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():
parameters["reorder_dofs_serial"] = False
parameters["form_compiler"]["cpp_optimize"] = True
parameters["form_compiler"]["optimize"] = True
# Set-up cardiac model
heart = setup_model()
# Set-up solver
ps = BasicSplittingSolver.default_parameters()
ps["BasicBidomainSolver"]["linear_variational_solver"][
"linear_solver"] = "direct"
ps["BasicBidomainSolver"]["theta"] = 1.0
ps["theta"] = 1.0
ps["BasicCardiacODESolver"]["S_polynomial_family"] = "CG"
ps["BasicCardiacODESolver"]["S_polynomial_degree"] = 1
ps["BasicCardiacODESolver"]["V_polynomial_family"] = "CG"
ps["BasicCardiacODESolver"]["V_polynomial_degree"] = 1
solver = BasicSplittingSolver(heart, ps)
# Define end-time and (constant) timesteps
dt = 0.25 # mS
T = 1.0 # + 1.e-6 # mS
# Define initial condition(s)
ic = InitialCondition(degree=1) # Should use degree=0 here for
# correctness, but to match
# reference, using 1
vs0 = project(ic, solver.VS)
(vs_, vs, u) = solver.solution_fields()
vs_.assign(vs0)
# Solve
solutions = solver.solve((0, T), dt)
for (timestep, (vs_, vs, vur)) in solutions:
continue
u = project(vur[1], vur.function_space().sub(1).collapse())
norm_u = norm(u)
reference = 10.3756526773
print(("norm_u = ", norm_u))
print(("reference = ", reference))
assert_almost_equal(reference, norm_u, 1.e-4)
def main(N, dt, T, theta):
if dolfin_adjoint:
adj_reset()
# Create cardiac model
mesh = UnitSquareMesh(N, N)
time = Constant(0.0)
cell_model = NoCellModel()
ac_str = "cos(t)*cos(2*pi*x[0])*cos(2*pi*x[1]) + 4*pow(pi, 2)*cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)"
stimulus = Expression(ac_str, t=time, degree=3)
heart = CardiacModel(mesh, time, 1.0, 1.0, cell_model, stimulus=stimulus)
# Set-up solver
ps = BasicSplittingSolver.default_parameters()
ps["theta"] = theta
ps["BasicBidomainSolver"]["linear_variational_solver"][
"linear_solver"] = "direct"
solver = BasicSplittingSolver(heart, params=ps)
# Define exact solution (Note: v is returned at end of time
# interval(s), u is computed at somewhere in the time interval
# depending on theta)
v_exact = Expression("cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)", t=T, degree=3)
u_exact = Expression("-cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)/2.0",
t=T - (1 - theta) * dt,
degree=3)
# Define initial condition(s)
vs0 = Function(solver.VS)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(vs0)
# Solve
solutions = solver.solve((0, T), dt)
for (timestep, (vs_, vs, vur)) in solutions:
continue
# Compute errors
(v, s) = vs.split(deepcopy=True)
v_error = errornorm(v_exact, v, "L2", degree_rise=2)
(v, u, r) = vur.split(deepcopy=True)
u_error = errornorm(u_exact, u, "L2", degree_rise=2)
return (v_error, u_error, mesh.hmin(), dt, T)