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#include <AbstractDiscreteContinuumSolver.hpp>
Public Member Functions | |
AbstractDiscreteContinuumSolver () | |
virtual | ~AbstractDiscreteContinuumSolver () |
void | AddBoundaryCondition (boost::shared_ptr< DiscreteContinuumBoundaryCondition< DIM > > pBoundaryCondition) |
bool | CellPopulationIsSet () |
virtual std::vector< units::quantity< unit::concentration > > | GetConcentrations () |
virtual std::vector< units::quantity< unit::concentration > > | GetConcentrations (boost::shared_ptr< RegularGrid< DIM > > pGrid)=0 |
virtual std::vector< units::quantity< unit::concentration > > | GetConcentrations (const std::vector< DimensionalChastePoint< DIM > > &rSamplePoints)=0 |
virtual std::vector< units::quantity< unit::concentration > > | GetConcentrations (boost::shared_ptr< DiscreteContinuumMesh< DIM > > pMesh)=0 |
const std::string & | GetLabel () |
boost::shared_ptr< AbstractDiscreteContinuumNonLinearEllipticPde< DIM, DIM > > | GetNonLinearPde () |
boost::shared_ptr< AbstractDiscreteContinuumLinearEllipticPde< DIM, DIM > > | GetPde () |
units::quantity< unit::concentration > | GetReferenceConcentration () |
virtual std::vector< double > | GetSolution () |
virtual std::vector< double > | GetSolution (const std::vector< DimensionalChastePoint< DIM > > &rSamplePoints)=0 |
virtual std::vector< double > | GetSolution (boost::shared_ptr< RegularGrid< DIM > > pGrid)=0 |
virtual std::vector< double > | GetSolution (boost::shared_ptr< DiscreteContinuumMesh< DIM > > pMesh)=0 |
bool | HasRegularGrid () |
bool | HasUnstructuredGrid () |
void | SetCellPopulation (AbstractCellPopulation< DIM > &rCellPopulation, units::quantity< unit::length > cellPopulationReferenceLength, units::quantity< unit::concentration > cellPopulationReferenceConcentration) |
void | SetFileHandler (boost::shared_ptr< OutputFileHandler > pOutputFileHandler) |
void | SetFileName (const std::string &rFilename) |
void | SetLabel (const std::string &rLabel) |
void | SetPde (boost::shared_ptr< AbstractDiscreteContinuumLinearEllipticPde< DIM, DIM > > pPde) |
void | SetNonLinearPde (boost::shared_ptr< AbstractDiscreteContinuumNonLinearEllipticPde< DIM, DIM > > pPde) |
virtual void | Setup ()=0 |
void | SetReferenceConcentration (units::quantity< unit::concentration > referenceConcentration) |
void | SetVesselNetwork (boost::shared_ptr< VesselNetwork< DIM > > pNetwork) |
void | SetWriteSolution (bool write=true) |
virtual void | Solve ()=0 |
virtual void | Update ()=0 |
virtual void | UpdateCellData ()=0 |
virtual void | UpdateSolution (const std::vector< double > &rData) |
virtual void | UpdateSolution (const std::vector< units::quantity< unit::concentration > > &rData) |
virtual void | Write ()=0 |
Protected Attributes | |
boost::shared_ptr< VesselNetwork< DIM > > | mpNetwork |
AbstractCellPopulation< DIM > * | mpCellPopulation |
units::quantity< unit::length > | mCellPopulationReferenceLength |
units::quantity< unit::concentration > | mCellPopulationReferenceConcentration |
boost::shared_ptr< OutputFileHandler > | mpOutputFileHandler |
std::string | mFilename |
std::string | mLabel |
bool | IsSetupForSolve |
bool | mWriteSolution |
boost::shared_ptr< AbstractDiscreteContinuumLinearEllipticPde< DIM, DIM > > | mpPde |
boost::shared_ptr< AbstractDiscreteContinuumNonLinearEllipticPde< DIM, DIM > > | mpNonLinearPde |
std::vector< boost::shared_ptr< DiscreteContinuumBoundaryCondition< DIM > > > | mBoundaryConditions |
units::quantity< unit::concentration > | mReferenceConcentration |
std::vector< double > | mSolution |
std::vector< units::quantity< unit::concentration > > | mConcentrations |
bool | mHasRegularGrid |
bool | mHasUnstructuredGrid |
An abstract solver class for continuum-discrete field problems. The class is used by the MicrovesselSolver to provide a concentration or dimensionless field for a single, labelled quantity for cells and/or vessels. It contains methods for sampling on structured and unstructured grids. Derived classes are responsible for updating the values of data fields in cells and vessels on each call and optionally writing the solution to file.
