Cell gradient reconstruction. More...

#include <Kokkos_Core.hpp>
#include "common.h"
#include "boundary.h"
#include "mesh.h"

Classes
struct	LSQSystem
	Inverse-distance-squared weighted least-squares normal equations M g = b, with M stored as its upper triangle (row-major). More...

struct	LSQGradientFunctor
	Weighted least-squares gradient of W = [rho, u, p] over face neighbors, with boundary ghost states placed at the mirror image of the cell centroid across the boundary face. More...

struct	VertexGradientWeights
	Weights of LSQVertexGradientFunctor, aligned with cells_of_cell and faces_of_cell (zero for interior faces). More...

struct	LSQVertexGradientFunctor
	Gradient over all vertex neighbors plus the boundary ghost states of the cell's own boundary faces, as a fixed linear combination of the differences to the cell's state. More...

Functions
template<uint8_t N, typename T >
KOKKOS_INLINE_FUNCTION bool	cholesky (const T A[N][N], T L[N][N])
	Cholesky factorization A = L L^T of a symmetric positive definite matrix given by its upper triangle. Returns false if a pivot falls below 1e-10 of its diagonal entry, i.e. the matrix is (nearly) singular.

template<uint8_t N, typename T >
KOKKOS_INLINE_FUNCTION void	cholesky_solve (const T L[N][N], T *x)
	Solve L L^T x = b in place.

LSQGradientFunctor	make_gradient (const Mesh &mesh, const BoundaryData &boundaries, Kokkos::View< rtype [N_CONSERVATIVE]> W, Kokkos::View< rtype [N_CONSERVATIVE][N_DIM]> gradients)
	LSQGradientFunctor of the states W into gradients over a mesh.

LSQVertexGradientFunctor	make_vertex_gradient (const LSQGradientFunctor &faces, const Mesh &mesh, bool quadratic=true)
	LSQVertexGradientFunctor over the given gradient functor's mesh, boundaries, states and gradients, with its weights computed for a quadratic or a linear fit.

Detailed Description

Cell gradient reconstruction.

Author: Matthew Bonanni (mbona.nosp@m.nni0.nosp@m.01@gm.nosp@m.ail..nosp@m.com)

Version: 0.1

Date: 2026-10-02

Copyright: Copyright (c) 2026 Matthew Bonanni

Function Documentation

◆ cholesky()

template<uint8_t N, typename T >

KOKKOS_INLINE_FUNCTION bool cholesky	(	const T	A[N][N],
		T	L[N][N]
	)

Cholesky factorization A = L L^T of a symmetric positive definite matrix given by its upper triangle. Returns false if a pivot falls below 1e-10 of its diagonal entry, i.e. the matrix is (nearly) singular.

◆ cholesky_solve()

template<uint8_t N, typename T >

KOKKOS_INLINE_FUNCTION void cholesky_solve	(	const T	L[N][N],
		T *	x
	)

Solve L L^T x = b in place.

◆ make_gradient()

LSQGradientFunctor make_gradient	(	const Mesh &	mesh,
		const BoundaryData &	boundaries,
		Kokkos::View< rtype *[N_CONSERVATIVE]>	W,
		Kokkos::View< rtype *[N_CONSERVATIVE][N_DIM]>	gradients
	)

inline

LSQGradientFunctor of the states W into gradients over a mesh.

◆ make_vertex_gradient()

LSQVertexGradientFunctor make_vertex_gradient	(	const LSQGradientFunctor &	faces,
		const Mesh &	mesh,
		bool	quadratic = `true`
	)