Complete LU factorization of the cell-local Jacobian for GMRES preconditioning. More...

#include <EulerJacobian.hpp>

Inheritance diagram for DNDS::Euler::JacobianLocalLU< nVarsFixed >:

Collaboration diagram for DNDS::Euler::JacobianLocalLU< nVarsFixed >:

Public Types
using	tLocalMat = ArrayEigenUniMatrixBatch< nVarsFixed, nVarsFixed >
	Batch storage for nVars×nVars blocks.

using	tComponent = Eigen::Matrix< real, nVarsFixed, nVarsFixed >
	Single block matrix type.

using	tVec = ArrayDOFV< nVarsFixed >
	Distributed vector type.

using	tBase = Direct::LocalLUBase< JacobianLocalLU< nVarsFixed >, Eigen::Matrix< real, nVarsFixed, nVarsFixed >, ArrayDOFV< nVarsFixed > >
	CRTP base providing decompose/solve.

Public Member Functions
	JacobianLocalLU (const ssp< Direct::SerialSymLUStructure > &nMesh, int nVarsC)
	Construct and allocate the LU storage for the given adjacency structure.

void	setZero ()
	Zero all D, L, U blocks and mark the factorization as not yet decomposed.

auto	GetDiag (index i)
	Return the diagonal block for row `i` (compliant with LocalLUBase CRTP).

auto	GetLower (index i, int iInLow)
	Return lower-triangular block `iInLow` for row `i` (compliant with LocalLUBase CRTP).

auto	GetUpper (index i, int iInUpp)
	Return upper-triangular block `iInUpp` for row `i` (compliant with LocalLUBase CRTP).

void	PrintLog ()
	Print all non-zero entries (with diagonal inverted) to the log stream.

tComponent	InvertDiag (const tComponent &v)
	Invert a diagonal block using diagonal-preconditioned full-pivot LU.

Public Member Functions inherited from DNDS::Direct::LocalLUBase< JacobianLocalLU< nVarsFixed >, Eigen::Matrix< real, nVarsFixed, nVarsFixed >, ArrayDOFV< nVarsFixed > >
	LocalLUBase (ssp< Direct::SerialSymLUStructure > _symLU)

virtual	~LocalLUBase ()=default

void	GetDiag (index i)

void	GetLower (index i, int ij)

void	GetUpper (index i, int ij)

void	InvertDiag (const Eigen::Matrix< real, nVarsFixed, nVarsFixed > &v)

void	InPlaceDecompose ()

void	InPlaceDecomposeV1 ()

void	InPlaceDecomposeV2 ()

void	MatMul (ArrayDOFV< nVarsFixed > &x, ArrayDOFV< nVarsFixed > &result)

void	Solve (ArrayDOFV< nVarsFixed > &b, ArrayDOFV< nVarsFixed > &result)

Public Attributes
tLocalMat	LDU
	Sparse row storage for D, L, U blocks.

Public Attributes inherited from DNDS::Direct::LocalLUBase< JacobianLocalLU< nVarsFixed >, Eigen::Matrix< real, nVarsFixed, nVarsFixed >, ArrayDOFV< nVarsFixed > >
ssp< Direct::SerialSymLUStructure >	symLU

bool	isDecomposed

Detailed Description

template<int nVarsFixed>
struct DNDS::Euler::JacobianLocalLU< nVarsFixed >

Complete LU factorization of the cell-local Jacobian for GMRES preconditioning.

Stores diagonal (D), lower-triangular (L), and upper-triangular (U) blocks indexed by the mesh adjacency graph (SerialSymLUStructure). Inherits the decompose/solve interface from Direct::LocalLUBase via CRTP.

Row layout in LDU for each cell iCell:

Index 0: diagonal block D.
Indices [1, 1 + nLower): lower-triangular off-diagonal blocks L.
Indices [1 + nLower, end): upper-triangular off-diagonal blocks U.

where nLower = symLU->lowerTriStructure[iCell].size().

Template Parameters

nVarsFixed Compile-time number of conservative variables (or Eigen::Dynamic).

Definition at line 268 of file EulerJacobian.hpp.

Member Typedef Documentation

◆ tBase

template<int nVarsFixed>

using DNDS::Euler::JacobianLocalLU< nVarsFixed >::tBase = Direct::LocalLUBase< JacobianLocalLU<nVarsFixed>, Eigen::Matrix<real, nVarsFixed, nVarsFixed>, ArrayDOFV<nVarsFixed> >

CRTP base providing decompose/solve.

Definition at line 277 of file EulerJacobian.hpp.

◆ tComponent

template<int nVarsFixed>

using DNDS::Euler::JacobianLocalLU< nVarsFixed >::tComponent = Eigen::Matrix<real, nVarsFixed, nVarsFixed>

Single block matrix type.

