DUBeat  1.0.1
High-order discontinuous Galerkin methods and applications to cardiac electrophysiology
DUBeat::models::LaplaceDG< basis > Class Template Reference

Class to solve the Laplace equation using the Discontinuous Galerkin method. More...

#include <laplace_dg.hpp>

Inheritance diagram for DUBeat::models::LaplaceDG< basis >:
Collaboration diagram for DUBeat::models::LaplaceDG< basis >:

Public Member Functions

 LaplaceDG ()
 Constructor. More...
 
- Public Member Functions inherited from ModelDG< basis >
 ModelDG (std::string model_name)
 Constructor. More...
 
 ModelDG (ModelDG< basis > &ModelDG)=default
 Default copy constructor. More...
 
 ModelDG (const ModelDG< basis > &ModelDG)=default
 Default const copy constructor. More...
 
 ModelDG (ModelDG< basis > &&ModelDG)=default
 Default move constructor. More...
 
virtual void declare_parameters (lifex::ParamHandler &params) const override
 Declare main parameters. More...
 
virtual void parse_parameters (lifex::ParamHandler &params) override
 Parse parameters from .prm file. More...
 
unsigned int get_dofs_per_cell () const
 Return the number of degrees of freedom per element. More...
 
virtual void run () override
 Run the simulation. More...
 
virtual ~ModelDG ()=default
 Destructor. More...
 

Private Member Functions

void assemble_system () override
 Assembly of the linear system. More...
 

Additional Inherited Members

- Protected Member Functions inherited from ModelDG< basis >
virtual void setup_system ()
 Setup of the problem before the resolution. More...
 
void make_sparsity_pattern (const DoFHandlerDG< basis > &dof, dealii::DynamicSparsityPattern &sparsity, const dealii::AffineConstraints< double > &constraints=dealii::AffineConstraints< double >(), const bool keep_constrained_dofs=true, const dealii::types::subdomain_id subdomain_id=dealii::numbers::invalid_subdomain_id)
 Creation of the sparsity pattern to assign to the system matrix before assembling. More...
 
void initialize_solution (lifex::LinAlg::MPI::Vector &solution_owned, lifex::LinAlg::MPI::Vector &solution)
 To inizialize the solutions using the deal.II reinit. More...
 
void create_mesh ()
 Load the mesh from the default path. More...
 
void create_mesh (std::string mesh_path)
 Load the mesh from a user-defined path. More...
 
void solve_system ()
 System solving. More...
 
void compute_errors (const lifex::LinAlg::MPI::Vector &solution_owned, const lifex::LinAlg::MPI::Vector &solution_ex_owned, const std::shared_ptr< dealii::Function< lifex::dim >> &u_ex, const std::shared_ptr< dealii::Function< lifex::dim >> &grad_u_ex, const char *solution_name=(char *)"u") const
 To compute the \(L^\infty\) error, the \(L^2\) error, the \(H^1\) error and the \(DG\) error at the end of system solving, it exploits the DGComputeErrors<basis> class. More...
 
virtual void output_results (std::string output_name="solution") const
 Output of results. More...
 
virtual void conversion_to_fem (lifex::LinAlg::MPI::Vector &sol_owned)
 To convert a discretized solution from modal to nodal basis (does nothing if problem is already in nodal basis), in-place version. More...
 
virtual lifex::LinAlg::MPI::Vector conversion_to_fem (const lifex::LinAlg::MPI::Vector &sol_owned) const
 To convert a discretized solution from modal to nodal basis (does nothing if problem is already in nodal basis), const version. More...
 
virtual void conversion_to_fem (lifex::LinAlg::MPI::Vector &sol_owned, const std::string fem_file_path, const unsigned int degree_fem=1, const double scaling_factor=1) const
 
virtual void conversion_to_dub (lifex::LinAlg::MPI::Vector &sol_owned)
 To convert a discretized solution in Dubiner basis (only for problems using Dubiner basis). More...
 
virtual lifex::LinAlg::MPI::Vector conversion_to_dub (const lifex::LinAlg::MPI::Vector &sol_owned) const
 To convert a discretized solution in Dubiner basis (only for problems using Dubiner basis). More...
 
virtual void conversion_to_dub (lifex::LinAlg::MPI::Vector &sol_owned, const std::string fem_file_path, const unsigned int degree_fem=1, const double scaling_factor=1) const
 
void discretize_analytical_solution (const std::shared_ptr< dealii::Function< lifex::dim >> &u_analytical, lifex::LinAlg::MPI::Vector &sol_owned)
 Conversion of an analytical solution from FEM to basis coefficients. More...
 
void conversion_to_fem (lifex::LinAlg::MPI::Vector &sol_owned)
 Conversion of a discretized solution from Dubiner coefficients to FEM coefficients. More...
 
lifex::LinAlg::MPI::Vector conversion_to_fem (const lifex::LinAlg::MPI::Vector &sol_owned) const
 Conversion to FEM coefficients, const version. More...
 
void conversion_to_fem (lifex::LinAlg::MPI::Vector &sol_owned, const std::string fem_file_path, const unsigned int degree_fem, const double scaling_factor) const
 
void conversion_to_dub (lifex::LinAlg::MPI::Vector &sol_owned)
 Conversion of a discretized solution from FEM coefficients to Dubiner coefficients. More...
 
