def SetUp (maxh = 0.3, order = 0, condense = False, jump = 1, nref = 0):
def make_geo():
geometry = CSGeometry()
box = OrthoBrick(Pnt(-1,-1,-1),Pnt(2,1,2)).bc("outer")
core = OrthoBrick(Pnt(0,-0.05,0),Pnt(0.8,0.05,1))- \
OrthoBrick(Pnt(0.1,-1,0.1),Pnt(0.7,1,0.9))- \
OrthoBrick(Pnt(0.5,-1,0.4),Pnt(1,1,0.6)).mat("core")
coil = (Cylinder(Pnt(0.05,0,0), Pnt(0.05,0,1), 0.3) - \
Cylinder(Pnt(0.05,0,0), Pnt(0.05,0,1), 0.15)) * \
OrthoBrick (Pnt(-1,-1,0.3),Pnt(1,1,0.7)).mat("coil")
geometry.Add ((box-core-coil).mat("air"))
geometry.Add (core)
geometry.Add (coil)
return geometry
geo = make_geo()
comm = mpi_world
if comm.rank==0:
# ngsglobals.msg_level = 0
ngmesh = geo.GenerateMesh(maxh=maxh)
# ngsglobals.msg_level = 1
if comm.size > 1:
ngmesh.Distribute(comm)
else:
from netgen.meshing import Mesh as NGMesh
ngmesh = NGMesh.Receive(comm)
ngmesh.SetGeometry(geo)
for k in range(nref):
ngmesh.Refine()
mesh = Mesh(ngmesh)
ngsglobals.msg_level = 0
mesh.Curve(3)
ngsglobals.msg_level = 1
HC = HCurl(mesh, order=order, dirichlet="outer")
mur = { "core" : jump, "coil" : 1, "air" : 1 }
mu0 = 1.257e-6
nu_coef = [ 1/(mu0*mur[mat]) for mat in mesh.GetMaterials() ]
nu = CoefficientFunction(nu_coef)
alpha = nu
beta = 1e-6 * nu
sigma, tau = HC.TnT()
a = BilinearForm(HC)
a += alpha * curl(sigma) * curl(tau) * dx
a += beta * sigma * tau * dx
f = LinearForm(HC)
f += SymbolicLFI(CoefficientFunction((y,0.05-x,0)) * tau, definedon=mesh.Materials("coil"))
return mesh, HC, a, f, alpha, beta
def make1DMesh(maxh):
netmesh = NetMesh()
netmesh.dim = 1
start = -5
L = 10
N = int(L/maxh)+1
pnums = []
for i in range(0, N + 1):
pnums.append(netmesh.Add(MeshPoint(Pnt(start + L * i / N, 0, 0))))
for i in range(0, N):
netmesh.Add(Element1D([pnums[i], pnums[i + 1]], index=i+1))
netmesh.SetMaterial(i+1, 'top'+str(i+1))
netmesh.Add(Element0D(pnums[0], index=1))
netmesh.Add(Element0D(pnums[N], index=2))
return netmesh
def Make1DMesh(start, end, maxh, periodic=False):
netmesh = NetMesh()
netmesh.dim = 1
L = end-start
N = int(L/maxh)+1
pnums = []
for i in range(0, N + 1):
pnums.append(netmesh.Add(MeshPoint(Pnt(start + L * i / N, 0, 0))))
for i in range(0, N):
netmesh.Add(Element1D([pnums[i], pnums[i + 1]]))
# netmesh.SetMaterial(i+1, 'top'+str(i+1))
# netmesh.Add(Element1D([pnums[i], pnums[i + 1]], index=1))
netmesh.Add(Element0D(pnums[0], index=1))
netmesh.Add(Element0D(pnums[N], index=2))
netmesh.SetMaterial(1, 'top')
if periodic:
netmesh.AddPointIdentification(pnums[0], pnums[-1], 1, 2)
return netmesh
def Mesh1D(elements, interval=(0, 1), periodic=False):
"""
generate an equidistant 1D mesh with N cells
"""
N = elements
left = interval[0]
right = interval[1]
mesh = NGMesh(dim=1)
pids = []
for i in range(N + 1):
pids.append(
mesh.Add(MeshPoint(Pnt(left + i / N * (right - left), 0, 0))))
for i in range(N):
mesh.Add(Element1D([pids[i], pids[i + 1]], index=1))
mesh.Add(Element0D(pids[0], index=1))
mesh.Add(Element0D(pids[N], index=2))
mesh.SetBCName(0, "left")
mesh.SetBCName(1, "right")
if periodic:
mesh.AddPointIdentification(pids[0], pids[N], 1, 2)
ngsmesh = NGSMesh(mesh)
return ngsmesh
# cut off above 1.0
result_gridfunc.Set(IfPos(c0-1.0,1.0,c0))
total_mass = Integrate(result_gridfunc,mesh,VOL)
print()
if usegeo == "circle":
geo = SplineGeometry()
MakeCircle(geo, (0,0), 1)
