AMRMultigridKrylovOp< T > Class Template Reference

Adapter presenting an already-defined AMRMultiGrid as a LinearOp over the AMR hierarchy. More...

#include <CD_AMRMultigridKrylovOp.H>

Inheritance diagram for AMRMultigridKrylovOp< T >:

Collaboration diagram for AMRMultigridKrylovOp< T >:

Public Member Functions
	AMRMultigridKrylovOp ()=default
	Default constructor. Call define() before use.
virtual	~AMRMultigridKrylovOp ()
	Destructor. Frees the preconditioner scratch storage.
void	define (AMRMultiGrid< LevelData< T > > *a_mg, const Vector< RefCountedPtr< LevelData< BaseFab< bool > > > > &a_validCells, const Vector< Real > &a_dx, const int a_lbase, const int a_lmax, const int a_numVCycles)
	Define the adapter. Call once per regrid (after the AMRMultiGrid has been defined and init'd).
void	applyOp (Vector< LevelData< T > * > &a_lhs, const Vector< LevelData< T > * > &a_phi, bool a_homogeneous=false) override
	Matrix-vector product L(phi) over the AMR hierarchy (always homogeneous for the Krylov path).
void	residual (Vector< LevelData< T > * > &a_lhs, const Vector< LevelData< T > * > &a_phi, const Vector< LevelData< T > * > &a_rhs, bool a_homogeneous=false) override
	AMR residual a_lhs = L(a_phi) - a_rhs.
void	preCond (Vector< LevelData< T > * > &a_cor, const Vector< LevelData< T > * > &a_residual) override
	Apply the preconditioner: a_cor approx L^{-1} a_residual via m_numVCycles multigrid cycles (cycle type from the AMRMultiGrid configuration; normally V-cycles).
void	create (Vector< LevelData< T > * > &a_lhs, const Vector< LevelData< T > * > &a_rhs) override
	Allocate a_lhs to mirror a_rhs.
void	clear (Vector< LevelData< T > * > &a_lhs) override
	Free a holder created by create().
void	assign (Vector< LevelData< T > * > &a_lhs, const Vector< LevelData< T > * > &a_rhs) override
	Copy a_rhs into a_lhs.
Real	dotProduct (const Vector< LevelData< T > * > &a_1, const Vector< LevelData< T > * > &a_2) override
	AMR-composite inner product (allocation-free, fine-covered cells masked out).
void	mDotProduct (const Vector< LevelData< T > * > &a_1, const int a_sz, const Vector< LevelData< T > * > a_2[], Real a_mdots[]) override
	Batched inner products a_mdots[k] = dotProduct(a_1, a_2[k]) for k=0..a_sz-1.
void	incr (Vector< LevelData< T > * > &a_lhs, const Vector< LevelData< T > * > &a_x, Real a_scale) override
	Increment a_lhs += a_scale*a_x.
void	axby (Vector< LevelData< T > * > &a_lhs, const Vector< LevelData< T > * > &a_x, const Vector< LevelData< T > * > &a_y, Real a_a, Real a_b) override
	Set a_lhs = a_a*a_x + a_b*a_y.
void	scale (Vector< LevelData< T > * > &a_lhs, const Real &a_scale) override
	Scale a_lhs *= a_scale.
Real	norm (const Vector< LevelData< T > * > &a_rhs, int a_ord) override
	Norm of a_rhs. For a_ord==2 this is the inner-product-induced norm sqrt(dotProduct(x,x)) so that it is consistent with dotProduct (a requirement of GMRES); other orders use the per-level max norm.
void	setToZero (Vector< LevelData< T > * > &a_lhs) override
	Set a_lhs = 0.

