DirichletBC.h

Note

The documentation on this page was automatically extracted from the DOLFIN C++ code and may need to be edited or expanded.

class DirichletBC

Parent class(es)

This class specifies the interface for setting (strong) Dirichlet boundary conditions for partial differential equations,

\[u = g \hbox{ on } G,\]

where \(u\) is the solution to be computed, \(g\) is a function and \(G\) is a sub domain of the mesh.

A DirichletBC is 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 SubDomain object, using the inside() function to specify on which facets the boundary conditions should be applied.

Alternatively, the boundary may be specified by a MeshFunction 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 which in turn is the slowest of the three possible methods. The three possibilties are “topological”, “geometric” and “pointwise”.

The ‘check_midpoint’ variable can be used to decide whether or not the midpoint of each facet should be checked when a user-defined SubDomain is 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.

DirichletBC(const FunctionSpace &V, const GenericFunction &g, const SubDomain &sub_domain, std::string method = "topological", bool check_midpoint = true)

Create boundary condition for subdomain

Arguments
V (FunctionSpace)
The function space.
g (GenericFunction)
The value.
sub_domain (SubDomain)
The subdomain.
method (std::string)
Optional argument: A string specifying the method to identify dofs.
DirichletBC(boost::shared_ptr<const FunctionSpace> V, boost::shared_ptr<const GenericFunction> g, boost::shared_ptr<const SubDomain> sub_domain, std::string method = "topological", bool check_midpoint = true)

Create boundary condition for subdomain

Arguments
V (FunctionSpace)
The function space
g (GenericFunction)
The value
sub_domain (SubDomain)
The subdomain
method (std::string)
Optional argument: A string specifying the method to identify dofs
DirichletBC(const FunctionSpace &V, const GenericFunction &g, const MeshFunction<std::size_t> &sub_domains, std::size_t sub_domain, std::string method = "topological")

Create boundary condition for subdomain specified by index

Arguments
V (FunctionSpace)
The function space.
g (GenericFunction)
The value.
sub_domains (MeshFunction <std::size_t>)
Subdomain markers
sub_domain (std::size_t)
The subdomain index (number)
method (std::string)
Optional argument: A string specifying the method to identify dofs.
DirichletBC(boost::shared_ptr<const FunctionSpace> V, boost::shared_ptr<const GenericFunction> g, boost::shared_ptr<const MeshFunction<std::size_t>> sub_domains, std::size_t sub_domain, std::string method = "topological")

Create boundary condition for subdomain specified by index

Arguments
V (FunctionSpace)
The function space.
g (GenericFunction)
The value.
sub_domains (MeshFunction <std::size_t>)
Subdomain markers
sub_domain (std::size_t)
The subdomain index (number)
method (std::string)
Optional argument: A string specifying the method to identify dofs.
DirichletBC(const FunctionSpace &V, const GenericFunction &g, std::size_t sub_domain, std::string method = "topological")

Create boundary condition for boundary data included in the mesh

Arguments
V (FunctionSpace)
The function space.
g (GenericFunction)
The value.
sub_domain (std::size_t)
The subdomain index (number)
method (std::string)
Optional argument: A string specifying the method to identify dofs.
DirichletBC(boost::shared_ptr<const FunctionSpace> V, boost::shared_ptr<const GenericFunction> g, std::size_t sub_domain, std::string method = "topological")

Create boundary condition for boundary data included in the mesh

Arguments
V (FunctionSpace)
The function space.
g (GenericFunction)
The value.
sub_domain (std::size_t)
The subdomain index (number)
method (std::string)
Optional argument: A string specifying the method to identify dofs.
DirichletBC(boost::shared_ptr<const FunctionSpace> V, boost::shared_ptr<const GenericFunction> g, const std::vector<std::size_t> &markers, std::string method = "topological")

Create boundary condition for subdomain by boundary markers (cells, local facet numbers)

Arguments
V (FunctionSpace)
The function space.
g (GenericFunction)
The value.
markers (std::vector<std::pair<std::size_t, std::size_t> >)
Subdomain markers (cells, local facet number)
method (std::string)
Optional argument: A string specifying the method to identify dofs.
DirichletBC(const DirichletBC &bc)

