def test_new_integrateX_via_straight_cutted_quad3D_polynomial(order, domain, quad_dominated, alpha, dim):
ngsglobals.msg_level = 0
if (quad_dominated):
mesh = MakeUniform3DGrid(quads = True, N=1, P1=(0,0,0),P2=(1,1,1))
else:
cube = OrthoBrick( Pnt(0,0,0), Pnt(1,1,1) ).bc(1)
geom = CSGeometry()
geom.Add (cube)
ngmesh = geom.GenerateMesh(maxh=1.3, quad_dominated=quad_dominated)
mesh = Mesh(ngmesh)
levelset = 1 - 2*x- 2*y - 2*z
val_pos = pow(2,-alpha-3)/(pow(alpha,3)+6*alpha*alpha + 11*alpha+6)
referencevals = {POS: val_pos, NEG: 1./(alpha+1) - val_pos}
lset_approx = GridFunction(H1(mesh,order=1))
InterpolateToP1(levelset,lset_approx)
f = dim**alpha
integral = Integrate(levelset_domain = { "levelset" : lset_approx, "domain_type" : domain},
cf=f, mesh=mesh, order = order)
error = abs(integral - referencevals[domain])
assert error < 5e-15*(order+1)*(order+1)
def test_new_integrateX_via_sphere_geom_quad(order, domain):
r=0.7234436998
levelset = sqrt(x*x+y*y+z*z)-r
referencevals = { POS : 1-pi*r*r*r/6, NEG : pi*r*r*r/6, IF : r*r*pi/2}
n_ref = 6
errors = []
for i in range(n_ref):
mesh = MakeUniform3DGrid(quads = True, N=int(pow(2,i)), P1=(0,0,0),P2=(1,1,1))
print("i: " +str(i))
print("Argument Meshing: ",str(int(pow(2,i))))
V = H1(mesh,order=1)
lset_approx = GridFunction(V)
InterpolateToP1(levelset,lset_approx)
f = CoefficientFunction(1)
integral = Integrate(levelset_domain = { "levelset" : lset_approx, "domain_type" : domain},
cf=f, mesh=mesh, order = order)
print("Result of Integration Reflevel ",i,", Key ",domain," : ", integral)
errors.append(abs(integral - referencevals[domain]))
eoc = [log(errors[i+1]/errors[i])/log(0.5) for i in range(n_ref-1)]
print("L2-errors:", errors)
print("experimental order of convergence (L2):", eoc)
mean_eoc_array = eoc[1:]
mean_eoc = sum(mean_eoc_array)/len(mean_eoc_array)
assert mean_eoc > 1.75
def test_new_integrateX_via_straight_cutted_quad3D(order, domain,
quad_dominated):
if (quad_dominated):
mesh = MakeUniform3DGrid(quads=True, N=1, P1=(0, 0, 0), P2=(1, 1, 1))
else:
cube = OrthoBrick(Pnt(0, 0, 0), Pnt(1, 1, 1)).bc(1)
geom = CSGeometry()
geom.Add(cube)
ngmesh = geom.GenerateMesh(maxh=1.3, quad_dominated=quad_dominated)
mesh = Mesh(ngmesh)
levelset = 1 - 2 * x - 2 * y - 2 * z
referencevals = {POS: 1. / 48, NEG: 47. / 48, IF: sqrt(3) / 8}
lset_approx = GridFunction(H1(mesh, order=1))
InterpolateToP1(levelset, lset_approx)
f = CoefficientFunction(1)
integral = Integrate(levelset_domain={
"levelset": lset_approx,
"domain_type": domain
},
cf=f,
mesh=mesh,
order=order)
print("Integral: ", integral)
error = abs(integral - referencevals[domain])
assert error < 5e-15 * (order + 1) * (order + 1)
def test_new_integrateX_via_straight_cutted_quad3D_polynomial_zero_val_challenge(
order=4, domain=POS, alpha=2, dim=x):
ngsglobals.msg_level = 0
mesh = MakeUniform3DGrid(quads=True, N=2, P1=(0, 0, 0), P2=(1, 1, 1))
levelset = 1 - 2 * x - 2 * y - 2 * z
val_pos = pow(
2, -alpha - 3) / (pow(alpha, 3) + 6 * alpha * alpha + 11 * alpha + 6)