Protected Attributes
AMRMultiGrid< LevelData< T > > *	m_mg = nullptr
	Reused multigrid solver (not owned).
Vector< AMRLevelOp< LevelData< T > > * >	m_amrOps
	Per-level AMR operators borrowed from m_mg (not owned).
Vector< Real >	m_dxScale
	Per-level dx^SpaceDim, the AMR inner-product weight.
Vector< RefCountedPtr< LevelData< BaseFab< bool > > > >	m_validMask
	Per-level valid-cell mask: false where the level is covered by a finer level (excluded from the inner product). Shared (refcounted) with AmrMesh's valid-cell mask rather than built here.
Vector< Real >	m_volume
	Per-level reduced total volume (geometry-only, vector-independent); cached on first dotProduct.
bool	m_volumeCached = false
	Whether m_volume has been computed and reduced. Reset to false in define() (regrid invalidates it).
int	m_lbase = 0
	Coarsest level in the solve.
int	m_lmax = 0
	Finest level in the solve.
int	m_numVCycles = 1
	Number of multigrid cycles per preconditioner application (cycle type from the AMRMultiGrid configuration; normally V-cycles).
bool	m_precondInit = false
	Whether the preconditioner scratch has been allocated.
Vector< LevelData< T > * >	m_precondTmp
	Preconditioner scratch (residual), lazily allocated on first preCond.
Vector< LevelData< T > * >	m_precondDcor
	Preconditioner scratch (cycle correction), lazily allocated on first preCond.

Detailed Description

template<class T>
class AMRMultigridKrylovOp< T >

Adapter presenting an already-defined AMRMultiGrid as a LinearOp over the AMR hierarchy.

This lets an outer Krylov solver (GMRES/BiCGStab, operating on Vector<LevelData<T>*>) use the multigrid cycle as a preconditioner. The matrix-vector product and the preconditioner delegate to the supplied, fully set-up AMRMultiGrid (its AMR operators and multigrid cycle; the cycle type follows the AMRMultiGrid configuration / cycle, normally a V-cycle for efficiency). The vector operations delegate to the per-level AMR operators, and the AMR inner product is computed allocation-free using a per-level fine-covered mask precomputed in define().

Note

T is the FAB type (EBCellFAB or MFCellFAB); the LinearOp acts on Vector<LevelData<T>*>.

Member Function Documentation

applyOp()

template<class T >

void AMRMultigridKrylovOp< T >::applyOp ( Vector< LevelData< T > * > &  a_lhs, const Vector< LevelData< T > * > &  a_phi, bool  a_homogeneous = false  )

override

Matrix-vector product L(phi) over the AMR hierarchy (always homogeneous for the Krylov path).

Parameters

[out]	a_lhs	Result L(phi)
[in]	a_phi	Input vector
[in]	a_homogeneous	Use homogeneous boundary conditions

assign()

template<class T >

void AMRMultigridKrylovOp< T >::assign ( Vector< LevelData< T > * > &  a_lhs, const Vector< LevelData< T > * > &  a_rhs  )

override

Copy a_rhs into a_lhs.

Parameters

[out]	a_lhs	Destination
[in]	a_rhs	Source

axby()

template<class T >

void AMRMultigridKrylovOp< T >::axby ( Vector< LevelData< T > * > &  a_lhs, const Vector< LevelData< T > * > &  a_x, const Vector< LevelData< T > * > &  a_y, Real  a_a, Real  a_b  )

override

Set a_lhs = a_a*a_x + a_b*a_y.

Parameters

[out]	a_lhs	Result
[in]	a_x	First operand
[in]	a_y	Second operand
[in]	a_a	Scale of a_x
[in]	a_b	Scale of a_y

clear()

template<class T >

void AMRMultigridKrylovOp< T >::clear ( Vector< LevelData< T > * > &  a_lhs )

override

Free a holder created by create().

Parameters

[in,out]

a_lhs

Holder to free

create()

template<class T >

void AMRMultigridKrylovOp< T >::create ( Vector< LevelData< T > * > &  a_lhs, const Vector< LevelData< T > * > &  a_rhs  )

override

Allocate a_lhs to mirror a_rhs.

Parameters

[out]	a_lhs	New holder
[in]	a_rhs	Template holder

define()

template<class T >

void AMRMultigridKrylovOp< T >::define	(	AMRMultiGrid< LevelData< T > > *	a_mg,
		const Vector< RefCountedPtr< LevelData< BaseFab< bool > > > > &	a_validCells,
		const Vector< Real > &	a_dx,
		const int	a_lbase,
		const int	a_lmax,
		const int	a_numVCycles
	)

Define the adapter. Call once per regrid (after the AMRMultiGrid has been defined and init'd).