mesh = Mesh(geo.GenerateMesh(maxh=maxh))
mesh.Curve(order)
elif usegeo == "square":
mesh = Mesh(unit_square.GenerateMesh(maxh=maxh))
elif usegeo == "1d":
netmesh = NetMesh()
netmesh.dim = 1
N = 1000
pnums = []
for i in range(0, N + 1):
pnums.append(netmesh.Add(MeshPoint(Pnt(i * 1 / N, 0, 0))))
for i in range(0, N):
netmesh.Add(Element1D([pnums[i], pnums[i + 1]], index=1))
netmesh.Add(Element0D(pnums[0], index=1))
netmesh.Add(Element0D(pnums[N], index=2))
mesh = Mesh(netmesh)
UV = H1(mesh, order=order, dirichlet=[1,2,3,4])
from netgen.meshing import Mesh as NGMesh
comm = mpi_world
dim, geo = 2, geom2d.SplineGeometry()
geo.AddRectangle((0, 0), (10, 1),
leftdomain=1,
rightdomain=0,
bcs=("left", "outer", "outer", "outer"))
geo.SetMaterial(1, "mat")
if comm.rank == 0:
ngm = geo.GenerateMesh(maxh=0.05)
ngm.Distribute(comm)
else:
ngm = NGMesh.Receive(comm)
ngm.SetGeometry(geo)
mesh = Mesh(ngm)
multidim = dim
V = H1(mesh, order=1, dirichlet="left", dim=multidim)
trials, tests = V.TnT()
u = CoefficientFunction(tuple(trials[k] for k in range(dim)))
gradu = CoefficientFunction(tuple(
grad(trials)[i, j] for i in range(dim) for j in range(dim)),
dims=(dim, dim))
epsu = 0.5 * (gradu + gradu.trans)
ut = CoefficientFunction(tuple(tests[k] for k in range(dim)))
gradut = CoefficientFunction(tuple(
grad(tests)[i, j] for i in range(dim) for j in range(dim)),
dims=(dim, dim))
from netgen.geom2d import unit_square, MakeCircle, SplineGeometry
from netgen.meshing import Element0D, Element1D, Element2D, MeshPoint, FaceDescriptor, Mesh
from netgen.csg import Pnt
quads = True
N = 5
mesh = Mesh()
mesh.SetGeometry(unit_square)
mesh.dim = 2
pnums = []
for i in range(N + 1):
for j in range(N + 1):
pnums.append(mesh.Add(MeshPoint(Pnt(i / N, j / N, 0))))
mesh.SetMaterial(1, "mat")
for j in range(N):
for i in range(N):
if quads:
mesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + (j + 1) * (N + 1)], pnums[i + 1 + j *
(N + 1)]
]))
else:
mesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + j * (N + 1)]
from netgen.geom2d import unit_square
from netgen.geom2d import *
geo = SplineGeometry()
pnts = [ (0,0), (1,0), (1,1), (0,1) ]
pnums = [geo.AppendPoint(*p) for p in pnts]
lbot = geo.Append ( ["line", pnums[0], pnums[1]],bc="bot")
# geo.Append ( ["line", pnums[3], pnums[2]], leftdomain=0, rightdomain=1, bc="top")
geo.Append ( ["line", pnums[3], pnums[2]], leftdomain=0, rightdomain=1, copy=lbot, bc="top")
lright = geo.Append ( ["line", pnums[1], pnums[2]], bc="right")
geo.Append ( ["line", pnums[0], pnums[3]], leftdomain=0, rightdomain=1, copy=lright, bc="left")
ngmesh = geo.GenerateMesh(maxh=0.05)
if comm.size>1:
ngmesh.Distribute(comm)
else:
from netgen.meshing import Mesh as NGMesh
ngmesh = NGMesh.Receive(comm)
mesh = Mesh(ngmesh)
V = L2(mesh, order=4)
u,v = V.TnT()
# b = CoefficientFunction( (0.2 + 0.5 * (y-0.5), 0.5 * (0.5-x)) )
b = CoefficientFunction( (0.3 + (y-0.5), (0.5-x)) )
bn = b*specialcf.normal(2)
a = BilinearForm(V)
a += SymbolicBFI (-u * b*grad(v))
a += SymbolicBFI ( bn*IfPos(bn, u, u.Other()) * (v-v.Other()), VOL, skeleton=True)
a += SymbolicBFI ( bn*IfPos(bn, u, 0) * v, BND, skeleton=True)
def MakeUniform3DGrid(quads = False, N=5, P1=(0,0,0),P2=(1,1,1)):
if not quads:
raise BaseException("Only hex cube so far...")
