Questions tagged [fenics]

Questions about the finite element method software FEniCS and its subpackages (Dolfin, UFL, FFC).

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4
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0answers
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Poisson equation with pure Neumann boundary conditions (using FEM)

I am trying to derive the correct variational form for the Poisson equation with pure Neumann boundary conditions, and an additional contraint $\int_{\Omega} u \, {\rm d} x = 0$, as described in this ...
1
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0answers
199 views

4th order tensor [closed]

I'm new with FEniCS and Python and I'm stuck with this issue: is there a way to write a 4th order tensor in an easy way to implement? I have to compute the following stiffnes tensor: $A_{ijkl}= \...
4
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1answer
2k views

Fenics, initialize vector of degrees of freedom for function

With the move away from launchpad I hope this is the right place for this question. Is there a way to initialize the DOFs for a function? generated by u = Function(V) When I run a code which I ...
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0answers
582 views

FEniCs: help in implementing the boundary condition for 1D problem [closed]

I have just started learning FEniCS and have used: http://www.scientificpython.net/pyblog/fenics-linear-two-point-bvp to write a script for solving: ...
11
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3answers
3k views

Poisson equation: Impose full gradient as boundary condition via Lagrange multipliers

I have a physical problem governed by the Poisson equation in two dimensions $$ -\nabla^2 u = f(x,y), \; in \; \Omega $$ I have measurements of the two gradient components $\partial{u}/\partial{x}$ ...
3
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1answer
448 views

Recommendations on FEM software for implementing Nitsche's method on interfaces between matching meshes?

Suppose: I have two domains, $\Omega_{1} = [0, 1/2] \times [0, 1]$ and $\Omega_{2} = [1/2, 1] \times [0, 1]$. The domains share an interface $\Gamma = \{1/2\} \times [0, 1] = \partial\Omega_{1} \cap \...
3
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1answer
1k views

weak formulation of coupled pdes for fenics

I am trying to implement the following system of time-dependent, coupled nonlinear pdes in FEniCS: $$\partial_{t}\rho+2\left(\nabla\rho\nabla\phi+\rho\nabla^{2}\phi\right)+2\sigma\rho\left(\rho-1\...
10
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2answers
3k views

Discontinuous Galerkin / Poisson / Fenics

I am trying to solve the 2D Poisson equation using the Discontinuous Galerkin method (DG) and the following discretization (I have a png file but I am not allowed to upload it, sorry): Equation : $$\...
1
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1answer
523 views

Tensor notation in fenics [closed]

Within Fenics what ordering is used for storing vectors as upper triangular matrices? Th:e question really is I define a green Lagrange strain tensor in the following way: ...
3
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2answers
601 views

Integrating an Ordinary Differential Equation over a domain in Finite Element Methods

I'm trying to get a deeper understanding of the Finite Element Method (FEM) to better understand what I do in COMSOL and FEniCS. The sketch below shows the problem that I want to solve in FEM. The ...
2
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1answer
461 views

PETSc Krylov Subspace and nullspace

How is the nullspace correction implemented in the PETSc conjugate gradient solver? I searched the source code and documentation, but could not find references on the actual implementation. For ...
2
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1answer
2k views

time-dependent nonlinear pde in fenics

I am interesting in solving the following nonlinear, time-dependent pde in 2 spatial dimensions (complex Gross-Pitaevskii eq): $$i \frac{\partial \psi}{\partial t} = \left[ -\nabla^2 + (1-i \sigma)(|\...
0
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1answer
1k views

defining subdomains in FEniCS (Python) using obtained (solved) variable [closed]

I'd very much appreciate if you could help me out with this as I think I'm missing something simple out or should be using alternate syntax: I am running the following Python code in FEniCS, where I ...
3
votes
2answers
1k views

Subdomain Integrals in Fenics

I'd like to compute $u(y) = \int f(x,y) dx$, but don't see a really efficient way to do this in FEniCS. My first thought was to just assemble(f*v*dx) for two different meshes. (try1, below), but it ...
15
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2answers
2k views

FeniCS: Visualizing high order elements

I've just started messing around with FEniCS. I am solving Poisson with 3rd order elements and would like to visualize the results. However, when I use plot(u), the visualization is just a linear ...
4
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1answer
138 views

Assembling FE tensors using different quadrature degrees

Assume we have few terms contributing to element tensor and each requires different quadrature degree to be integrated exactly. Does it generally worth using different quadrature degrees for each term ...
4
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2answers
2k views

FEniCS: importing mesh along with material and boundary data

Which is the preferred way to import into a FEniCS (python) program a mesh which was generated in an external generator which provides sub-domain and boundary markers? I was using MeshData->...
6
votes
1answer
2k views

FEniCS CFD work-flow for complex geometries

I have COMSOL and the CFD package therein available, which provides me with an all-in-one solution for solving CFD problems. I have modeled and solved the geometry shown in the pictures below, which ...
3
votes
2answers
884 views

Flux across a non-boundary line segment in FEniCS

I am solving an elliptic boundary value problem on a subset of the rectangle [-1,1]x[-1,1]. The domain contains the line segment x=0, however this does not need to be a part of the boundary, so it is ...
2
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1answer
373 views

Mixed FEM vector indices of pressure and velocity in FEniCS

Looking at the stokes-iterative demo of FEniCS, after solving the linear system using U = Function(W) solver.solve(U.vector(), bb) the solution ...
0
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2answers
155 views

Speed up DG FunctionSpace evalutation [closed]

today I tried some evaluation on a DG function space (Fenics 1.2.0). In my calculations I need to use meshes with a large number of cells (~10mio). At the moment it takes a very long time to create a ...
1
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2answers
912 views

How can I build a mesh with holes for use in FEniCS?

