How to specify boundary conditions on subdomain-FEniCS?

How to specify boundary conditions on subdomain-FEniCS?

I have read the fenics tutorial and have successfully made mesh subdomains (Sec 4.5 in the tutorial vol 1), but am uncertain as to how to specify the edges of these subdomains for boundary conditions.

How to define Dirichlet boundary conditions with meshfunction?

– FEniCS Q&A How to define Dirichlet Boundary Conditions with MeshFunction? run a 2D cavity case. First I defined the Dirichlet conditions as follow: from dolfin import * mesh = UnitSquare ( 50, 50 ) def BCtop(x, on_boundary): return x [ 0] > DOLFIN_EPS and x [ 0] < 1.

How to specify boundary conditions on a geometry?

This solution will allow you to specify a boundary condition on any whole subdomain within your geometry, and each subdomain can have its own separate boundary condition. I am posting this solution here as the old official Fenics QA forum has now closed, and this solution addresses several unanswered questions on those forums as well.

Can you use FEniCS to mesh imported mesh?

FEniCS can also be used to solve this problem, however unlike with the previous example specifying the mesh and boundary conditions with mshr* could be time consuming. Rather than doing this the geometry will be made and then subsequently meshed using Gmsh [3].

Which is a mesh entity in FEniCS Project?

A mesh entity in FEniCS is either a vertex, an edge, a face, or a cell (triangle or tetrahedron). A MeshFunction over cells is suitable to represent subdomains (materials), while a MeshFunction over facets (edges or faces) is used to represent pieces of external or internal boundaries.

How is the variable coefficient κ defined in FEniCS?

To define the variable coefficient κ, we will use a powerful tool in FEniCS called a MeshFunction. A MeshFunction is a discrete function that can be evaluated at a set of so-called mesh entities. A mesh entity in FEniCS is either a vertex, an edge, a face, or a cell (triangle or tetrahedron).

How to incorporate the Neumann condition in FEniCS?

Let us revisit our previous implementation ft01_poisson.py from the section FEniCS implementation (1) and examine which changes we need to make to incorporate the Neumann condition. It turns out that only two changes are necessary: The function boundary defining the Dirichlet boundary must be modified.

How are subdomains used to solve PDEs in FEniCS?

Solving PDEs in domains made up of different materials is a frequently encountered task. In FEniCS, these kinds of problems are handled by defining subdomains inside the domain. A simple example with two materials (subdomains) in 2D will demonstrate the idea.