Lx = P2[0]-P1[0]
Ly = P2[1]-P1[1]
Lz = P2[2]-P1[2]
cube = OrthoBrick( Pnt(P1[0],P1[1],P1[2]), Pnt(P2[0],P2[1],P2[2]) ).bc(1)
geom = CSGeometry()
geom.Add (cube)
netmesh = NetMesh()
netmesh.SetGeometry(geom)
netmesh.dim = 3
pids = []
for i in range(N+1):
for j in range(N+1):
for k in range(N+1):
pids.append (netmesh.Add (MeshPoint(Pnt(P1[0] + Lx * i / N,
P1[1] + Ly * j / N,
P1[2] + Lz * k / N))))
for i in range(N):
for j in range(N):
for k in range(N):
base = i * (N+1)*(N+1) + j*(N+1) + k
baseup = base+(N+1)*(N+1)
pnum = [base,base+1,base+(N+1)+1,base+(N+1),
baseup, baseup+1, baseup+(N+1)+1, baseup+(N+1)]
elpids = [pids[p] for p in pnum]
netmesh.Add (Element3D(1,elpids))
def AddSurfEls (p1, dx, dy, facenr):
for i in range(N):
for j in range(N):
base = p1 + i*dx+j*dy
pnum = [base, base+dx, base+dx+dy, base+dy]
elpids = [pids[p] for p in pnum]
netmesh.Add (Element2D(facenr,elpids))
netmesh.Add (FaceDescriptor(surfnr=1,domin=1,bc=1))
AddSurfEls (0, 1, N+1, facenr=1)
netmesh.Add (FaceDescriptor(surfnr=2,domin=1,bc=1))
AddSurfEls (0, (N+1)*(N+1), 1, facenr=2)
netmesh.Add (FaceDescriptor(surfnr=3,domin=1,bc=1))
AddSurfEls (0, N+1, (N+1)*(N+1), facenr=3)
netmesh.Add (FaceDescriptor(surfnr=4,domin=1,bc=1))
AddSurfEls ((N+1)**3-1, -(N+1), -1, facenr=1)
netmesh.Add (FaceDescriptor(surfnr=5,domin=1,bc=1))
AddSurfEls ((N+1)**3-1, -(N+1)*(N+1), -(N+1), facenr=1)
netmesh.Add (FaceDescriptor(surfnr=6,domin=1,bc=1))
AddSurfEls ((N+1)**3-1, -1, -(N+1)*(N+1), facenr=1)
netmesh.Compress()
mesh = NGSMesh(netmesh)
mesh.ngmesh.Save("tmp.vol.gz")
mesh = NGSMesh("tmp.vol.gz")
return mesh
order = 1
maxh = 0.1
tau = 0.005
tend = -1
usegeo = "1d"
if usegeo == "circle":
geo = SplineGeometry()
geo.AddCircle ( (0.0, 0.0), r=1, bc="cyl")
netgenMesh = geo.GenerateMesh(maxh=maxh)
elif usegeo == "1d":
netgenMesh = Make1DMesh(-1, 1, maxh)
elif usegeo == "test":
netgenMesh = NetMesh()
netgenMesh.dim = 1
start = -1
L = 2
N = 3 # Nof elements ? yep
pnums = []
for i in range(0, N + 1):
pnums.append(netgenMesh.Add(MeshPoint(Pnt(start + L * i / N, 0, 0))))
for i in range(0, N):
netgenMesh.Add(Element1D([pnums[i], pnums[i + 1]]))
# netgenMesh.Add(Element0D(pnums[0], index=1))
# netgenMesh.Add(Element0D(pnums[N], index=2))
mesh = Mesh(netgenMesh)
# EX 4: sub-communicators
from ngsolve import *
ngsglobals.msg_level = 1
comm = mpi_world
if comm.rank in [1,2]:
sub_comm = comm.SubComm([1,2])
if sub_comm.rank == 0:
from netgen.geom2d import unit_square
mesh = unit_square.GenerateMesh(maxh=0.1)
if sub_comm.size > 1:
mesh.Distribute(sub_comm)
else:
from netgen.meshing import Mesh as NGMesh
mesh = NGMesh.Receive(sub_comm)
mesh = Mesh(mesh)
print("rank", comm.rank, ", sub-comm rank", sub_comm.rank, "local NV =", mesh.nv, ", and NE =", mesh.ne)
V = H1(mesh, order=1, dirichlet=".*")
print("rank", comm.rank, ", sub-comm rank", sub_comm.rank, "has", V.ndof, "of", V.ndofglobal, "dofs!")