Definition at line 275 of file EulerJacobian.hpp.

◆ tLocalMat

template<int nVarsFixed>

using DNDS::Euler::JacobianLocalLU< nVarsFixed >::tLocalMat = ArrayEigenUniMatrixBatch<nVarsFixed, nVarsFixed>

Batch storage for nVars×nVars blocks.

Definition at line 274 of file EulerJacobian.hpp.

◆ tVec

template<int nVarsFixed>

using DNDS::Euler::JacobianLocalLU< nVarsFixed >::tVec = ArrayDOFV<nVarsFixed>

Distributed vector type.

Definition at line 276 of file EulerJacobian.hpp.

Constructor & Destructor Documentation

◆ JacobianLocalLU()

template<int nVarsFixed>

DNDS::Euler::JacobianLocalLU< nVarsFixed >::JacobianLocalLU	(	const ssp< Direct::SerialSymLUStructure > &	nMesh,
		int	nVarsC
	)

inline

Construct and allocate the LU storage for the given adjacency structure.

Parameters

nMesh	Shared pointer to the symmetric LU sparsity structure.
nVarsC	Runtime number of conservative variables.

Definition at line 297 of file EulerJacobian.hpp.

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Member Function Documentation

◆ GetDiag()

template<int nVarsFixed>

auto DNDS::Euler::JacobianLocalLU< nVarsFixed >::GetDiag ( index i )

inline

Return the diagonal block for row i (compliant with LocalLUBase CRTP).

Parameters

i	Cell (row) index.

Definition at line 326 of file EulerJacobian.hpp.

◆ GetLower()

template<int nVarsFixed>

auto DNDS::Euler::JacobianLocalLU< nVarsFixed >::GetLower	(	index	i,
		int	iInLow
	)

inline

Return lower-triangular block iInLow for row i (compliant with LocalLUBase CRTP).

Parameters

i	Cell (row) index.
iInLow	Index within the lower-triangular neighbor list.

Definition at line 333 of file EulerJacobian.hpp.

◆ GetUpper()

template<int nVarsFixed>

auto DNDS::Euler::JacobianLocalLU< nVarsFixed >::GetUpper	(	index	i,
		int	iInUpp
	)

inline

Return upper-triangular block iInUpp for row i (compliant with LocalLUBase CRTP).

Parameters

i	Cell (row) index.
iInUpp	Index within the upper-triangular neighbor list.

Definition at line 340 of file EulerJacobian.hpp.

◆ InvertDiag()

template<int nVarsFixed>

tComponent DNDS::Euler::JacobianLocalLU< nVarsFixed >::InvertDiag ( const tComponent & v )

inline

Invert a diagonal block using diagonal-preconditioned full-pivot LU.

Preconditions the matrix by scaling rows with the inverse of the diagonal, then applies Eigen's fullPivLu(). This two-step approach improves numerical stability for ill-conditioned Jacobian blocks.

Parameters

v	The nVars×nVars block matrix to invert.

Returns: The inverse matrix v^{-1}.

Definition at line 369 of file EulerJacobian.hpp.

◆ PrintLog()

template<int nVarsFixed>

void DNDS::Euler::JacobianLocalLU< nVarsFixed >::PrintLog ( )

inline

Print all non-zero entries (with diagonal inverted) to the log stream.

Definition at line 346 of file EulerJacobian.hpp.

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◆ setZero()

template<int nVarsFixed>

void DNDS::Euler::JacobianLocalLU< nVarsFixed >::setZero ( )

inline

Zero all D, L, U blocks and mark the factorization as not yet decomposed.

Definition at line 313 of file EulerJacobian.hpp.

Member Data Documentation

◆ LDU

template<int nVarsFixed>

tLocalMat DNDS::Euler::JacobianLocalLU< nVarsFixed >::LDU

Sparse row storage for D, L, U blocks.

Each row i stores blocks in the order: [0] = diag, [1, 1 + symLU->lowerTriStructure[i].size()) = lower-triangular, [1 + symLU->lowerTriStructure[i].size(), end) = upper-triangular.

Definition at line 290 of file EulerJacobian.hpp.

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

/home/runner/work/DNDSR/DNDSR/src/Euler/EulerJacobian.hpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ tBase

◆ tComponent

◆ tLocalMat

◆ tVec

Constructor & Destructor Documentation

◆ JacobianLocalLU()

Member Function Documentation

◆ GetDiag()

◆ GetLower()

◆ GetUpper()

◆ InvertDiag()

◆ PrintLog()

◆ setZero()

Member Data Documentation

◆ LDU