Definition at line 59 of file AbstractDiscreteContinuumSolver.hpp.
AbstractDiscreteContinuumSolver< DIM >::AbstractDiscreteContinuumSolver | ( | ) |
Constructor
Definition at line 40 of file AbstractDiscreteContinuumSolver.cpp.
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Destructor
Definition at line 63 of file AbstractDiscreteContinuumSolver.cpp.
void AbstractDiscreteContinuumSolver< DIM >::AddBoundaryCondition | ( | boost::shared_ptr< DiscreteContinuumBoundaryCondition< DIM > > | pBoundaryCondition | ) |
Add a DiscreteContinuum boundary condition for the domain
pBoundaryCondition | the boundary condition |
Definition at line 69 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mBoundaryConditions.
bool AbstractDiscreteContinuumSolver< DIM >::CellPopulationIsSet | ( | ) |
Has a cell population been set?
Definition at line 75 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mpCellPopulation.
Referenced by FiniteDifferenceSolver< DIM >::Setup(), AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateCellData(), and AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::UpdateCellData().
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Return the value of the field with ordering determined by child classes
Definition at line 81 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mConcentrations.
Referenced by AbstractRegularGridDiscreteContinuumSolver< DIM >::GetConcentrations(), and AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::GetConcentrations().
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Return the value of the field at all points on the supplied grid
pGrid | the sampling grid |
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, and AbstractRegularGridDiscreteContinuumSolver< DIM >.
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Return the value of the field at the requested points
rSamplePoints | a vector of sample points |
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, and AbstractRegularGridDiscreteContinuumSolver< DIM >.
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Return the value of the field on the nodes of the input mesh
pMesh | the mesh from which nodes are sampled |
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, and AbstractRegularGridDiscreteContinuumSolver< DIM >.
const std::string & AbstractDiscreteContinuumSolver< DIM >::GetLabel | ( | ) |
Return the name of the field being solved for
Definition at line 87 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mLabel.
Referenced by AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::UpdateElementSolution(), AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateSolution(), and AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::UpdateSolution().
boost::shared_ptr< AbstractDiscreteContinuumNonLinearEllipticPde< DIM, DIM > > AbstractDiscreteContinuumSolver< DIM >::GetNonLinearPde | ( | ) |
Return the nonlinear PDE
Definition at line 103 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mpNonLinearPde.
Referenced by FiniteDifferenceSolver< DIM >::Solve().
boost::shared_ptr< AbstractDiscreteContinuumLinearEllipticPde< DIM, DIM > > AbstractDiscreteContinuumSolver< DIM >::GetPde | ( | ) |
Return the PDE
Definition at line 93 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mpPde.
units::quantity< unit::concentration > AbstractDiscreteContinuumSolver< DIM >::GetReferenceConcentration | ( | ) |
Return the reference concentration value.
Definition at line 113 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mReferenceConcentration.
Referenced by FiniteDifferenceSolver< DIM >::Solve().
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Return the value of the field with ordering determined by child classes
Definition at line 119 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mSolution.
