Classes
struct	MixColumns
	The window columns the mix reads, oldest first. More...

struct	ScaledEig
	The Jacobi-scaled eigendecomposition of a Gram block G: A = D⁻¹ G D⁻¹, D = diag(G)^{1/2} (design §4.4 steps 1–3). More...

struct	SumN
	N independent double sums in one reduction. More...

Typedefs
using	InnerPolicy = Kokkos::MDRangePolicy< ExecSpace, Kokkos::IndexType< Index >, Kokkos::Rank< 3, Kokkos::Iterate::Left, Kokkos::Iterate::Left > >
	Inner-region policy, x (the first index) fastest in tiles and within a tile on every backend (suite CONVENTIONS §1; the same policy as flow's MDRange3).

template<class T >
using	DeviceScalar = Kokkos::View< T, MemSpace >
	A reduction result held on the device: a reduction into it does not synchronise the host, so a phase's reductions queue back to back and are read back behind one fence (design §6.1).

using	Mat = double[kMaxWindow][kMaxWindow]

Functions
InnerPolicy	innerPolicy (const IVec< 3 > &e, int g)

void	countChanged (View< const double > buf, View< const double > prev, const IVec< 3 > &e, int g, const DeviceScalar< Index > &out)
	COUNT: inner entries where buf != prev, into `out` (no host synchronisation).

void	mix (View< double > buf, View< double > xOut, View< const double > rPrev, const MixColumns &cols, double beta)
	MIX (design §4.3 step 1, §4.5): x = buf − ΔG γ − (1−β)(Rprev − ΔR γ); buf = X = x. Padded.

void	diff (View< const double > buf, View< double > x, View< const double > rPrev, View< const double > gPrev, View< double > dRs, View< double > dGs)
	DIFF (step 3): r = buf − X; dR_s = r − Rprev; dG_s = buf − Gprev; X = r. Padded.

void	residual (View< const double > buf, View< double > x)
	R (step 3, first evaluation): X = buf − X. Padded.

void	selfSums (View< const double > x, View< const double > buf, const IVec< 3 > &e, int g, const DeviceScalar< SumN< 2 > > &out)
	Pass 2, residual part: {Σ X², Σ buf²} over the inner entries of one Velocity field, into `out` (no host synchronisation).

void	columnSums (View< const double > dRs, View< const double > dRj, View< const double > x, const IVec< 3 > &e, int g, const DeviceScalar< SumN< 2 > > &out)
	Pass 2, one window column j against the new column s, over the inner entries of one Velocity field: {⟨dR_s,dR_j⟩, ⟨dR_j,X⟩}, into `out` (no host synchronisation).

void	jacobiEigen (int n, Mat &a, Mat &v, double(&lam)[kMaxWindow])
	Cyclic Jacobi eigendecomposition of the symmetric n×n `a` (overwritten), fixed sweep order p < q row-major; stops when the off-diagonal Frobenius norm is ≤ 1e-15·‖A‖_F or after 50 sweeps (design §4.4 step 3).

ScaledEig	scaledEigen (int n, const Mat &gram)

void	truncatedSolve (const ScaledEig &se, const double b, double condMin, double x)
	x = D⁻¹ Σ_i v_i (v_iᵀ D⁻¹ b)/λ_i over the eigenvalues λ_i ≥ condMin·λ_max (and > 0): the truncated solve of design §4.4 step 5 (after the caller's column drops, nothing is truncated).

Variables
constexpr int	kMaxWindow = 8

Typedef Documentation

◆ InnerPolicy

using peclet::core::solver::detail::anderson::InnerPolicy = typedef Kokkos::MDRangePolicy<ExecSpace, Kokkos::IndexType<Index>, Kokkos::Rank<3, Kokkos::Iterate::Left, Kokkos::Iterate::Left> >

Inner-region policy, x (the first index) fastest in tiles and within a tile on every backend (suite CONVENTIONS §1; the same policy as flow's MDRange3).

Definition at line 77 of file anderson.hpp.

◆ DeviceScalar

template<class T >

using peclet::core::solver::detail::anderson::DeviceScalar = typedef Kokkos::View<T, MemSpace>

A reduction result held on the device: a reduction into it does not synchronise the host, so a phase's reductions queue back to back and are read back behind one fence (design §6.1).

Definition at line 118 of file anderson.hpp.

◆ Mat

using peclet::core::solver::detail::anderson::Mat = typedef double[kMaxWindow][kMaxWindow]

Definition at line 215 of file anderson.hpp.

Function Documentation

◆ innerPolicy()

InnerPolicy peclet::core::solver::detail::anderson::innerPolicy	(	const IVec< 3 > &	e,
		int	g
	)

inline

Definition at line 81 of file anderson.hpp.

Referenced by columnSums(), countChanged(), and selfSums().

◆ countChanged()

void peclet::core::solver::detail::anderson::countChanged	(	View< const double >	buf,
		View< const double >	prev,
		const IVec< 3 > &	e,
		int	g,
		const DeviceScalar< Index > &	out
	)

inline

COUNT: inner entries where buf != prev, into out (no host synchronisation).