This is my first time using FEniCS. I am trying to solve an elliptic PDE, fairly similar to the Laplace equation, on a rectangle with two holes in it. The holes are level sets of an energy function, ...
2
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4answers
2k views

Simple FEniCS problem shape mismatch

EDIT: THE ORIGINAL POST DID NOT MAKE MUCH SENSE, SO I ADJUSTED IT Ok, so I have thought about it, googled it and put some more thought into it. This presentation by the Imperial College in London has ...
2
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4answers
396 views
7
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2answers
2k views

FEniCS: boundary conditions for electrostatic problems with dielectrics

I carefully read all circa 70 pages of FEniCS tutorial and I still do not understand how to solve electrostatic problems when I have materials with different dielectric constant. The self contained ...
6
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1answer
4k views

FEniCS: how to specify boundary conditions on a circle inside 2D mesh

I would like to numerically find a mutual capacitance of two stripes of metal on the opposites sides of a cylinder. The problem is obviously a 2D Laplace equation. I would like to find the potential ...
4
votes
1answer
4k views

Fenics: Meshfunction usage

I am confused most of the time with the application of boundary conditions in Fenics. Suppose I have an xml mesh for a rectangular beam and want to apply Dirichlet BC ($u =0$) on the left side of the ...
8
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0answers
412 views

Simple turbulence model appropriate for buoyancy-driven cavity like problem

Which turbulence model is suitable for resolving incompressible buoyancy-driven flow of a fluid within an cylindrical ampoule? I prefer turbulence model which is sufficiently simple so that fully ...
3
votes
1answer
464 views

Fenics: time-independent Sine-Gordon equation

Is there a code for the equation $$ \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2} = \sin(u) $$ or for the sine gordon equation in two dimensions because I want to change some ...
5
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1answer
841 views

Compute lengths of the longest edge of each cell

Having mesh = UnitSquareMesh(2, 2) Q = FunctionSpace(mesh, 'DG', 0) this works as expected ...
-3
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1answer
630 views

Fenics : boundary condition

`I am working on a problem found here " http://www.caesarsystems.co.uk/NAFEMS_benchmarks/le10.html" ..I am really confused about the boundary conditions and tried my level best to compute it but ...
2
votes
0answers
688 views

How to apply periodic boundary conditions to a Raviart-Thomas finite element space in Fenics? [closed]

I'm trying to use periodic boundary conditions within a Raviart-Thomas finite element space in Fenics (dolfin 1.2.0) in a Ubuntu 12.04 (amd64) machine (with python 2.7). If other FE space is used, ...
2
votes
1answer
830 views

Fenics : Elementwise stress computation

In a elastodynamics problem, I define the stress as def sigma(v): return 2.0*mu*sym(grad(v)) + lmbda*tr(sym(grad(v)))*Identity(v.cell().d) I have computed ...
0
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1answer
405 views

Fenics : looking forward to compute displacements at nodes

I just went through the Fenics book to get the nodal displacements and tried this code .... ...
1
vote
1answer
297 views

Fenics: problem with the mesh generation

while executing my script i get this error Traceback (most recent call last): File "/media/oss/Fenics/demo/box_3delasticity.py", line 33, in mesh = Box (0, 0, 0, 1, 1, 1, 1, 1, 1) File "/usr/...
4
votes
2answers
965 views

FEniCS: custom quadrature rule

For the numerical integration of reaction terms in my PDE on a 2D triangular mesh, I would like to use the scheme $$ \int_T \Phi(x) \approx \frac{|T|}{3} (\Phi(x_0) + \Phi(x_1) + \Phi(x_2)) $$ where ...
4
votes
2answers
455 views

Poiseuille flow

I have probably a very stupid problem. I can't solve a simple Poiseuille flow in a straight 2-D channel driven by a pressure drop. Results are complete nonsense. (Setting zero pressure on the outflow ...
4
votes
2answers
1k views

CFD: multiphase flow modeling of a laminar flow reactor

I am planning to model the laminar flow reactor shown in the picture below using computational fluid dynamics (CFD). The laminar flow reactor is used to study a multiphase flow: a layer of sheath air ...
4
votes
4answers
1k views

FEniCS : How to interpolate data at vertices of (3D) cells?

I am trying to get an interpolation function $f$ (in 3D) at all vertices of cells. I extract all vertices of cells and then I assign the value to each vertex: if it's in a sphere of radius $R$, then I ...
4
votes
1answer
144 views

compute max(||u||) for vector field

Given a vector-valued Dolfin function u from the function space V*V with ...
3
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1answer
266 views

Fast function evaluation on a grid

I am trying to calculate a 3D Function f on a large set of points, say a uniform cubic grid. Besides, the cubic grid points do not coincide with the mesh vertices where the Function f is defined. For ...
2
votes
2answers
476 views

FEniCS: check if function is globally greater than 0

Given a Dolfin Function u on a mesh, I'd like to check if it is greater than 0 throughout the mesh. I noticed that the ...
3
votes
2answers
927 views

FEniCS: extracting points from a cell

I'd like to loop over all edges of a simplex (in a mesh). To this end: How can I extract the the points from a cell? This is for the eval method of a C++ ...

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