def main(solver, N: int, dt: float, T: float, theta: float) -> Tuple[float, float, float, float]:
"""Run monodomain MMS."""
mesh = UnitSquareMesh(N, N)
time = Constant(0.0)
lam = Constant(1.0)
cell_model = NoCellModel()
ac_str = "(8*pi*pi*lam*sin(t) + (lam + 1)*cos(t))*cos(2*pi*x[0])*cos(2*pi*x[1])/(lam + 1)"
stimulus = Expression(ac_str, t=time, lam=lam, degree=3)
parameters = solver.default_parameters()
_solver = solver(mesh, time, 1.0, I_s=stimulus, parameters=parameters)
vs0 = Function(_solver.V)
vs_, vs = _solver.solution_fields()
vs_.assign(vs0)
for timestep, (v_, v) in _solver.solve(0, T, dt):
continue
v_exact = Expression(
"sin(t)*cos(2*pi*x[0])*cos(2*pi*x[1])",
t=T,
degree=3
)
# compute errors
# v, s = vs.split(deepcopy=True)
v_error = errornorm(v_exact, v, "L2", degree_rise=2)
return (v_error, mesh.hmin(), dt, T)
def main(N: int, dt: float, T: float, theta: float) -> Tuple[float, float, float, float]:
"""Set up solver and return errors and mesh size."""
mesh = UnitSquareMesh(N, N)
time = Constant(0.0)
ac_str = "(8*pi*pi*lam*sin(t) + (lam + 1)*cos(t))*cos(2*pi*x[0])*cos(2*pi*x[1])/(lam + 1)"
stimulus = Expression(ac_str, t=time, lam=Constant(1), degree=3)
M_i = Constant(1.0)
# Set up solver
parameters = BasicMonodomainSolver.default_parameters()
parameters["theta"] = theta
solver = BasicMonodomainSolver(mesh, time, M_i, I_s=stimulus, parameters=parameters)
v_exact = Expression("sin(t)*cos(2*pi*x[0])*cos(2*pi*x[1])", t=T, degree=3)
# Define initial conditions
v_, v = solver.solution_fields()
# Solve
solutions = solver.solve(0, T, dt)
for interval, fields in solutions:
continue
# Compute errors
v_error = errornorm(v_exact, v, "L2", degree_rise=2)
return v_error, mesh.hmin(), dt, T
def main(N: int, dt: float, T: float,
theta: float) -> Tuple[float, float, float, float, float]:
"""Run bidomain MMA."""
# Create data
mesh = UnitSquareMesh(N, N)
time = Constant(0.0)
ac_str = "cos(t)*cos(2*pi*x[0])*cos(2*pi*x[1]) + 4*pi*pi*cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)"
stimulus = Expression(ac_str, t=time, degree=5)
M_i = 1.
M_e = 1.0
# Set-up solver
parameters = BidomainSolver.default_parameters()
parameters["theta"] = theta
parameters["linear_solver_type"] = "direct"
parameters["use_avg_u_constraint"] = True
parameters["Chi"] = 1.0
parameters["Cm"] = 1.0
solver = BidomainSolver(mesh,
time,
M_i,
M_e,
I_s=stimulus,
parameters=parameters)
# 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)
v_, vu = solver.solution_fields()
# Solve
solutions = solver.solve(0, T, dt)
for interval, fields in solutions:
continue
# Compute errors
v, u = vu.split(deepcopy=True)[:2]
v_error = errornorm(v_exact, v, "L2", degree_rise=2)
u_error = errornorm(u_exact, u, "L2", degree_rise=2)
return v_error, u_error, mesh.hmin(), dt, T
def main(solver, N: int, dt: float, T: float,
theta: float) -> Tuple[float, float, float, float, float]:
# 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=5)
ps = solver.default_parameters()
ps["Chi"] = 1.0
ps["Cm"] = 1.0
_solver = solver(mesh, time, 1.0, 1.0, stimulus, parameters=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=5)
u_exact = Expression("-cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)/2.0",
t=T - (1 - theta) * dt,
degree=5)
# Define initial condition(s)
vs0 = Function(_solver.V)
vs_, *_ = _solver.solution_fields()
vs_.assign(vs0)
# Solve
for _, (vs_, vur) in _solver.solve(0, T, dt):
continue
# Compute errors
v, u, *_ = vur.split(deepcopy=True)
v_error = errornorm(v_exact, v, "L2", degree_rise=5)
u_error = errornorm(u_exact, u, "L2", degree_rise=5)
return v_error, u_error, mesh.hmin(), dt, T