Copy constructor

Arguments
bc (DirichletBC)
The object to be copied.
const DirichletBC &operator=(const DirichletBC &bc)

Assignment operator

Arguments
bc (DirichletBC)
Another DirichletBC object.
void apply(GenericMatrix &A) const

Apply boundary condition to a matrix

Arguments
A (GenericMatrix)
The matrix to apply boundary condition to.
void apply(GenericVector &b) const

Apply boundary condition to a vector

Arguments
b (GenericVector)
The vector to apply boundary condition to.
void apply(GenericMatrix &A, GenericVector &b) const

Apply boundary condition to a linear system

Arguments
A (GenericMatrix)
The matrix to apply boundary condition to.
b (GenericVector)
The vector to apply boundary condition to.
void apply(GenericVector &b, const GenericVector &x) const

Apply boundary condition to vectors for a nonlinear problem

Arguments
b (GenericVector)
The vector to apply boundary conditions to.
x (GenericVector)
Another vector (nonlinear problem).
void apply(GenericMatrix &A, GenericVector &b, const GenericVector &x) const

Apply boundary condition to a linear system for a nonlinear problem

Arguments
A (GenericMatrix)
The matrix to apply boundary conditions to.
b (GenericVector)
The vector to apply boundary conditions to.
x (GenericVector)
Another vector (nonlinear problem).
void get_boundary_values(Map &boundary_values, std::string method = "default") const

Get Dirichlet dofs and values. If a method other than ‘pointwise’ is used in parallel, the map may not be complete for local vertices since a vertex can have a bc applied, but the partition might not have a facet on the boundary. To ensure all local boundary dofs are marked, it is necessary to call gather() on the returned boundary values.

Arguments
boundary_values (boost::unordered_map<std::size_t, double>)
Map from dof to boundary value.
method (std::string)
Optional argument: A string specifying which method to use.
void gather(Map &boundary_values) const

Get boundary values from neighbour processes. If a method other than “pointwise” is used, this is necessary to ensure all boundary dofs are marked on all processes.

Arguments
boundary_values (boost::unordered_map<std::size_t, double>)
Map from dof to boundary value.
void zero(GenericMatrix &A) const

Make rows of matrix associated with boundary condition zero, useful for non-diagonal matrices in a block matrix.

Arguments
A (GenericMatrix)
The matrix
void zero_columns(GenericMatrix &A, GenericVector &b, double diag_val = 0) const

Make columns of matrix associated with boundary condition zero, and update a (right-hand side) vector to reflect the changes. Useful for non-diagonals.

Arguments
A (GenericMatrix)
The matrix
b (GenericVector)
The vector
diag_val (double)
This parameter would normally be -1, 0 or 1.
const std::vector<std::size_t> &markers() const

Return boundary markers

Returns
std::vector<std::pair<std::size_t, std::size_t> >
Boundary markers (facets stored as pairs of cells and local facet numbers).
boost::shared_ptr<const FunctionSpace> function_space() const

Return function space V

Returns
_FunctionSPace_
The function space to which boundary conditions are applied.
boost::shared_ptr<const GenericFunction> value() const

Return boundary value g

Returns
GenericFunction
The boundary values.
boost::shared_ptr<const SubDomain> user_sub_domain() const

Return shared pointer to subdomain

Returns
SubDomain
Shared pointer to subdomain.
bool is_compatible(GenericFunction &v) const

Check if given function is compatible with boundary condition (checking only vertex values)

Arguments
v (GenericFunction)
The function to check for compability with boundary condition.
Returns
bool
True if compatible.
void set_value(const GenericFunction &g)

Set value g for boundary condition, domain remains unchanged

Arguments
g (GenericFunction)
The value.
void set_value(boost::shared_ptr<const GenericFunction> g)

Set value g for boundary condition, domain remains unchanged

Arguments
g (GenericFunction)
The value.
void homogenize()

Set value to 0.0

std::string method() const

Return method used for computing Dirichet dofs

Returns
std::string
Method used for computing Dirichet dofs (“topological”, “geometric” or “pointwise”).
static Parameters default_parameters()

Default parameter values

class LocalData