Laplacian equation with instationnary term solver using continuous approximation spaces solve \( \dfrac{\partial u}{\partial t} - nu*\Delta u = f\) on \(\Omega\) and \(u= g\) on \(\Gamma\)
Dim | the geometric dimension of the problem = 2 |
Inherits Simget.
Public Types | |
typedef bases< Lagrange< Order, Scalar > > | basis_type |
the basis type of our approximation space | |
typedef boost::shared_ptr < bdf_type > | bdf_ptrtype |
typedef Bdf< space_type > | bdf_type |
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 < error_type > | error_ptrtype |
typedef ErrorBase< Dim, Order > | error_type |
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 | |
Laplacian_parabolic () | |
void | run () |
Function to compute the equation and find the unknown. More... | |
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inline |
Constructor
void Laplacian_parabolic< Dim, Order >::run | ( | ) |
Function to compute the equation and find the unknown.
Loading variables from cfg file
Creation of a new mesh depending on the information of the geofile
The function space and some associated elements (functions) are then defined
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Add extra parameters ( t for example )
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Initializing u, g and f from initial temperature expression
BDF implementation
create the matrix that will hold the algebraic representation of the left hand side (only stationnary terms)
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assemble $ u v$
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weak dirichlet conditions treatment for the boundaries marked 1 and 3
assemble $ u^{n+1} v$
add temporal term to the lhs and the rhs
add time depending terms for the left hand side
strong(algebraic) dirichlet conditions treatment for the boundaries marked 1 and 3
solve the system
Computing L2 and H1 error
save the results
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