def adjust_stepsize(self, state, h, order, y, y_err, dydt):
# [y] = A/m.
# [dydt] = A/m (deriviative of y).
# [y_err] = A/m (estimated error dydt).
# - One RK step: y = y_prev + (h*dydt +- y_err)
max_y_err = magneto.scaled_abs_max(
y_err, state.Ms
) # max_y_err = max_i(|y_err[i]| / Ms[i]), [max_y_err] = rad
max_dydt = magneto.scaled_abs_max(
dydt, state.Ms
) # max_dydt = max_i(|dydt[i]| / Ms[i]), [max_dydt] = rad/s
# Calculate estimated absolute and relative error.
try:
e_abs = max_y_err # [e_abs] = rad
e_rel = e_abs / (h * max_dydt) # [e_rel] = 1
except ZeroDivisionError:
print("ZeroDivisionError!")
return True, 5e-14
# Accept the step only with tolerable errors.
accept = (e_abs <= self.allowed_absolute_error) and (
e_rel <= self.allowed_relative_error)
# Determine step size scaling factor for allowed absolute and relative errors.
h_scale_abs = self.STEP_HEADROOM * pow(
self.allowed_absolute_error / e_abs, 1.0 / (order + 1.0))
h_scale_rel = self.STEP_HEADROOM * pow(
self.allowed_relative_error / e_rel, 1.0 / order)
def clamp(x, min_x, max_x):
if x < min_x: x = min_x
if x > max_x: x = max_x
return x
# Take the most pessimistic (= smallest) scaling factor and clamp by [max_step_decrease, max_step_increase]
h_scale = clamp(min([h_scale_abs, h_scale_rel]),
self.MIN_TIMESTEP_SCALE, self.MAX_TIMESTEP_SCALE)
# Determine next step size and clamp by [min_h, max_h]
h_next = clamp(h * h_scale, self.MIN_TIMESTEP, self.MAX_TIMESTEP)
# Accept step anyway if time step can not go any smaller.
if h_next == self.MIN_TIMESTEP: accept = True
return accept, h_next
def test_1(self):
mesh = RectangularMesh((10,10,10), (1e-9,1e-9,1e-9))
M = VectorField(mesh); M.fill((-8e5,0,0))
Ms = Field(mesh); Ms.fill(8e5)
sam = magneto.scaled_abs_max(M, Ms)
self.assertEqual(1.0, sam)
def test_1(self):
mesh = RectangularMesh((10,10,10), (1e-9,1e-9,1e-9))
M = VectorField(mesh); M.fill((-8e5,0,0))
Ms = Field(mesh); Ms.fill(8e5)
sam = magneto.scaled_abs_max(M, Ms)
self.assertEqual(1.0, sam)
def test_2(self):
mesh = RectangularMesh((10, 10, 10), (1e-9, 1e-9, 1e-9))
M = VectorField(mesh)
M.fill((-8e5, 0, 0))
Ms = Field(mesh)
Ms.fill(8e5)
Ms.set(0, 0)
Ms.set(0, 8e5)
self.assertFalse(Ms.isUniform())
sam = magneto.scaled_abs_max(M, Ms)
self.assertEqual(1.0, sam)
def test_2(self):
mesh = RectangularMesh((10, 10, 10), (1e-9, 1e-9, 1e-9))
M = VectorField(mesh)
M.fill((-8e5, 0, 0))
Ms = Field(mesh)
Ms.fill(8e5)
Ms.set(0, 0)
Ms.set(0, 8e5)
self.assertFalse(Ms.isUniform())
sam = magneto.scaled_abs_max(M, Ms)
self.assertEqual(1.0, sam)
def adjust_stepsize(self, state, h, order, y, y_err, dydt):
# [y] = A/m.
# [dydt] = A/m (deriviative of y).
# [y_err] = A/m (estimated error dydt).
# - One RK step: y = y_prev + (h*dydt +- y_err)
max_y_err = magneto.scaled_abs_max(y_err, state.Ms) # max_y_err = max_i(|y_err[i]| / Ms[i]), [max_y_err] = rad
max_dydt = magneto.scaled_abs_max(dydt, state.Ms) # max_dydt = max_i(|dydt[i]| / Ms[i]), [max_dydt] = rad/s
# Calculate estimated absolute and relative error.
try:
e_abs = max_y_err # [e_abs] = rad
e_rel = e_abs / (h*max_dydt) # [e_rel] = 1
except ZeroDivisionError:
print("ZeroDivisionError!")
return True, 5e-14
# Accept the step only with tolerable errors.
accept = (e_abs <= self.allowed_absolute_error) and (e_rel <= self.allowed_relative_error)
# Determine step size scaling factor for allowed absolute and relative errors.
h_scale_abs = self.STEP_HEADROOM * pow(self.allowed_absolute_error / e_abs, 1.0/(order+1.0))
h_scale_rel = self.STEP_HEADROOM * pow(self.allowed_relative_error / e_rel, 1.0/order)
def clamp(x, min_x, max_x):
if x < min_x: x = min_x
if x > max_x: x = max_x
return x
# Take the most pessimistic (= smallest) scaling factor and clamp by [max_step_decrease, max_step_increase]
h_scale = clamp(min([h_scale_abs, h_scale_rel]), self.MIN_TIMESTEP_SCALE, self.MAX_TIMESTEP_SCALE)
# Determine next step size and clamp by [min_h, max_h]
h_next = clamp(h * h_scale, self.MIN_TIMESTEP, self.MAX_TIMESTEP)
# Accept step anyway if time step can not go any smaller.
if h_next == self.MIN_TIMESTEP: accept = True
return accept, h_next