Referenced by AbstractRegularGridDiscreteContinuumSolver< DIM >::GetSolution(), and AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::GetSolution().
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Return the value of the field at the requested points
rSamplePoints | the points for sampling |
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, and AbstractRegularGridDiscreteContinuumSolver< DIM >.
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Return the value of the field at all points on the supplied grid
pGrid | the grid to be sampled |
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, and AbstractRegularGridDiscreteContinuumSolver< DIM >.
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Return the value of the field at all points on the supplied mesh nodes
pMesh | the mesh for point sampling |
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, and AbstractRegularGridDiscreteContinuumSolver< DIM >.
bool AbstractDiscreteContinuumSolver< DIM >::HasRegularGrid | ( | ) |
Return true if the solver uses a regular grid to store solutions
Definition at line 125 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mHasRegularGrid.
bool AbstractDiscreteContinuumSolver< DIM >::HasUnstructuredGrid | ( | ) |
Return true if the solver uses a unstructured grid to store solutions
Definition at line 131 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mHasUnstructuredGrid.
void AbstractDiscreteContinuumSolver< DIM >::SetCellPopulation | ( | AbstractCellPopulation< DIM > & | rCellPopulation, |
units::quantity< unit::length > | cellPopulationReferenceLength, | ||
units::quantity< unit::concentration > | cellPopulationReferenceConcentration | ||
) |
Set the cell population
rCellPopulation | a reference to the cell population |
cellPopulationReferenceLength | the length scale for the cell population |
cellPopulationReferenceConcentration | the concentration scale for the cell population |
Definition at line 137 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mCellPopulationReferenceConcentration, AbstractDiscreteContinuumSolver< DIM >::mCellPopulationReferenceLength, and AbstractDiscreteContinuumSolver< DIM >::mpCellPopulation.
void AbstractDiscreteContinuumSolver< DIM >::SetFileHandler | ( | boost::shared_ptr< OutputFileHandler > | pOutputFileHandler | ) |
Set the file handler containing the working directory
pOutputFileHandler | the file handler containing the working directory |
Definition at line 147 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mpOutputFileHandler.
void AbstractDiscreteContinuumSolver< DIM >::SetFileName | ( | const std::string & | rFilename | ) |
Set the file name for output
rFilename | the file name |
Definition at line 153 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mFilename.
void AbstractDiscreteContinuumSolver< DIM >::SetLabel | ( | const std::string & | rLabel | ) |
Set the name of the field being solved for
rLabel | a reference to the field name |
Definition at line 159 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mLabel.
void AbstractDiscreteContinuumSolver< DIM >::SetNonLinearPde | ( | boost::shared_ptr< AbstractDiscreteContinuumNonLinearEllipticPde< DIM, DIM > > | pPde | ) |
Set the nonlinear PDE to be solved
pPde | the pde to be solved |
Definition at line 171 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mpNonLinearPde.
void AbstractDiscreteContinuumSolver< DIM >::SetPde | ( | boost::shared_ptr< AbstractDiscreteContinuumLinearEllipticPde< DIM, DIM > > | pPde | ) |
Set the PDE to be solved
pPde | the pde to be solved |
Definition at line 165 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mpPde.
void AbstractDiscreteContinuumSolver< DIM >::SetReferenceConcentration | ( | units::quantity< unit::concentration > | referenceConcentration | ) |
Set the reference concentration
referenceConcentration | the reference concentration |
Definition at line 177 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mReferenceConcentration.
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Operations to be performed prior to the first solve
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, AbstractRegularGridDiscreteContinuumSolver< DIM >, and FiniteDifferenceSolver< DIM >.
void AbstractDiscreteContinuumSolver< DIM >::SetVesselNetwork | ( | boost::shared_ptr< VesselNetwork< DIM > > | pNetwork | ) |
Set the vessel network
pNetwork | the vessel network |
Definition at line 183 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mpNetwork.
void AbstractDiscreteContinuumSolver< DIM >::SetWriteSolution | ( | bool | write = true | ) |
Set whether to write the solution to file on next solve
write | write the solution |
Definition at line 189 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mWriteSolution.
