# High RAM usage

Hello,

I am trying to run what should be a fairly simple simulation. My code is given below:

``````from netgen.csg import *

# Defining solid
sphere=Sphere(Pnt(0,0,0),0.55).bc('FSI')
pX=Plane(Pnt(0.5,0,0),Vec(1,0,0))
nX=Plane(Pnt(-0.5,0,0),Vec(-1,0,0))
pY=Plane(Pnt(0,0.5,0),Vec(0,1,0))
nY=Plane(Pnt(0,-0.5,0),Vec(0,-1,0))
pZ=Plane(Pnt(0,0,0.5),Vec(0,0,1))
nZ=Plane(Pnt(0,0,-0.5),Vec(0,0,-1))
Zielinski=sphere*pX*nX*pY*nY*pZ*nZ

# Making geometry from solid
geo=CSGeometry()
# Marking periodic surfaces
geo.PeriodicSurfaces(pX,nX)
geo.PeriodicSurfaces(pY,nY)
geo.PeriodicSurfaces(pZ,nZ)

# Meshing
from ngsolve.comp import Mesh
netgenMesh=geo.GenerateMesh(maxh=0.05)
mesh = Mesh(netgenMesh)		# Converting netgen mesh to ngsolve mesh
Draw (mesh)

k = 3
velocityFiniteElementSpace = Periodic(VectorH1(mesh, order=k, dirichlet="FSI"))	#discrete velocity space
pressureFiniteElementSpace = Periodic(H1(mesh, order=(k-1), dirichlet="FSI"))	#discrete pressure space
productSpace = FESpace([velocityFiniteElementSpace,pressureFiniteElementSpace])

(trialFunction1,trialFunction2), (testFunction1,testFunction2) = productSpace.TnT()
e = CoefficientFunction( (1,0,0) )	# conservative source flux in COMSOL

LHS = BilinearForm(productSpace)
LHS.Assemble()

RHS = LinearForm(productSpace)
RHS += SymbolicLFI(e*testFunction1)
RHS.Assemble()

gfu = GridFunction(productSpace)

inv = LHS.mat.Inverse(freedofs=productSpace.FreeDofs(), inverse="umfpack")
res = RHS.vec.CreateVector()
res.data = RHS.vec - LHS.mat*gfu.vec
gfu.vec.data += inv * res
Redraw()
velocity = CoefficientFunction(gfu.components[0:2][0])``````

This is a modified version of the Stokes part of the Navier-Stokes tutorial (3.2 Incompressible Navier-Stokes equations — NGS-Py 6.2.2302 documentation). I am not trying to simulate a flow - this is a corollary for an acoustic problem.

The script runs, but if I increase the order (k) beyond 3 or if I decrease the element size any further, my workstation (which has 96GB RAM) runs out of memory and NGSolve closes with the message “Killed”. I am able to run the same simulation with the same geometry on OpenFOAM without it requiring nearly as much RAM. I know that OpenFOAM uses FVM and so this is an apples to oranges comparison, but surely, the simulation shouldn’t be taking so much RAM. Am I doing something wrong?

Hi,
With order 3 you already have ~500k dofs on this mesh and direct solvers will get expensive. With order 4 you get ~1.1 mio dofs and a denser matrix . This is the region where you have to start using iterative methods.
You could save dofs and increase accuracy by curving the mesh though:

``mesh.Curve(5)``

Best
Christopher

Thank you for your quick reply. What does Curve() do? Python help only says that it curves the elements.