_embedded = np.linalg.norm( (usub-usub_).flatten(), np.inf)
res_standard = self.sdc.residual(u0, u)
res_embedded = self.sdc.sub_residual(u0, usub)
fu_sub_ = copy.deepcopy(fu_sub)
assert update_standard<1e-12, ("Standard update failed to converge to zero. Value: %5.3e" % update_standard)
assert update_embedded<1e-12, ("Embedded update failed to converge to zero. Value: %5.3e" % update_embedded)
assert res_standard<1e-12, ("Standard residual failed to converge to zero. Value: %5.3e" % res_standard)
assert res_embedded<1e-12, ("Embedded residual failed to converge to zero. Value: %5.3e" % res_embedded)
# Continue test to validate collocation update formula
u0_sub = u0
for m in range(self.M):
u0_coll = self.sdc.collocation_update(u0_sub, u, usub, m)
u0_sub = usub[m,-1]
err = np.linalg.norm(u0_coll - u0_sub)
assert err<1e-12, ("For collocation solution, update formula failed to reproduce last stage. Error: %5.3e" % err)
tend = 1.0
nue=500
a = 1.0
alpha_vec = np.linspace(0.0, 60.0, 120)
nu_vec = np.linspace(0.0, nue, 50)
P_vec = [8] #range(M,M+11)
stab = np.zeros((np.size(alpha_vec), np.size(nu_vec)))
theta=0.25
K_iter = 2
for P in P_vec:
for kk in range(np.size(alpha_vec)):
for ll in range(np.size(nu_vec)):
prob = problem_model(a=a, nu=nu_vec[ll], alpha=alpha_vec[kk], v0=0.0)
sdc = sdc_step(M, P, 0.0, 1.0, prob, theta)
R = np.zeros((prob.dim,prob.dim))
u0 = np.eye(prob.dim)
for mm in range(prob.dim):
#### run multirate SDC
u = np.zeros((M,prob.dim))
usub = np.zeros((M,P,prob.dim))
u_ = np.zeros((M,prob.dim))
usub_ = np.zeros((M,P,prob.dim))
fu = np.zeros((M,prob.dim))
fu_sub = np.zeros((M,P,prob.dim))
tend = 2.5
nsteps = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70]
K_iter = [2, 3, 4]
err = np.zeros((np.size(K_iter),np.size(nsteps)))
err_ros2 = np.zeros(np.size(nsteps))
err_std = np.zeros((np.size(K_iter),np.size(nsteps)))
order = np.zeros((np.size(K_iter),np.size(nsteps)))
fs = 8
a = 1.0
nu = 1.1
alpha = 1.0e-2
v0 = 0.25
prob = problem_model(a, nu, alpha, v0)
u_ex = np.zeros(prob.dim)
u0 = np.zeros(prob.dim)
u0[0] = 1.0
sol = odeint(prob.f, u0, [0.0, tend], rtol=1e-12, atol=1e-12)
u_ex = sol[-1]
for kk in range(np.size(K_iter)):
order_p = np.min([K_iter[kk], 2*M-1, 2*P-1])
for ll in range(np.size(nsteps)):
dt = (tend - tstart)/float(nsteps[ll])
u0 = np.zeros(prob.dim)
a = 1.0
alpha_vec = np.linspace(0.0, 35.0, 10)
nu_vec = np.linspace(0.0, nue, 10)
stab = np.zeros((np.size(alpha_vec), np.size(nu_vec)))
stab_ros = np.zeros((np.size(alpha_vec), np.size(nu_vec)))
stab_std = np.zeros((np.size(alpha_vec), np.size(nu_vec)))
stab_c = np.zeros((np.size(alpha_vec), np.size(nu_vec)))
K_iter = 2
for kk in range(np.size(alpha_vec)):
for ll in range(np.size(nu_vec)):
prob = problem_model(a=a, nu=nu_vec[ll], alpha=alpha_vec[kk], v0=0.0)
eigv, eigvec = np.linalg.eig(prob.S + prob.get_mat1(0.1))
stab_c[kk, ll] = np.max(eigv)
sdc = sdc_step(M, P, 0.0, 1.0, prob, 0.0)
sdc_std = sdc_standard_step(M, 0.0, 1.0, prob)
ros = ros2_step(0.0, 1.0, prob)
R = np.zeros((prob.dim, prob.dim))
R_ros = np.zeros((prob.dim, prob.dim))
R_std = np.zeros((prob.dim, prob.dim))
u0 = np.eye(prob.dim)
u0_ros = np.eye(prob.dim)
u0_std = np.eye(prob.dim)
tend = 2.5
nsteps = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70]
K_iter = [2, 3, 4]
err = np.zeros((np.size(K_iter), np.size(nsteps)))
err_ros2 = np.zeros(np.size(nsteps))
err_std = np.zeros((np.size(K_iter), np.size(nsteps)))
order = np.zeros((np.size(K_iter), np.size(nsteps)))
fs = 8
a = 1.0
nu = 1.1
alpha = 1.0e-2
v0 = 0.25
prob = problem_model(a, nu, alpha, v0)
u_ex = np.zeros(prob.dim)
u0 = np.zeros(prob.dim)
u0[0] = 1.0
sol = odeint(prob.f, u0, [0.0, tend], rtol=1e-12, atol=1e-12)
u_ex = sol[-1]
for kk in range(np.size(K_iter)):
order_p = np.min([K_iter[kk], 2 * M - 1, 2 * P - 1])
for ll in range(np.size(nsteps)):
dt = (tend - tstart) / float(nsteps[ll])
u0 = np.zeros(prob.dim)
u+= 1.0/np.pi*( np.cos(float(k)*a*t)*np.cos(float(k)*x) + np.sin(float(k)*a*t)*np.sin(float(k)*x) ) return u M = 3 P = 5 tstart = 0.0 tend = 0.25 nsteps = 5 dt = (tend - tstart)/float(nsteps) Nx = 50 xaxis = np.linspace(0, 2*np.pi, Nx+1) xaxis = xaxis[0:Nx] prob = problem_model(a=1.0, nu=1.0, alpha=2.0, v0=0.25) K_iter = 12 u0 = [2.0, 0.0, 0.0, 0.0, 0.0] u_plot = np.zeros((nsteps+1,prob.dim)) u_euler = np.zeros((nsteps+1, prob.dim)) t_axis = np.zeros(nsteps+1) t_axis[0] = tstart u_plot[0] = u0 u_euler[0] = u0 fig = plt.figure() for n in range(nsteps): tstart = float(n)*dt tend = float(n+1)*dt