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Do the solve
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, AbstractRegularGridDiscreteContinuumSolver< DIM >, GreensFunctionSolver< DIM >, FiniteDifferenceSolver< DIM >, FiniteElementSolver< DIM >, DistanceMap< DIM >, DensityMap< DIM >, LacunarityCalculator< DIM >, and FunctionMap< DIM >.
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Operations to be performed prior to every solve
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, AbstractRegularGridDiscreteContinuumSolver< DIM >, FiniteElementSolver< DIM >, FiniteDifferenceSolver< DIM >, and LacunarityCalculator< DIM >.
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Set the cell data to the values in the field
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, AbstractRegularGridDiscreteContinuumSolver< DIM >, and LacunarityCalculator< DIM >.
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Update the solution manually
rData | solution data map |
Reimplemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >.
Definition at line 195 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mSolution.
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Update the solution manually
rData | solution data map |
Reimplemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >.
Definition at line 201 of file AbstractDiscreteContinuumSolver.cpp.
References AbstractDiscreteContinuumSolver< DIM >::mConcentrations.
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Write the solution to file
Implemented in AbstractUnstructuredGridDiscreteContinuumSolver< DIM >, and AbstractRegularGridDiscreteContinuumSolver< DIM >.
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Has the Setup function been called.
Definition at line 102 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by FiniteDifferenceSolver< DIM >::Setup(), FiniteElementSolver< DIM >::Solve(), and FiniteDifferenceSolver< DIM >::Solve().
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The DiscreteContinuum boundary conditions, optional
Definition at line 122 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::AddBoundaryCondition(), FiniteDifferenceSolver< DIM >::Setup(), FiniteElementSolver< DIM >::Solve(), and FiniteDifferenceSolver< DIM >::Update().
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The reference concentration scale for the cellpopulation.
Definition at line 82 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::SetCellPopulation(), and AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateCellData().
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The reference length scale for the cellpopulation.
Definition at line 77 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::SetCellPopulation(), FiniteDifferenceSolver< DIM >::Setup(), and AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateCellData().
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A solution field. Ordering is decided in child classes.
Definition at line 139 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::GetConcentrations(), FiniteElementSolver< DIM >::Solve(), FiniteDifferenceSolver< DIM >::Solve(), GreensFunctionSolver< DIM >::Solve(), AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateCellData(), AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateSolution(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::UpdateSolution(), and AbstractDiscreteContinuumSolver< DIM >::UpdateSolution().
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The filename for output
Definition at line 92 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::SetFileName(), AbstractRegularGridDiscreteContinuumSolver< DIM >::Write(), and AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::Write().
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Used to check the type of solver
Definition at line 144 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractRegularGridDiscreteContinuumSolver< DIM >::AbstractRegularGridDiscreteContinuumSolver(), and AbstractDiscreteContinuumSolver< DIM >::HasRegularGrid().
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Used to check the type of solver
Definition at line 149 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::AbstractUnstructuredGridDiscreteContinuumSolver(), and AbstractDiscreteContinuumSolver< DIM >::HasUnstructuredGrid().
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The label for the quantity being solved for
Definition at line 97 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractRegularGridDiscreteContinuumSolver< DIM >::GetConcentrations(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::GetConcentrations(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::GetConcentrationsAtCentroids(), AbstractDiscreteContinuumSolver< DIM >::GetLabel(), AbstractRegularGridDiscreteContinuumSolver< DIM >::GetSolution(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::GetSolution(), AbstractDiscreteContinuumSolver< DIM >::SetLabel(), GreensFunctionSolver< DIM >::Solve(), and AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateCellData().
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The cell population.
