The recommended way to define subdomains.įrom _future_ import print_function from fenics import * import time def make_sine_Function ( N, method ): """Fill a Function with sin(x*y*z) values.""" mesh = UnitCubeMesh ( N, N, N ) V = FunctionSpace ( mesh, 'Lagrange', 2 ) if method. In such cases the method demonstrated here is Perhaps generated as part of the mesh generation process, and not as a
Subdomains may be available as a MeshFunction (from a data file), Since we make use of geometric tests to define the two SubDomainsįor \(\Omega_0\) and \(\Omega_1\), the MeshFunction method may seem likeĪn unnecessary complication of the simple method using anĮxpression with an if-test. This version of the evaluation function has anĪddition cell argument which we can use to check on which cell we are Make use of the member function eval_cell in place of the regularĮval function. This is similar to the Expression subclass we defined above, but we k_1 k = K ( materials, k_0, k_1, degree = 0 ) k_1 = k_1 def eval_cell ( self, values, x, cell ): if self. Integers ( 'size_t') for numbering the subdomains:Ĭlass K ( Expression ): def _init_ ( self, materials, k_0, k_1, ** kwargs ): self. We start with creating a CellFunction whose values are non-negative
Numbers, and 'bool' for logical values 2) a Mesh object.Īlternatively, the constructor can take just a filename and initialize 'size_t' for non-negative (unsigned) integers, 'double' for real Is fed with two arguments: 1) the type of value: 'int' for integers, Since we need to define subdomains of \(\Omega\) in the present example, Provided for easy definition of a MeshFunction of a particular Special subclasses VertexFunction, EdgeFunction etc. Integers or booleans) and its dimension (0 = vertex, 1 = edgeĮtc.). AįEniCS MeshFunction is parameterized both over its data type (like A MeshFunction over cellsĬan also be used to represent boundary markers for mesh refinement. Pieces of external or internal boundaries. MeshFunction over facets (edges or faces) is used to represent Is suitable to represent subdomains (materials), while a A mesh entity in FEniCS is either a vertex, an edge, aįace, or a cell (triangle or tetrahedron). A MeshFunction is a discreteįunction that can be evaluated at a set of so-called meshĮntities. To define the variable coefficient \(\kappa\), we will use a powerful tool inįEniCS called a MeshFunction. Make the cells both above and below the internal boundary belong to This is a little counter-intuitive, but is necessary to Vertices on the internal boundary at \(y = 0.5\) will belong to both In addition, we use a tolerance to make sure that Important that the test holds for all vertices in cells aligned with Not the cell belongs to a particular subdomain. Inside function for each vertex in a cell to determine whether or Tol = 1E-14 class Omega_0 ( SubDomain ): def inside ( self, x, on_boundary ): return x = 0.5 - tol
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