referencevals = {POS: val_pos, NEG: 1. / (alpha + 1) - val_pos}
print("Val_pos: ", val_pos)
lset_approx = GridFunction(H1(mesh, order=1))
InterpolateToP1(levelset, lset_approx)
f = dim**alpha
integral = Integrate(levelset_domain={
"levelset": lset_approx,
"domain_type": domain,
"quad_dir_policy": OPTIMAL
},
cf=f,
mesh=mesh,
order=order)
print("Integral:", integral)
error = abs(integral - referencevals[domain])
assert error < 5e-15 * (order + 1) * (order + 1)
def test_new_integrateX_TPMC_case_quad3D2(order, quad_dominated, high_order):
if quad_dominated:
mesh = MakeUniform3DGrid(quads=True, N=10, P1=(0, 0, 0), P2=(1, 1, 1))
else:
geom = CSGeometry()
geom.Add(OrthoBrick(Pnt(0, 0, 0), Pnt(1, 1, 1)).bc(1))
ngmesh = geom.GenerateMesh(maxh=0.2134981)
for i in range(4):
ngmesh.Refine()
mesh = Mesh(ngmesh)
#phi = -4*(1-x)*(1-y)*(1-z) + 4*(1-x)*(1-y)*z -1*(1-x)*y*(1-z) - 1*(1-x)*y*z + 2*x*(1-y)*(1-z) -3 *x*(1-y)*z + 5 * x * y * (1-z) -1 *x *y*z
phi = x * ((7 * y - 13) * z + 6) + y * (3 - 8 * z) + 8 * z - 4
if high_order:
print("Creating LevelSetMeshAdaptation class")
lsetmeshadap = LevelSetMeshAdaptation(mesh,
order=order,
threshold=0.2,
discontinuous_qn=True)
lsetp1 = lsetmeshadap.lset_p1
deformation = lsetmeshadap.CalcDeformation(phi)
mesh.SetDeformation(deformation)
else:
lsetp1 = GridFunction(H1(mesh, order=1))
lsetp1.Set(phi)
f = CoefficientFunction(1)
print("Doing integration")
for domain in [POS, NEG, IF]:
integral = Integrate(levelset_domain={
"levelset": lsetp1,
"domain_type": domain
},
cf=f,
mesh=mesh,
order=order)
print("Integral: ", integral, " ; domain = ", domain)
if domain == IF:
assert abs(integral - 1.82169) < 5e-3
elif domain == NEG:
assert abs(integral - 0.51681) < 1e-3
else:
assert abs(integral - 0.48319) < 1e-3
def test_new_integrateX_via_straight_cutted_quad3D(order, domain, quad_dominated):
mesh = MakeUniform3DGrid(quads = True, N=2, P1=(0,0,0),P2=(1,1,1))
levelset = 1 - 2*x - 2*y - 2*z
referencevals = { POS : 1./48, NEG : 47./48, IF : sqrt(3)/8 }
lset_approx = GridFunction(H1(mesh,order=1))
InterpolateToP1(levelset,lset_approx)
f = CoefficientFunction(1)
integral = Integrate(levelset_domain = { "levelset" : lset_approx, "domain_type" : domain},
cf=f, mesh=mesh, order = order)
print("Integral: ", integral)
error = abs(integral - referencevals[domain])
assert error < 5e-15*(order+1)*(order+1)
def test_new_integrateX_TPMC_case_quad3D(order, domain, quad_dominated):
mesh = MakeUniform3DGrid(quads = True, N=1, P1=(0,0,0),P2=(1,1,1))
lset_approx = GridFunction(H1(mesh,order=1))
for i,v in enumerate([-4,4,-1,-1,2,-3,5,-1]):
lset_approx.vec[i] = v
f = CoefficientFunction(1)
integral = Integrate(levelset_domain = { "levelset" : lset_approx, "domain_type" : domain},
cf=f, mesh=mesh, order = order, heapsize=10000000)
print("Integral: ", integral)
if domain == IF:
assert integral < 10
elif domain == NEG:
assert abs(integral - 0.5167820912197415) < 3.4e-3
else:
assert abs(integral - 0.4825797907263282) < 3.4e-3