A global linear system. More...
#include <GlobalLinSysDirect.h>
Public Member Functions | |
| GlobalLinSysDirect (const GlobalLinSysKey &pKey, const std::weak_ptr< ExpList > &pExp, const std::shared_ptr< AssemblyMap > &pLocToGloMap) | |
| Constructor for full direct matrix solve. More... | |
| ~GlobalLinSysDirect () override | |
 Public Member Functions inherited from Nektar::MultiRegions::GlobalLinSys | |
| GlobalLinSys (const GlobalLinSysKey &pKey, const std::weak_ptr< ExpList > &pExpList, const std::shared_ptr< AssemblyMap > &pLocToGloMap) | |
| Constructor for full direct matrix solve. More... | |
| virtual | ~GlobalLinSys () |
| const GlobalLinSysKey & | GetKey (void) const |
| Returns the key associated with the system. More... | |
| const std::weak_ptr< ExpList > & | GetLocMat (void) const |
| void | InitObject () |
| void | Initialise (const std::shared_ptr< AssemblyMap > &pLocToGloMap) |
| void | Solve (const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const AssemblyMapSharedPtr &locToGloMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray) |
| Solve the linear system for given input and output vectors using a specified local to global map. More... | |
| std::shared_ptr< GlobalLinSys > | GetSharedThisPtr () |
| Returns a shared pointer to the current object. More... | |
| int | GetNumBlocks () |
| DNekScalMatSharedPtr | GetBlock (unsigned int n) |
| void | DropBlock (unsigned int n) |
| DNekScalBlkMatSharedPtr | GetStaticCondBlock (unsigned int n) |
| void | DropStaticCondBlock (unsigned int n) |
| void | SolveLinearSystem (const int pNumRows, const Array< OneD, const NekDouble > &pInput, Array< OneD, NekDouble > &pOutput, const AssemblyMapSharedPtr &locToGloMap, const int pNumDir=0) |
| Solve the linear system for given input and output vectors. More... | |
Protected Attributes | |
| DNekLinSysSharedPtr | m_linSys |
| Basic linear system object. More... | |
| Protected Attributes inherited from Nektar::MultiRegions::GlobalLinSys | |
| const GlobalLinSysKey | m_linSysKey |
| Key associated with this linear system. More... | |
| const std::weak_ptr< ExpList > | m_expList |
| Local Matrix System. More... | |
| const std::map< int, RobinBCInfoSharedPtr > | m_robinBCInfo |
| Robin boundary info. More... | |
| bool | m_verbose |
Additional Inherited Members | |
| Protected Member Functions inherited from Nektar::MultiRegions::GlobalLinSys | |
| virtual void | v_Solve (const Array< OneD, const NekDouble > &in, Array< OneD, NekDouble > &out, const AssemblyMapSharedPtr &locToGloMap, const Array< OneD, const NekDouble > &dirForcing=NullNekDouble1DArray)=0 |
| Solve a linear system based on mapping. More... | |
| virtual void | v_SolveLinearSystem (const int pNumRows, const Array< OneD, const NekDouble > &pInput, Array< OneD, NekDouble > &pOutput, const AssemblyMapSharedPtr &locToGloMap, const int pNumDir)=0 |
| Solve a basic matrix system. More... | |
| virtual void | v_InitObject () |
| virtual void | v_Initialise (const std::shared_ptr< AssemblyMap > &pLocToGloMap) |
| virtual int | v_GetNumBlocks () |
| Get the number of blocks in this system. More... | |
| virtual DNekScalMatSharedPtr | v_GetBlock (unsigned int n) |
| Retrieves the block matrix from n-th expansion using the matrix key provided by the m_linSysKey. More... | |
| virtual void | v_DropBlock (unsigned int n) |
| Releases the local block matrix from NekManager of n-th expansion using the matrix key provided by the m_linSysKey. More... | |
| virtual DNekScalBlkMatSharedPtr | v_GetStaticCondBlock (unsigned int n) |
| Retrieves a the static condensation block matrices from n-th expansion using the matrix key provided by the m_linSysKey. More... | |
| virtual void | v_DropStaticCondBlock (unsigned int n) |
| Releases the static condensation block matrices from NekManager of n-th expansion using the matrix key provided by the m_linSysKey. More... | |
| PreconditionerSharedPtr | CreatePrecon (AssemblyMapSharedPtr asmMap) |
| Create a preconditioner object from the parameters defined in the supplied assembly map. More... | |
Detailed Description
A global linear system.
Solves a linear system using direct methods.
Consider a linear system \(\boldsymbol{M\hat{u}}_g=\boldsymbol{\hat{f}}\) to be solved, where \(\boldsymbol{M}\) is a matrix of type specified by mkey. This function assembles the global system matrix \(\boldsymbol{M}\) out of the elemental submatrices \(\boldsymbol{M}^e\). This is equivalent to:
\[ \boldsymbol{M}=\boldsymbol{\mathcal{A}}^T \underline{\boldsymbol{M}}^e\boldsymbol{\mathcal{A}}.\]
where the matrix \(\boldsymbol{\mathcal{A}}\) is a sparse permutation matrix of size \(N_{\mathrm{eof}}\times N_{\mathrm{dof}}\). However, due to the size and sparsity of the matrix \(\boldsymbol{\mathcal{A}}\), it is more efficient to assemble the global matrix using the mapping array map \([e][i]\) contained in the input argument locToGloMap. The global assembly is then evaluated as:
\[ \boldsymbol{M}\left[\mathrm{\texttt{map}}[e][i]\right] \left[\mathrm{\texttt{map}}[e][j]\right] =\mathrm{\texttt{sign}}[e][i]\cdot \mathrm{\texttt{sign}}[e][j] \cdot\boldsymbol{M}^e[i][j]\]
where the values sign \([e][i]\) ensure the correct connectivity.
Solves a linear system using single- or multi-level static condensation.
Definition at line 46 of file GlobalLinSysDirect.h.
Constructor & Destructor Documentation
◆ GlobalLinSysDirect()
| Nektar::MultiRegions::GlobalLinSysDirect::GlobalLinSysDirect | ( | const GlobalLinSysKey & | pKey, |
| const std::weak_ptr< ExpList > & | pExp, | ||
| const std::shared_ptr< AssemblyMap > & | pLocToGloMap | ||
| ) |
Constructor for full direct matrix solve.
Definition at line 46 of file GlobalLinSysDirect.cpp.
◆ ~GlobalLinSysDirect()
|
override |
Definition at line 53 of file GlobalLinSysDirect.cpp.
Member Data Documentation
◆ m_linSys
|
protected |
Basic linear system object.
Definition at line 57 of file GlobalLinSysDirect.h.
Referenced by Nektar::MultiRegions::GlobalLinSysDirectFull::AssembleFullMatrix(), Nektar::MultiRegions::GlobalLinSysDirectStaticCond::v_AssembleSchurComplement(), Nektar::MultiRegions::GlobalLinSysDirectFull::v_SolveLinearSystem(), and Nektar::MultiRegions::GlobalLinSysDirectStaticCond::v_SolveLinearSystem().