else:
print("rank", comm.rank, "is bored, give me some work!")
def MakeUniform2DGrid(quads=False, N=5, P1=(0, 0), P2=(1, 1)):
geom = SplineGeometry()
geom.AddRectangle(P1, P2, bc=1)
Lx = P2[0] - P1[0]
Ly = P2[1] - P1[1]
netmesh = NetMesh()
netmesh.SetGeometry(geom)
netmesh.dim = 2
pnums = []
for i in range(N + 1):
for j in range(N + 1):
pnums.append(
netmesh.Add(
MeshPoint(Pnt(P1[0] + Lx * i / N, P1[1] + Ly * j / N, 0))))
netmesh.Add(FaceDescriptor(surfnr=1, domin=1, bc=1))
netmesh.SetMaterial(1, "mat")
for j in range(N):
for i in range(N):
if quads:
netmesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + (j + 1) * (N + 1)], pnums[i + 1 + j *
(N + 1)]
]))
else:
netmesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + j * (N + 1)]
]))
netmesh.Add(
Element2D(1, [
pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + (j + 1) * (N + 1)], pnums[i + 1 + j *
(N + 1)]
]))
for j in range(N):
netmesh.Add(
Element1D([pnums[N + j * (N + 1)], pnums[N + (j + 1) * (N + 1)]],
index=1))
netmesh.Add(
Element1D([pnums[0 + j * (N + 1)], pnums[0 + (j + 1) * (N + 1)]],
index=1))
for i in range(N):
netmesh.Add(Element1D([pnums[i], pnums[i + 1]], index=1))
netmesh.Add(
Element1D([pnums[i + N * (N + 1)], pnums[i + 1 + N * (N + 1)]],
index=1))
netmesh.SetGeometry(geom)
netmesh.Compress()
mesh = NGSMesh(netmesh)
mesh.ngmesh.Save("tmp.vol.gz")
mesh = NGSMesh("tmp.vol.gz")
return mesh
def GenerateCubeMesh(n): # create a n x n x n mesh of cubes
mesh = Mesh()
pids = []
for i in range(n + 1):
for j in range(n + 1):
for k in range(n + 1):
pids.append(mesh.Add(MeshPoint(Pnt(i / n, j / n, k / n))))
for i in range(n):
for j in range(n):
for k in range(n):
base = i * (n + 1) * (n + 1) + j * (n + 1) + k
baseup = base + (n + 1) * (n + 1)
pnum = [
base, base + 1, base + (n + 1) + 1, base + (n + 1), baseup,
baseup + 1, baseup + (n + 1) + 1, baseup + (n + 1)
]
elpids = [pids[p] for p in pnum]
mesh.Add(Element3D(1, elpids))
def AddSurfEls(p1, dx, dy, facenr):
for i in range(n):
for j in range(n):
base = p1 + i * dx + j * dy
pnum = [base, base + dx, base + dx + dy, base + dy]
elpids = [pids[p] for p in pnum]
mesh.Add(Element2D(facenr, elpids))
# Face X = 0
mesh.Add(FaceDescriptor(surfnr=1, domin=1, bc=1))
AddSurfEls(0, 1, n + 1, facenr=1)
# Face Y = 0
mesh.Add(FaceDescriptor(surfnr=2, domin=1, bc=2))
AddSurfEls(0, (n + 1) * (n + 1), 1, facenr=2)
# Face Z = 0
mesh.Add(FaceDescriptor(surfnr=3, domin=1, bc=3))
AddSurfEls(0, n + 1, (n + 1) * (n + 1), facenr=3)
# Face X = 1
mesh.Add(FaceDescriptor(surfnr=4, domin=1, bc=4))
AddSurfEls((n + 1)**3 - 1, -(n + 1), -1, facenr=4)
# Face Z = 1
mesh.Add(FaceDescriptor(surfnr=5, domin=1, bc=5))
AddSurfEls((n + 1)**3 - 1, -(n + 1) * (n + 1), -(n + 1), facenr=5)
# Face Y = 1
mesh.Add(FaceDescriptor(surfnr=6, domin=1, bc=6))
AddSurfEls((n + 1)**3 - 1, -1, -(n + 1) * (n + 1), facenr=6)
# Set names for the above boundary parts (0-based indexing!)
mesh.SetBCName(0, 'X0')
mesh.SetBCName(1, 'Y0')
mesh.SetBCName(2, 'Z0')
mesh.SetBCName(3, 'X1')
mesh.SetBCName(4, 'Z1')
mesh.SetBCName(5, 'Y1')
return mesh