DAR Solver using continuous approximation spaces solve \( -\Delta u = f\) on \(\Omega\) and \(u= g\) on \(\Gamma\)
Dim | the geometric dimension of the problem (e.g. Dim=1, 2 or 3) |
Inherits Simget.
Public Types | |
typedef bases< Lagrange< Order, Scalar > > | basis_type |
the basis type of our approximation space | |
typedef Simplex< Dim > | convex_type |
geometry entities type composing the mesh, here Simplex in Dimension Dim of Order 1 | |
typedef space_type::element_type | element_type |
an element type of the approximation function space | |
typedef boost::shared_ptr < export_type > | export_ptrtype |
the exporter factory (shared_ptr<> type) | |
typedef Exporter< mesh_type > | export_type |
the exporter factory type | |
typedef boost::shared_ptr < mesh_type > | mesh_ptrtype |
mesh shared_ptr<> type | |
typedef Mesh< convex_type > | mesh_type |
mesh type | |
typedef boost::shared_ptr < space_type > | space_ptrtype |
the approximation function space type (shared_ptr<> type) | |
typedef FunctionSpace < mesh_type, basis_type > | space_type |
the approximation function space type | |
typedef double | value_type |
numerical type is double | |
Public Member Functions | |
DAR () | |
void | run () |
Static Public Attributes | |
static const uint16_type | Order = 2 |
Polynomial order \(P_2\). | |
void Feel::DAR< Dim >::run | ( | ) |
The function space and some associated elements(functions) are then defined
define \(g\) the expression of the exact solution and \(f\) the expression of the right hand side such that \(g\) is the exact solution
Construction of the right hand side. F is the vector that holds the algebraic representation of the right habd side of the problem
create the matrix that will hold the algebraic representation of the left hand side
assemble $ u v$
weak dirichlet conditions treatment for the boundaries marked 1 and 3
strong(algebraic) dirichlet conditions treatment for the boundaries marked 1 and 3
solve the system
compute the
save the results