def test_solver_with_domains():
mesh = UnitCubeMesh(5, 5, 5)
time = Constant(0.0)
stimulus = Expression("2.0*t", t=time, degree=1)
# Create ac
applied_current = Expression("sin(2*pi*x[0])*t", t=time, degree=3)
# Create conductivity "tensors"
M_i = 1.0
M_e = 2.0
cell_model = FitzHughNagumoManual()
cardiac_model = CardiacModel(mesh, time, M_i, M_e, cell_model,
stimulus, applied_current)
dt = 0.1
t0 = 0.0
dt = dt
T = t0 + 5*dt
ics = cell_model.initial_conditions()
# Create basic solver
params = SplittingSolver.default_parameters()
params["ode_solver_choice"] = "BasicCardiacODESolver"
solver = SplittingSolver(cardiac_model, params=params)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(ics)
# Solve
solutions = solver.solve((t0, T), dt)
for (interval, fields) in solutions:
(vs_, vs, vur) = fields
class SolverWrapper(object):
def __init__(self):
self.mesh = UnitCubeMesh(5, 5, 5)
# Create time
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0*t", t=self.time, degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, self.time, self.M_i,
self.M_e, self.cell_model,
self.stimulus,
self.applied_current)
dt = 0.1
self.t0 = 0.0
if Solver == SplittingSolver:
# FIXME: Dolfin-adjoint fails with adaptive timestep and SplittingSolver
self.dt = dt
else:
self.dt = [(0.0, dt), (dt * 2, dt / 2), (dt * 4, dt)]
# Test using variable dt interval but using the same dt.
self.T = self.t0 + 5 * dt
# Create solver object
params = Solver.default_parameters()
if Solver == SplittingSolver:
params.enable_adjoint = enable_adjoint
params.BidomainSolver.linear_solver_type = solver_type
params.BidomainSolver.petsc_krylov_solver.relative_tolerance = 1e-12
else:
params.BasicBidomainSolver.linear_variational_solver.linear_solver = \
"gmres" if solver_type == "iterative" else "lu"
params.BasicBidomainSolver.linear_variational_solver.krylov_solver.relative_tolerance = 1e-12
params.BasicBidomainSolver.linear_variational_solver.preconditioner = 'ilu'
self.solver = Solver(self.cardiac_model, params=params)
(vs_, vs, vur) = self.solver.solution_fields()
if ics is None:
self.ics = self.cell_model.initial_conditions()
vs_.assign(self.ics)
else:
vs_.vector()[:] = ics.vector()
def run_forward_model(self):
solutions = self.solver.solve((self.t0, self.T), self.dt)
for (interval, fields) in solutions:
pass
(vs_, vs, vur) = self.solver.solution_fields()
return vs_, vs
class TestSplittingSolver(object):
"Test functionality for the splitting solvers."
def setup(self):
self.mesh = UnitCubeMesh(5, 5, 5)
# Create time
self.time = Constant(0.0)
# Create stimulus
self.stimulus = Expression("2.0*t", t=self.time, degree=1)
# Create ac
self.applied_current = Expression("sin(2*pi*x[0])*t",
t=self.time,
degree=3)
# Create conductivity "tensors"
self.M_i = 1.0
self.M_e = 2.0
self.cell_model = FitzHughNagumoManual()
self.cardiac_model = CardiacModel(self.mesh, self.time, self.M_i,
self.M_e, self.cell_model,
self.stimulus, self.applied_current)
dt = 0.1
self.t0 = 0.0
self.dt = [(0.0, dt), (dt * 2, dt / 2), (dt * 4, dt)]
# Test using variable dt interval but using the same dt.
self.T = self.t0 + 5 * dt
self.ics = self.cell_model.initial_conditions()
@medium
@parametrize(("solver_type"), ["direct", "iterative"])
def test_basic_and_optimised_splitting_solver_exact(self, solver_type):
"""Test that basic and optimised splitting solvers yield
very comparative results when configured identically."""
# Create basic solver
params = BasicSplittingSolver.default_parameters()
params["BasicCardiacODESolver"]["S_polynomial_family"] = "CG"
params["BasicCardiacODESolver"]["S_polynomial_degree"] = 1
solver = BasicSplittingSolver(self.cardiac_model, params=params)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(self.ics)
# Solve
solutions = solver.solve((self.t0, self.T), self.dt)
for (interval, fields) in solutions:
(vs_, vs, vur) = fields
a = vs.vector().norm("l2")
c = vur.vector().norm("l2")
assert_almost_equal(interval[1], self.T, 1e-10)
if dolfin_adjoint:
adj_reset()
# Create optimised solver with direct solution algorithm
params = SplittingSolver.default_parameters()
params["BidomainSolver"]["linear_solver_type"] = solver_type
params["enable_adjoint"] = False
if solver_type == "direct":
params["BidomainSolver"]["use_avg_u_constraint"] = True
solver = SplittingSolver(self.cardiac_model, params=params)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(self.ics)
# Solve again
solutions = solver.solve((self.t0, self.T), self.dt)
for (interval, fields) in solutions:
(vs_, vs, vur) = fields
assert_almost_equal(interval[1], self.T, 1e-10)
b = vs.vector().norm("l2")
d = vur.vector().norm("l2")
print "a, b = ", a, b
print "c, d = ", c, d
print "a - b = ", (a - b)
print "c - d = ", (c - d)
# Compare results, discrepancy is in difference in ODE
# solves.
assert_almost_equal(a, b, tolerance=1.)
assert_almost_equal(c, d, tolerance=1.)
def test_fitzhugh_nagumo_manual(self):
"""Test that the manually written FitzHugh-Nagumo model gives
comparable results to a given reference from Sundnes et al,
2006."""
class Stimulus(Expression):
def __init__(self, **kwargs):
self.t = kwargs["t"]
def eval(self, value, x):
if float(self.t) >= 50 and float(self.t) < 60:
v_amp = 125
value[0] = 0.05 * v_amp
else:
value[0] = 0.0
if dolfin_adjoint:
from dolfin_adjoint import adj_reset
adj_reset()
cell = FitzHughNagumoManual()
time = Constant(0.0)
cell.stimulus = Stimulus(t=time, degree=0)
solver = BasicSingleCellSolver(cell, time)
# Setup initial condition
(vs_, vs) = solver.solution_fields()
ic = cell.initial_conditions()
vs_.assign(ic)
# Initial set-up
interval = (0, 400)
dt = 1.0
times = []
v_values = []
s_values = []
# Solve
solutions = solver.solve(interval, dt=dt)
for (timestep, vs) in solutions:
(t0, t1) = timestep
times += [(t0 + t1) / 2]
v_values += [vs.vector()[0]]
s_values += [vs.vector()[1]]
# Regression test
v_max_reference = 2.6883308148064152e+01
s_max_reference = 6.8660144687023219e+01
tolerance = 1.e-14
print "max(v_values) %.16e" % max(v_values)
print "max(s_values) %.16e" % max(s_values)
msg = "Maximal %s value does not match reference: diff is %.16e"
v_diff = abs(max(v_values) - v_max_reference)
s_diff = abs(max(s_values) - s_max_reference)
assert (v_diff < tolerance), msg % ("v", v_diff)
assert (s_diff < tolerance), msg % ("s", s_diff)
# Correctness test
import os
if int(os.environ.get("DOLFIN_NOPLOT", 0)) != 1:
import pylab
pylab.plot(times, v_values, 'b*')
pylab.plot(times, s_values, 'r-')