anderson.hpp File Reference

#include <algorithm>
#include <cmath>
#include <cstddef>
#include <cstdio>
#include <exception>
#include <functional>
#include <limits>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>
#include "peclet/core/common/types.hpp"
#include "peclet/core/common/view.hpp"

Go to the source code of this file.

Classes
struct	peclet::core::solver::AndersonComm
	The collectives of a distributed run. More...
struct	peclet::core::solver::AndersonState
	The state descriptor (design §5.1): exactly what the caller's step reads across steps, as full padded x-fastest buffers over one box, with their roles. More...
struct	peclet::core::solver::detail::anderson::SumN< N >
	N independent double sums in one reduction. More...
struct	Kokkos::reduction_identity< peclet::core::solver::detail::anderson::SumN< N > >
struct	peclet::core::solver::detail::anderson::MixColumns
	The window columns the mix reads, oldest first. More...
struct	peclet::core::solver::detail::anderson::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...
class	peclet::core::solver::AndersonCore

Namespaces
namespace	peclet
namespace	peclet::core
namespace	peclet::core::solver
namespace	peclet::core::solver::detail
namespace	peclet::core::solver::detail::anderson
namespace	Kokkos

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

Enumerations
enum class	peclet::core::solver::AndersonRole : int { peclet::core::solver::Velocity = 0 , peclet::core::solver::Carried = 2 }
	What a state field is to the metric (design §3.1–3.2, rev 1: the metric is velocity only). More...

Functions
InnerPolicy	peclet::core::solver::detail::anderson::innerPolicy (const IVec< 3 > &e, int g)
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)
	COUNT: inner entries where buf != prev, into out (no host synchronisation).
void	peclet::core::solver::detail::anderson::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	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)
	DIFF (step 3): r = buf − X; dR_s = r − Rprev; dG_s = buf − Gprev; X = r. Padded.
void	peclet::core::solver::detail::anderson::residual (View< const double > buf, View< double > x)
	R (step 3, first evaluation): X = buf − X. Padded.
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)
	Pass 2, residual part: {Σ X², Σ buf²} over the inner entries of one Velocity field, into out (no host synchronisation).
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)
	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	peclet::core::solver::detail::anderson::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	peclet::core::solver::detail::anderson::scaledEigen (int n, const Mat &gram)
void	peclet::core::solver::detail::anderson::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	peclet::core::solver::detail::anderson::kMaxWindow = 8