def test_polynomial_ET_Segm(domain, alpha):
order = alpha
m = ngm.Mesh()
m.dim = 1
nel = 1
pnums = []
for i in range(0, nel+1):
pnums.append (m.Add (ngm.MeshPoint (ngm.Pnt(i/nel, 0, 0))))
for i in range(0,nel):
m.Add (ngm.Element1D ([pnums[i],pnums[i+1]], index=1))
m.Add (ngm.Element0D (pnums[0], index=1))
m.Add (ngm.Element0D (pnums[nel], index=2))
mesh = Mesh(m)
x_ast = 0.78522
levelset = x_ast-x
referencevals = {POS:pow(x_ast, alpha+1)/(alpha+1), NEG:(1-pow(x_ast, alpha+1))/(alpha+1), IF: pow(x_ast, alpha)}
V = H1(mesh, order=1)
lset_approx = GridFunction(V)
#InterpolateToP1(levelset,lset_approx)
lset_approx.Set(levelset)
f = x**alpha
integral = Integrate(levelset_domain = { "levelset" : lset_approx, "domain_type" : domain},
cf=f, mesh=mesh, order = order)
print("Result of Integration Key ",domain," : ", integral)
error = abs(integral - referencevals[domain])
print("Error: ", error)
assert error < 5e-15*(order+1)*(order+1)
def test_convection1d_dg():
m = meshing.Mesh()
m.dim = 1
nel = 20
pnums = []
for i in range(0, nel + 1):
pnums.append(m.Add(meshing.MeshPoint(Pnt(i / nel, 0, 0))))
for i in range(0, nel):
m.Add(meshing.Element1D([pnums[i], pnums[i + 1]], index=1))
m.Add(meshing.Element0D(pnums[0], index=1))
m.Add(meshing.Element0D(pnums[nel], index=2))
m.AddPointIdentification(pnums[0],
pnums[nel],
identnr=1,
type=meshing.IdentificationType.PERIODIC)
mesh = Mesh(m)
fes = L2(mesh, order=4)
u = fes.TrialFunction()
v = fes.TestFunction()
b = CoefficientFunction(1)
bn = b * specialcf.normal(1)
a = BilinearForm(fes)
a += SymbolicBFI(-u * b * grad(v))
a += SymbolicBFI(bn * IfPos(bn, u, u.Other()) * v, element_boundary=True)
u = GridFunction(fes)
pos = 0.5
u0 = exp(-100 * (x - pos) * (x - pos))
u.Set(u0)
w = u.vec.CreateVector()
t = 0
tau = 1e-4
tend = 1
with TaskManager():
while t < tend - tau / 2:
a.Apply(u.vec, w)
fes.SolveM(rho=CoefficientFunction(1), vec=w)
u.vec.data -= tau * w
t += tau
l2error = sqrt(Integrate((u - u0) * (u - u0), mesh))
print(l2error)
assert l2error < 1e-2
def test_1dlaplace():
m = meshing.Mesh()
m.dim = 1
nel = 20
pnums = []
for i in range(0, nel + 1):
pnums.append(m.Add(meshing.MeshPoint(meshing.Pnt(i / nel, 0, 0))))
for i in range(0, nel):
m.Add(meshing.Element1D([pnums[i], pnums[i + 1]], index=1))
m.Add(meshing.Element0D(pnums[0], index=1))
m.Add(meshing.Element0D(pnums[nel], index=2))
mesh = Mesh(m)
order = 10
fes = H1(mesh, order=order, dirichlet=[1, 2])
u = fes.TrialFunction()
v = fes.TestFunction()
n = specialcf.normal(mesh.dim)
h = specialcf.mesh_size
ugf = GridFunction(fes)
uex = GridFunction(fes)
uex.Set(sin(pi * x))
a = BilinearForm(fes)
a += SymbolicBFI(grad(u) * grad(v))
l = LinearForm(fes)
l += SymbolicLFI(pi * pi * uex * v)
l.Assemble()
a.Assemble()
invmat = a.mat.Inverse(fes.FreeDofs())
ugf.vec.data = invmat * l.vec
error = sqrt(Integrate((ugf - uex) * (ugf - uex), mesh))
assert error <= 1e-14
def MakeMesh1D():
a = 0
b = 1
nel = 10
m = msh.Mesh()
m.dim = 1
pnums = []
for i in range(nel + 1):
pnums.append(m.Add(msh.MeshPoint(msh.Pnt(a + (b - a) * i / nel, 0,
0))))
for i in range(2):
m.Add(msh.Element1D([pnums[i], pnums[i + 1]], index=1))
for i in range(2, 5):
m.Add(msh.Element1D([pnums[i], pnums[i + 1]], index=3))
for i in range(5, 7):
m.Add(msh.Element1D([pnums[i], pnums[i + 1]], index=1))
for i in range(7, nel):
m.Add(msh.Element1D([pnums[i], pnums[i + 1]], index=2))
m.SetMaterial(1, 'base')
m.SetMaterial(2, 'chip')
m.SetMaterial(3, 'top')
# add points
m.Add(msh.Element0D(pnums[0], index=1))
m.Add(msh.Element0D(pnums[2], index=2))
m.Add(msh.Element0D(pnums[5], index=2))
m.Add(msh.Element0D(pnums[7], index=2))
m.Add(msh.Element0D(pnums[nel], index=2))
# set boundary condition names
m.SetBCName(0, 'bottom')
m.SetBCName(1, 'other')
m.Save('temp.vol')
return m
x_min = -50
x_max = 50
length = x_max - x_min
pnums = []
xs = []
for i in range(0, n_elems + 1):
pnt_x = x_min + length * i / n_elems
xs.append(pnt_x)
pnums.append(m.Add(ngm.MeshPoint(ngm.Pnt(pnt_x, 0, 0))))
for i in range(0, n_elems):
m.Add(ngm.Element1D([pnums[i], pnums[i + 1]], index=1))
m.SetMaterial(1, 'material')
m.Add(ngm.Element0D(pnums[0], index=1))
m.Add(ngm.Element0D(pnums[n_elems], index=2))
## NGSolve
mesh = ngs.Mesh(m)
fes = ngs.H1(mesh, order=1, dirichlet=[1, 2], complex=True)
u = fes.TrialFunction()
v = fes.TestFunction()
## Potentials
### Potential barrier
barrier_w = 2
barrier_h = 1
potential = ngs.CoefficientFunction(
ngs.IfPos(x, barrier_h, 0) - ngs.IfPos(x - barrier_w, barrier_h, 0))