def test_GaussLegendre():
bt = GaussLegendre(2)
A = array([[1 / 4, 1 / 4 - sqrt(3) / 6], [1 / 4 + sqrt(3) / 6, 1 / 4]])
b = array([1 / 2, 1 / 2])
# btilde = array([1 / 2 + sqrt(3) / 6, 1 / 2 - sqrt(3) / 6])
c = array([1 / 2 - sqrt(3) / 6, 1 / 2 + sqrt(3) / (6)])
# assert allclose(btilde, bt.btilde)
for (X, Y) in zip([A, b, c], [bt.A, bt.b, bt.c]):
assert allclose(X, Y)
def test_appctx():
msh = UnitIntervalMesh(2)
V = FunctionSpace(msh, "CG", 1)
u = Function(V)
v = TestFunction(V)
F = inner(Dt(u) + u, v) * dx
bt = GaussLegendre(1)
t = Constant(0.0)
dt = Constant(0.1)
stepper = TimeStepper(F, bt, t, dt, u, appctx={"hello": "world"})
assert "hello" in stepper.solver._ctx.appctx
def heat(n, deg, time_stages, stage_type="deriv", splitting=IA):
N = 2**n
msh = UnitIntervalMesh(N)
params = {
"snes_type": "ksponly",
"ksp_type": "preonly",
"mat_type": "aij",
"pc_type": "lu"
}
V = FunctionSpace(msh, "CG", deg)
x, = SpatialCoordinate(msh)
t = Constant(0.0)
dt = Constant(2.0 / N)
uexact = exp(-t) * sin(pi * x)
rhs = expand_derivatives(diff(uexact, t)) - div(grad(uexact))
butcher_tableau = GaussLegendre(time_stages)
u = project(uexact, V)
v = TestFunction(V)
F = (inner(Dt(u), v) * dx + inner(grad(u), grad(v)) * dx -
inner(rhs, v) * dx)
bc = DirichletBC(V, Constant(0), "on_boundary")
stepper = TimeStepper(F,
butcher_tableau,
t,
dt,
u,
bcs=bc,
solver_parameters=params,
stage_type=stage_type,
splitting=splitting)
while (float(t) < 1.0):
if (float(t) + float(dt) > 1.0):
dt.assign(1.0 - float(t))
stepper.advance()
t.assign(float(t) + float(dt))
return errornorm(uexact, u) / norm(uexact)
import pytest
from firedrake import *
from math import isclose
from irksome import LobattoIIIA, GaussLegendre, Dt, TimeStepper
from ufl.algorithms.ad import expand_derivatives
@pytest.mark.parametrize("butcher_tableau", [GaussLegendre(3), LobattoIIIA(2)])
def test_1d_heat_dirichletbc(butcher_tableau):
# Boundary values
u_0 = Constant(2.0)
u_1 = Constant(3.0)
N = 100
x0 = 0.0
x1 = 10.0
msh = IntervalMesh(N, x1)
V = FunctionSpace(msh, "CG", 1)
dt = Constant(10.0 / N)
t = Constant(0.0)
(x,) = SpatialCoordinate(msh)
# Method of manufactured solutions copied from Heat equation demo.
S = Constant(2.0)
C = Constant(1000.0)
B = (x - Constant(x0)) * (x - Constant(x1)) / C
R = (x * x) ** 0.5
# Note end linear contribution
uexact = (
B * atan(t) * (pi / 2.0 - atan(S * (R - t)))
def test_inhomog_bc(deg, N, time_stages):
error = heat_inhomog(N, deg, GaussLegendre(time_stages))
assert abs(error) < 1e-10
def test_wave_eq(deg, N, time_stages, splitting):
energy = wave(N, deg, GaussLegendre(time_stages), splitting)
print(energy)
assert np.allclose(energy[1:], energy[:-1])
def test_subdomainbc(deg, N, time_stages, splitting):
error = heat_subdomainbc(N, deg, GaussLegendre(time_stages), splitting)
assert abs(error) < 1e-10
def test_bc(time_stages, splitting):
assert elastodynamics(4, 1, GaussLegendre(time_stages), splitting)
def test_curl(deg, N, time_stages, splitting):
error = curltest(N, deg, GaussLegendre(time_stages), AI)
assert abs(error) < 1e-10
def test_RTCF(deg, N, time_stages, splitting):
error = RTCFtest(N, deg, GaussLegendre(time_stages), splitting)
assert abs(error) < 1e-10
from firedrake import * # noqa: F403
from irksome import GaussLegendre, getForm, Dt, TimeStepper
import numpy
ButcherTableau = GaussLegendre(1)
# Corners of the box.
x0 = 0.0
x1 = 2.2
y0 = 0.0
y1 = 0.41
#Mesh
stepfile = "circle.step"
# Close to what Turek's time-dependent benchmark has on coarsest mesh
h = 0.1
order = 2
lvl = 3
mh = OpenCascadeMeshHierarchy(stepfile,
element_size=h,
levels=lvl,
order=order,
cache=False,
verbose=True)
#Space
msh = mh[-1]
V = VectorFunctionSpace(msh, "CG", 4)
W = FunctionSpace(msh, "DG", 3)
Z = V * W