Interface for setting (strong) Dirichlet boundary conditions. u = g on G, where u is the solution to be computed, g is a function and G is a sub domain of the mesh. A
DirichletBCis specified by the function g, the function space (trial space) and boundary indicators on (a subset of) the mesh boundary. The boundary indicators may be specified in a number of different ways. The simplest approach is to specify the boundary by a
SubDomainobject, using the inside() function to specify on which facets the boundary conditions should be applied. The boundary facets will then be searched for and marked only on the first call to apply. This means that the mesh could be moved after the first apply and the boundary markers would still remain intact. Alternatively, the boundary may be specified by a
MeshFunctionover facets labeling all mesh facets together with a number that specifies which facets should be included in the boundary. The third option is to attach the boundary information to the mesh. This is handled automatically when exporting a mesh from for example VMTK. The ‘method’ variable may be used to specify the type of method used to identify degrees of freedom on the boundary. Available methods are: topological approach (default), geometric approach, and pointwise approach. The topological approach is faster, but will only identify degrees of freedom that are located on a facet that is entirely on the boundary. In particular, the topological approach will not identify degrees of freedom for discontinuous elements (which are all internal to the cell). A remedy for this is to use the geometric approach. In the geometric approach, each dof on each facet that matches the boundary condition will be checked. To apply pointwise boundary conditions e.g. pointloads, one will have to use the pointwise approach. The three possibilities are “topological”, “geometric” and “pointwise”. Note: when using “pointwise”, the boolean argument
SubDomain::insidewill always be false. The ‘check_midpoint’ variable can be used to decide whether or not the midpoint of each facet should be checked when a user-defined
SubDomainis used to define the domain of the boundary condition. By default, midpoints are always checked. Note that this variable may be of importance close to corners, in which case it is sometimes important to check the midpoint to avoid including facets “on the diagonal close” to a corner. This variable is also of importance for curved boundaries (like on a sphere or cylinder), in which case it is important not to check the midpoint which will be located in the interior of a domain defined relative to a radius. Note that there may be caching employed in BC computation for performance reasons. In particular, applicable DOFs are cached by some methods on a first
apply. This means that changing a supplied object (defining boundary subdomain) after first use may have no effect. But this is implementation and method specific.
Copy constructor. Either cached DOF data are copied.
Parameters: DirichletBC & bc (const) – (
DirichletBC&) The object to be copied. [direction=in]