Parameters

[in]	a_mg	The fully set-up multigrid solver to reuse for matvec and preconditioning
[in]	a_validCells	Per-level valid-cell mask (true where not covered by a finer level). Reused from AmrMesh::getValidCells rather than rebuilt here.
[in]	a_dx	Grid spacing on each level (index 0..a_lmax)
[in]	a_lbase	Coarsest level in the solve
[in]	a_lmax	Finest level in the solve
[in]	a_numVCycles	Number of multigrid cycles applied per preconditioner invocation (cycle type from the AMRMultiGrid configuration; normally a V-cycle)

dotProduct()

template<class T >

Real AMRMultigridKrylovOp< T >::dotProduct ( const Vector< LevelData< T > * > &  a_1, const Vector< LevelData< T > * > &  a_2  )

override

AMR-composite inner product (allocation-free, fine-covered cells masked out).

Parameters

[in]	a_1	First operand
[in]	a_2	Second operand

Returns

Inner product

incr()

template<class T >

void AMRMultigridKrylovOp< T >::incr ( Vector< LevelData< T > * > &  a_lhs, const Vector< LevelData< T > * > &  a_x, Real  a_scale  )

override

Increment a_lhs += a_scale*a_x.

Parameters

[in,out]	a_lhs	Accumulator
[in]	a_x	Increment
[in]	a_scale	Scale factor

mDotProduct()

template<class T >

void AMRMultigridKrylovOp< T >::mDotProduct ( const Vector< LevelData< T > * > &  a_1, const int  a_sz, const Vector< LevelData< T > * >  a_2[], Real  a_mdots[]  )

override

Batched inner products a_mdots[k] = dotProduct(a_1, a_2[k]) for k=0..a_sz-1.

Overrides the LinearOp default (which loops dotProduct, one MPI reduction each). Here all a_sz*nLevel rank-local partials are reduced in a single MPI_Allreduce. This is the per-iteration cost of Krylov orthogonalization (Gram-Schmidt), so the single fused reduction is the dominant scaling win.

Parameters

[in]	a_1	Fixed operand
[in]	a_sz	Number of right operands
[in]	a_2	Array of a_sz right operands
[out]	a_mdots	Array of a_sz inner products

norm()

template<class T >

Real AMRMultigridKrylovOp< T >::norm ( const Vector< LevelData< T > * > &  a_rhs, int  a_ord  )

override

Norm of a_rhs. For a_ord==2 this is the inner-product-induced norm sqrt(dotProduct(x,x)) so that it is consistent with dotProduct (a requirement of GMRES); other orders use the per-level max norm.

Parameters

[in]	a_rhs	Vector
[in]	a_ord	Norm order

Returns

Norm

preCond()

template<class T >

void AMRMultigridKrylovOp< T >::preCond ( Vector< LevelData< T > * > &  a_cor, const Vector< LevelData< T > * > &  a_residual  )

override

Apply the preconditioner: a_cor approx L^{-1} a_residual via m_numVCycles multigrid cycles (cycle type from the AMRMultiGrid configuration; normally V-cycles).

Parameters

[out]	a_cor	Preconditioned correction
[in]	a_residual	Residual to precondition

residual()

template<class T >

void AMRMultigridKrylovOp< T >::residual ( Vector< LevelData< T > * > &  a_lhs, const Vector< LevelData< T > * > &  a_phi, const Vector< LevelData< T > * > &  a_rhs, bool  a_homogeneous = false  )

override

AMR residual a_lhs = L(a_phi) - a_rhs.

Parameters

[out]	a_lhs	Residual
[in]	a_phi	Solution estimate
[in]	a_rhs	Right-hand side
[in]	a_homogeneous	Use homogeneous boundary conditions

scale()

template<class T >

void AMRMultigridKrylovOp< T >::scale ( Vector< LevelData< T > * > &  a_lhs, const Real &  a_scale  )

override

Scale a_lhs *= a_scale.

Parameters

[in,out]	a_lhs	Vector
[in]	a_scale	Scale factor

setToZero()

template<class T >

void AMRMultigridKrylovOp< T >::setToZero ( Vector< LevelData< T > * > &  a_lhs )

override

Set a_lhs = 0.

Parameters

[out]

a_lhs

Vector

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

• Source/Elliptic/CD_AMRMultigridKrylovOp.H
• Source/Elliptic/CD_AMRMultigridKrylovOpImplem.H