Definition at line 121 of file anderson.hpp.

References innerPolicy().

Referenced by peclet::core::solver::AndersonCore::prepare().

◆ mix()

void peclet::core::solver::detail::anderson::mix	(	View< double >	buf,
		View< double >	xOut,
		View< const double >	rPrev,
		const MixColumns &	cols,
		double	beta
	)

inline

MIX (design §4.3 step 1, §4.5): x = buf − ΔG γ − (1−β)(Rprev − ΔR γ); buf = X = x. Padded.

Definition at line 143 of file anderson.hpp.

Referenced by peclet::core::solver::AndersonCore::prepare().

◆ diff()

void peclet::core::solver::detail::anderson::diff	(	View< const double >	buf,
		View< double >	x,
		View< const double >	rPrev,
		View< const double >	gPrev,
		View< double >	dRs,
		View< double >	dGs
	)

inline

DIFF (step 3): r = buf − X; dR_s = r − Rprev; dG_s = buf − Gprev; X = r. Padded.

Definition at line 161 of file anderson.hpp.

◆ residual()

void peclet::core::solver::detail::anderson::residual	(	View< const double >	buf,
		View< double >	x
	)

inline

R (step 3, first evaluation): X = buf − X. Padded.

Definition at line 174 of file anderson.hpp.

◆ selfSums()

void peclet::core::solver::detail::anderson::selfSums	(	View< const double >	x,
		View< const double >	buf,
		const IVec< 3 > &	e,
		int	g,
		const DeviceScalar< SumN< 2 > > &	out
	)

inline

Pass 2, residual part: {Σ X², Σ buf²} over the inner entries of one Velocity field, into out (no host synchronisation).

Definition at line 183 of file anderson.hpp.

References innerPolicy().

◆ columnSums()

void peclet::core::solver::detail::anderson::columnSums	(	View< const double >	dRs,
		View< const double >	dRj,
		View< const double >	x,
		const IVec< 3 > &	e,
		int	g,
		const DeviceScalar< SumN< 2 > > &	out
	)

inline

Pass 2, one window column j against the new column s, over the inner entries of one Velocity field: {⟨dR_s,dR_j⟩, ⟨dR_j,X⟩}, into out (no host synchronisation).

Reads dR_s, dR_j and X only (design §6.1, rev 2: no reduction reads a dG column; dG is read by MIX alone).

Definition at line 199 of file anderson.hpp.

References innerPolicy().

◆ jacobiEigen()

void peclet::core::solver::detail::anderson::jacobiEigen	(	int	n,
		Mat &	a,
		Mat &	v,
		double(&)	lam[kMaxWindow]
	)

inline

Cyclic Jacobi eigendecomposition of the symmetric n×n a (overwritten), fixed sweep order p < q row-major; stops when the off-diagonal Frobenius norm is ≤ 1e-15·‖A‖_F or after 50 sweeps (design §4.4 step 3).

Eigenvalue i is lam[i], its eigenvector the column v[·][i].

Definition at line 220 of file anderson.hpp.

Referenced by scaledEigen().

◆ scaledEigen()

ScaledEig peclet::core::solver::detail::anderson::scaledEigen	(	int	n,
		const Mat &	gram
	)

inline

Definition at line 274 of file anderson.hpp.

References peclet::core::solver::detail::anderson::ScaledEig::dinv, jacobiEigen(), peclet::core::solver::detail::anderson::ScaledEig::lam, peclet::core::solver::detail::anderson::ScaledEig::lamMax, peclet::core::solver::detail::anderson::ScaledEig::lamMin, peclet::core::solver::detail::anderson::ScaledEig::n, and peclet::core::solver::detail::anderson::ScaledEig::v.

◆ truncatedSolve()

void peclet::core::solver::detail::anderson::truncatedSolve	(	const ScaledEig &	se,
		const double *	b,
		double	condMin,
		double *	x
	)

inline

x = D⁻¹ Σ_i v_i (v_iᵀ D⁻¹ b)/λ_i over the eigenvalues λ_i ≥ condMin·λ_max (and > 0): the truncated solve of design §4.4 step 5 (after the caller's column drops, nothing is truncated).

Definition at line 296 of file anderson.hpp.

References kMaxWindow, and peclet::core::solver::detail::anderson::ScaledEig::n.

Variable Documentation

◆ kMaxWindow

constexpr int peclet::core::solver::detail::anderson::kMaxWindow = 8

inlineconstexpr

Definition at line 73 of file anderson.hpp.

Referenced by truncatedSolve().

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ InnerPolicy

◆ DeviceScalar

◆ Mat

Function Documentation

◆ innerPolicy()

◆ countChanged()

◆ mix()

◆ diff()

◆ residual()

◆ selfSums()

◆ columnSums()

◆ jacobiEigen()

◆ scaledEigen()

◆ truncatedSolve()

Variable Documentation

◆ kMaxWindow