Definition at line 72 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::CellPopulationIsSet(), AbstractDiscreteContinuumSolver< DIM >::SetCellPopulation(), FiniteDifferenceSolver< DIM >::Setup(), and AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateCellData().
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The vessel network.
Definition at line 67 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by GreensFunctionSolver< DIM >::GenerateSubSegments(), FiniteDifferenceSolver< DIM >::Setup(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::Setup(), AbstractDiscreteContinuumSolver< DIM >::SetVesselNetwork(), LacunarityCalculator< DIM >::Solve(), DensityMap< DIM >::Solve(), and DistanceMap< DIM >::Solve().
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The non-linear PDE to be solved
Definition at line 117 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by FiniteDifferenceSolver< DIM >::DoLinearSolve(), AbstractDiscreteContinuumSolver< DIM >::GetNonLinearPde(), AbstractDiscreteContinuumSolver< DIM >::SetNonLinearPde(), FiniteDifferenceSolver< DIM >::Setup(), FiniteElementSolver< DIM >::Solve(), FiniteDifferenceSolver< DIM >::Update(), and FiniteElementSolver< DIM >::Update().
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File handler containing the output directory
Definition at line 87 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::SetFileHandler(), LacunarityCalculator< DIM >::Solve(), AbstractRegularGridDiscreteContinuumSolver< DIM >::Write(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::Write(), and GreensFunctionSolver< DIM >::WriteSolution().
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The PDE to be solved
Definition at line 112 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by FiniteDifferenceSolver< DIM >::DoLinearSolve(), AbstractDiscreteContinuumSolver< DIM >::GetPde(), AbstractDiscreteContinuumSolver< DIM >::SetPde(), FiniteDifferenceSolver< DIM >::Setup(), FiniteElementSolver< DIM >::Solve(), FiniteDifferenceSolver< DIM >::Solve(), GreensFunctionSolver< DIM >::Solve(), FiniteDifferenceSolver< DIM >::Update(), and FiniteElementSolver< DIM >::Update().
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This is used internally to scale concentrations before and after linear system solves, reads and writes. Since those functions don't use Boost Units. It should not affect the solution, but can be judiciously chosen to avoid precision problems.
Definition at line 129 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by FiniteDifferenceSolver< DIM >::DoLinearSolve(), AbstractRegularGridDiscreteContinuumSolver< DIM >::GetConcentrations(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::GetConcentrations(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::GetConcentrationsAtCentroids(), AbstractDiscreteContinuumSolver< DIM >::GetReferenceConcentration(), AbstractDiscreteContinuumSolver< DIM >::SetReferenceConcentration(), FiniteDifferenceSolver< DIM >::Setup(), FiniteElementSolver< DIM >::Solve(), FiniteDifferenceSolver< DIM >::Solve(), GreensFunctionSolver< DIM >::Solve(), AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateSolution(), and AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::UpdateSolution().
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A solution field. Ordering is decided in child classes.
Definition at line 134 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by AbstractDiscreteContinuumSolver< DIM >::GetSolution(), AbstractRegularGridDiscreteContinuumSolver< DIM >::Setup(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::Setup(), FiniteElementSolver< DIM >::Solve(), AbstractRegularGridDiscreteContinuumSolver< DIM >::UpdateSolution(), AbstractUnstructuredGridDiscreteContinuumSolver< DIM >::UpdateSolution(), and AbstractDiscreteContinuumSolver< DIM >::UpdateSolution().
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Should the solution be written to file
Definition at line 107 of file AbstractDiscreteContinuumSolver.hpp.
Referenced by FiniteDifferenceSolver< DIM >::DoLinearSolve(), AbstractDiscreteContinuumSolver< DIM >::SetWriteSolution(), DensityMap< DIM >::Solve(), DistanceMap< DIM >::Solve(), FiniteElementSolver< DIM >::Solve(), FiniteDifferenceSolver< DIM >::Solve(), and GreensFunctionSolver< DIM >::Solve().