lifex::LinAlg::MPI::Vector conversion_to_dub (const lifex::LinAlg::MPI::Vector &sol_owned) const
 Conversion to DUB coefficients, const version. More...
 
void conversion_to_dub (lifex::LinAlg::MPI::Vector &sol_owned, const std::string fem_file_path, const unsigned int degree_fem, const double scaling_factor) const
 
void discretize_analytical_solution (const std::shared_ptr< dealii::Function< lifex::dim >> &u_analytical, lifex::LinAlg::MPI::Vector &sol_owned)
 Conversion of an analytical solution from FEM to basis coefficients. More...
 
void discretize_analytical_solution (const std::shared_ptr< dealii::Function< lifex::dim >> &u_analytical, lifex::LinAlg::MPI::Vector &sol_owned)
 Conversion of an analytical solution from FEM to basis coefficients. More...
 
- Protected Attributes inherited from ModelDG< basis >
const std::string model_name
 Name of the class/problem. More...
 
unsigned int prm_fe_degree
 Polynomials degree. More...
 
unsigned int prm_n_refinements
 Mesh refinement level (>=1). More...
 
double prm_penalty_coeff
 DG Penalty coefficient. More...
 
double prm_stability_coeff
 DG stabilty coefficient. More...
 
double scaling_factor = 1
 Scaling factor. More...
 
std::shared_ptr< lifex::utils::MeshHandler > triangulation
 Triangulation (internal use for useful already implemented methods). More...
 
unsigned int dofs_per_cell
 Number of degrees of freedom per cell. More...
 
DoFHandlerDG< basis > dof_handler
 DoFHandler (internal use for useful already implemented methods). More...
 
std::shared_ptr< DUBFEMHandler< basis > > dub_fem_values
 Member used for conversions between analytical, nodal and modal representations of the solutions. More...
 
std::unique_ptr< AssembleDG< basis > > assemble
 Matrix assembler. More...
 
lifex::utils::LinearSolverHandler< lifex::LinAlg::MPI::Vector > linear_solver
 Linear solver handler. More...
 
lifex::utils::PreconditionerHandler preconditioner
 Preconditioner handler. More...
 
lifex::LinAlg::MPI::SparseMatrix matrix
 Distributed matrix of the linear system. More...
 
lifex::LinAlg::MPI::Vector rhs
 Distributed right hand side vector of the linear system. More...
 
lifex::LinAlg::MPI::Vector solution_owned
 Distributed solution vector, without ghost entries. More...
 
lifex::LinAlg::MPI::Vector solution
 Distributed solution vector, with ghost entries. More...
 
lifex::LinAlg::MPI::Vector solution_ex_owned
 Distributed exact solution vector, without ghost entries. More...
 
lifex::LinAlg::MPI::Vector solution_ex
 Distributed exact solution vector, without ghost entries. More...
 
std::shared_ptr< lifex::utils::FunctionDirichlet > u_ex
 Pointer to exact solution function. More...
 
std::shared_ptr< dealii::Function< lifex::dim > > grad_u_ex
 Pointer to exact gradient solution Function. More...
 
std::shared_ptr< dealii::Function< lifex::dim > > f_ex
 Known forcing term. More...
 
std::shared_ptr< dealii::Function< lifex::dim > > g_n
 Neumann boundary conditions. More...
 

Detailed Description

template<class basis>
class DUBeat::models::LaplaceDG< basis >

Class to solve the Laplace equation using the Discontinuous Galerkin method.

\[ \begin{aligned} -\Delta u &= f & \quad & \text{in } \Omega = (-1, 1)^d, \\ u &= u_\mathrm{ex} & \quad & \text{on } \partial\Omega \end{aligned} \]

In particular, it can be solved using the FEM basis (basis=dealii::FE_SimplexDGP<lifex::dim>) or the Dubiner basis (basis=DUBValues<lifex::dim>).

Boundary conditions and source terms are provided assuming that the exact solution is:

\[ \begin{aligned} &d=2: \, u_\mathrm{ex}(x,y) = e^{x+y}, \hspace{6mm} (x,y) \in \Omega=(1,1)^2, \\ &d=3: \, u_\mathrm{ex}(x,y,z) = e^{x+y+z}, \hspace{6mm} (x,y,z) \in \Omega=(1,1)^3. \end{aligned} \]

Finally, \(d\) is specified in the lifex configuration.

Definition at line 161 of file laplace_dg.hpp.

Constructor & Destructor Documentation

◆ LaplaceDG()

template<class basis >
DUBeat::models::LaplaceDG< basis >::LaplaceDG ( )
inline

Constructor.

Definition at line 111 of file laplace_dg.hpp.

Member Function Documentation

◆ assemble_system()

template<class basis >
void DUBeat::models::LaplaceDG< basis >::assemble_system
overrideprivatevirtual

Assembly of the linear system.

Implements ModelDG< basis >.

Definition at line 181 of file laplace_dg.hpp.


The documentation for this class was generated from the following file: