\( D_x\), \( D_y\) and \( D_z \) More...

Collaboration diagram for Create derivatives:

Enumerations
enum	dg::bc { dg::PER = 0 , dg::DIR = 1 , dg::DIR_NEU = 2 , dg::NEU_DIR = 3 , dg::NEU = 4 }
	Switch between boundary conditions. More...

enum	dg::direction { dg::forward , dg::backward , dg::centered }
	Direction of a discrete derivative. More...

enum	dg::space { dg::lspace , dg::xspace }
	Space of DG coefficients. More...

enum class	dg::coo2d : char { dg::coo2d::x = 'x' , dg::coo2d::y = 'y' }
	2d coordinates More...

enum class	dg::coo3d : char { dg::coo3d::x = 'x' , dg::coo3d::y = 'y' , dg::coo3d::z = 'z' }
	3d coordinates More...

Functions
template<class real_type , size_t Nd>
EllSparseBlockMat< real_type, thrust::host_vector >	dg::create::derivative (unsigned coord, const aRealTopology< real_type, Nd > &g, dg::bc bc, direction dir=centered)
	Create a derivative along given coordinate.

template<class real_type , size_t Nd>
EllSparseBlockMat< real_type, thrust::host_vector >	dg::create::jump (unsigned coord, const aRealTopology< real_type, Nd > &g, dg::bc bc)
	Create a jump matrix along given coordinate.

template<class Topology >
auto	dg::create::dx (const Topology &g, dg::bc bc, dg::direction dir=centered)

template<class Topology >
auto	dg::create::dy (const Topology &g, dg::bc bc, dg::direction dir=centered)
	Short for `dg::create::derivative( 1, g, bc, dir);`

template<class Topology >
auto	dg::create::dz (const Topology &g, dg::bc bc, dg::direction dir=centered)
	Short for `dg::create::derivative( 2, g, bc, dir);`

template<class Topology >
auto	dg::create::jumpX (const Topology &g, bc bc)
	Short for `dg::create::jump( 0, g, bc);`

template<class Topology >
auto	dg::create::jumpY (const Topology &g, bc bc)
	Short for `dg::create::jump( 1, g, bc);`

template<class Topology >
auto	dg::create::jumpZ (const Topology &g, bc bc)
	Short for `dg::create::jump( 2, g, bc);`

template<class Topology >
auto	dg::create::derivative (unsigned coord, const Topology &g, direction dir=centered)
	Short for `dg::create::derivative( coord, g, g.bcx(), dir);`

template<class Topology >
auto	dg::create::jump (unsigned coord, const Topology &g)
	Short for `dg::create::jump( coord, g, g.bcx());`

template<class Topology >
auto	dg::create::dx (const Topology &g, dg::direction dir=centered)
	Short for `dg::create::derivative( 0, g, g.bcx() dir);`

template<class Topology >
auto	dg::create::dy (const Topology &g, dg::direction dir=centered)
	Short for `dg::create::derivative( 1, g, g.bcy(), dir);`

template<class Topology >
auto	dg::create::dz (const Topology &g, dg::direction dir=centered)
	Short for `dg::create::derivative( 2, g, g.bcz(), dir);`

template<class Topology >
auto	dg::create::jumpX (const Topology &g)
	Short for `dg::create::jump( 0, g, g.bcx());`

template<class Topology >
auto	dg::create::jumpY (const Topology &g)
	Short for `dg::create::jump( 1, g, g.bcy());`

template<class Topology >
auto	dg::create::jumpZ (const Topology &g)
	Short for `dg::create::jump( 2, g, g.bcz());`

template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	dg::create::derivative (unsigned coord, const aRealTopologyX2d< real_type > &g, dg::bc bc, direction dir=centered)
	Create 2d derivative in x-direction.

template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	dg::create::jump (unsigned coord, const aRealTopologyX2d< real_type > &g, bc bc)
	Matrix that contains 2d jump terms in X direction.

template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	dg::create::jump (unsigned coord, const aRealTopologyX3d< real_type > &g, bc bc)
	Matrix that contains jump terms in X direction in 3D.

template<class real_type >
Composite< EllSparseBlockMat< real_type, thrust::host_vector > >	dg::create::derivative (unsigned coord, const aRealTopologyX3d< real_type > &g, bc bc, direction dir=centered)
	Create 3d derivative in x-direction.

template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	dg::create::dx (const RealGridX1d< real_type > &g, bc bcx, direction dir=centered)
	Create and assemble a host Matrix for the derivative in 1d.

template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	dg::create::dx (const RealGridX1d< real_type > &g, direction dir=centered)
	Create and assemble a host Matrix for the derivative in 1d.

template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	dg::create::jump (const RealGridX1d< real_type > &g, bc bcx)
	Create and assemble a host Matrix for the jump in 1d.

template<class real_type >
EllSparseBlockMat< real_type, thrust::host_vector >	dg::create::jump (const RealGridX1d< real_type > &g)
	Create and assemble a host Matrix for the jump in 1d.

template<class real_type , size_t Nd>
dg::MHMatrix_t< real_type >	dg::create::derivative (unsigned coord, const aRealMPITopology< real_type, Nd > &g, dg::bc bc, direction dir=centered)
	Create a derivative along the given coordinate for mpi.

template<class real_type , size_t Nd>
dg::MHMatrix_t< real_type >	dg::create::jump (unsigned coord, const aRealMPITopology< real_type, Nd > &g, dg::bc bc)
	Create a jump matrix along given coordinate for mpi.

std::string	dg::bc2str (bc bcx)
	write a string describing boundary condition to an output stream

bc	dg::str2bc (std::string s)
	convert a string to a bc

bc	dg::inverse (bc bound)
	invert boundary condition

direction	dg::str2direction (std::string s)
	convert a string to a direction

std::string	dg::direction2str (enum direction dir)
	convert a direciton to string

direction	dg::inverse (direction dir)
	invert direction

Detailed Description

\( D_x\), \( D_y\) and \( D_z \)

High level matrix creation functions

Enumeration Type Documentation

◆ bc

enum dg::bc

Switch between boundary conditions.

Enumerator
PER	periodic boundaries
DIR	homogeneous dirichlet boundaries
DIR_NEU	Dirichlet on left, Neumann on right boundary.
NEU_DIR	Neumann on left, Dirichlet on right boundary.
NEU	Neumann on both boundaries.

◆ coo2d

enum class dg::coo2d : char

strong

2d coordinates

Enumerator
x	x direction
y	y direction

◆ coo3d

enum class dg::coo3d : char

strong

3d coordinates

Enumerator
x	x direction
y	y direction
z	z direction

◆ direction

enum dg::direction

Direction of a discrete derivative.

Enumerator
forward	forward derivative (cell to the right and current cell)
backward	backward derivative (cell to the left and current cell)
centered	centered derivative (cell to the left and right and current cell)

◆ space

enum dg::space

Space of DG coefficients.

Enumerator
lspace	DG Polynomial space "modal values".
xspace	Configuration space "nodal values".

Function Documentation

◆ bc2str()

std::string dg::bc2str ( bc bcx )

inline

write a string describing boundary condition to an output stream

converts

dg::PER to PERIODIC
dg::DIR to DIRICHLET
dg::NEU to NEUMANN
dg::NEU_DIR to NEU_DIR
dg::DIR_NEU to DIR_NEU
or "Not specified!!"
Parameters

bcx the boundary condition

Returns
a string

◆ derivative() [1/5]

template<class real_type , size_t Nd>

dg::MHMatrix_t< real_type > dg::create::derivative	(	unsigned	coord,
		const aRealMPITopology< real_type, Nd > &	g,
		dg::bc	bc,
		direction	dir = centered )

Create a derivative along the given coordinate for mpi.

Parameters

coord	the coordinate along which to derive
g	A mpi grid
bc	boundary condition
dir	centered, forward or backward

Returns: A mpi matrix

◆ derivative() [2/5]

template<class real_type , size_t Nd>

EllSparseBlockMat< real_type, thrust::host_vector > dg::create::derivative	(	unsigned	coord,
		const aRealTopology< real_type, Nd > &	g,
		dg::bc	bc,
		direction	dir = centered )

Create a derivative along given coordinate.

Parameters

coord	the coordinate along which to derive
g	The grid on which to create derivative
bc	The boundary condition
dir	centered, forward or backward

Returns: A host matrix

◆ derivative() [3/5]

template<class real_type >

Composite< EllSparseBlockMat< real_type, thrust::host_vector > > dg::create::derivative	(	unsigned	coord,
		const aRealTopologyX2d< real_type > &	g,
		dg::bc	bc,
		direction	dir = centered )

Create 2d derivative in x-direction.

Parameters

coord	Either 0 (for x derivative) or 1 (for y derivative)
g	The grid on which to create dx
bc	The boundary condition
dir	The direction of the first derivative

Returns: A host matrix

◆ derivative() [4/5]

template<class real_type >

Composite< EllSparseBlockMat< real_type, thrust::host_vector > > dg::create::derivative	(	unsigned	coord,
		const aRealTopologyX3d< real_type > &	g,
		bc	bc,
		direction	dir = centered )

Create 3d derivative in x-direction.

Parameters

coord	Either 0 (for x derivative) or 1 (for y derivative) or 2 (for z derivative)
g	The grid on which to create dx
bc	The boundary condition
dir	The direction of the first derivative

Returns: A host matrix

◆ derivative() [5/5]

template<class Topology >

auto dg::create::derivative	(	unsigned	coord,
		const Topology &	g,
		direction	dir = centered )

Short for dg::create::derivative( coord, g, g.bcx(), dir);

◆ direction2str()

std::string dg::direction2str ( enum direction dir )

inline

convert a direciton to string

converts

forward to "forward"
backward to "backward"
centered to "centered"

Parameters

dir	the input direction

Returns: a string

◆ dx() [1/4]

template<class real_type >

EllSparseBlockMat< real_type, thrust::host_vector > dg::create::dx	(	const RealGridX1d< real_type > &	g,
		bc	bcx,
		direction	dir = centered )

Create and assemble a host Matrix for the derivative in 1d.

Parameters

g	1D grid with X-point topology
bcx	boundary condition
dir	The direction of the first derivative

Returns: Host Matrix

◆ dx() [2/4]

template<class real_type >

EllSparseBlockMat< real_type, thrust::host_vector > dg::create::dx	(	const RealGridX1d< real_type > &	g,
		direction	dir = centered )

Create and assemble a host Matrix for the derivative in 1d.

Take the boundary condition from the grid

Parameters

g	1D grid with X-point topology
dir	The direction of the first derivative

Returns: Host Matrix

◆ dx() [3/4]

template<class Topology >

auto dg::create::dx	(	const Topology &	g,
		dg::bc	bc,
		dg::direction	dir = centered )

Short for dg::create::derivative( 0, g, bc, dir);

◆ dx() [4/4]

template<class Topology >

auto dg::create::dx	(	const Topology &	g,
		dg::direction	dir = centered )

Short for dg::create::derivative( 0, g, g.bcx() dir);

◆ dy() [1/2]

template<class Topology >

auto dg::create::dy	(	const Topology &	g,
		dg::bc	bc,
		dg::direction	dir = centered )

Short for dg::create::derivative( 1, g, bc, dir);

◆ dy() [2/2]

template<class Topology >

auto dg::create::dy	(	const Topology &	g,
		dg::direction	dir = centered )

Short for dg::create::derivative( 1, g, g.bcy(), dir);

◆ dz() [1/2]

template<class Topology >

auto dg::create::dz	(	const Topology &	g,
		dg::bc	bc,
		dg::direction	dir = centered )

Short for dg::create::derivative( 2, g, bc, dir);

◆ dz() [2/2]

template<class Topology >

auto dg::create::dz	(	const Topology &	g,
		dg::direction	dir = centered )

Short for dg::create::derivative( 2, g, g.bcz(), dir);

◆ inverse() [1/2]

bc dg::inverse ( bc bound )

inline

invert boundary condition

Parameters

bound boundary condition to invert

Returns: NEU for DIR, DIR for NEU, NEU_DIR for DIR_NEU, DIR_NEU for NEU_DIR and PER for PER

◆ inverse() [2/2]

direction dg::inverse ( direction dir )

inline

invert direction

Parameters

dir	direction to invert

Returns: backward for forward, forward for backward, centered for centered

◆ jump() [1/7]

template<class real_type >

EllSparseBlockMat< real_type, thrust::host_vector > dg::create::jump ( const RealGridX1d< real_type > & g )

Create and assemble a host Matrix for the jump in 1d.

Take the boundary condition from the grid

Parameters

g	1D grid with X-point topology

Returns: Host Matrix

◆ jump() [2/7]

template<class real_type >

EllSparseBlockMat< real_type, thrust::host_vector > dg::create::jump	(	const RealGridX1d< real_type > &	g,
		bc	bcx )

Create and assemble a host Matrix for the jump in 1d.

Parameters

g	1D grid with X-point topology
bcx	boundary condition

Returns: Host Matrix

◆ jump() [3/7]

template<class real_type , size_t Nd>

dg::MHMatrix_t< real_type > dg::create::jump	(	unsigned	coord,
		const aRealMPITopology< real_type, Nd > &	g,
		dg::bc	bc )

Create a jump matrix along given coordinate for mpi.

Parameters

coord	the coordinate along which to jump
g	The mpi grid on which to create jump
bc	The boundary condition

Returns: A mpi matrix

◆ jump() [4/7]

template<class real_type , size_t Nd>

EllSparseBlockMat< real_type, thrust::host_vector > dg::create::jump	(	unsigned	coord,
		const aRealTopology< real_type, Nd > &	g,
		dg::bc	bc )

Create a jump matrix along given coordinate.

Parameters

coord	the coordinate along which to jump
g	The grid on which to create jump
bc	The boundary condition

Returns: A host matrix

◆ jump() [5/7]

template<class real_type >

Composite< EllSparseBlockMat< real_type, thrust::host_vector > > dg::create::jump	(	unsigned	coord,
		const aRealTopologyX2d< real_type > &	g,
		bc	bc )

Matrix that contains 2d jump terms in X direction.

Parameters

coord	Either 0 (for x derivative) or 1 (for y derivative)
g	grid
bc	boundary condition in x

Returns: A host matrix

◆ jump() [6/7]

template<class real_type >

Composite< EllSparseBlockMat< real_type, thrust::host_vector > > dg::create::jump	(	unsigned	coord,
		const aRealTopologyX3d< real_type > &	g,
		bc	bc )

Matrix that contains jump terms in X direction in 3D.

Parameters

coord	Either 0 (for x derivative) or 1 (for y derivative) or 2 (for z derivative)
g	The 3D grid
bc	boundary condition

Returns: A host matrix

◆ jump() [7/7]

template<class Topology >

auto dg::create::jump	(	unsigned	coord,
		const Topology &	g )

Short for dg::create::jump( coord, g, g.bcx());

◆ jumpX() [1/2]

template<class Topology >

auto dg::create::jumpX ( const Topology & g )

Short for dg::create::jump( 0, g, g.bcx());

◆ jumpX() [2/2]

template<class Topology >

auto dg::create::jumpX	(	const Topology &	g,
		bc	bc )

Short for dg::create::jump( 0, g, bc);

◆ jumpY() [1/2]

template<class Topology >

auto dg::create::jumpY ( const Topology & g )

Short for dg::create::jump( 1, g, g.bcy());

◆ jumpY() [2/2]

template<class Topology >

auto dg::create::jumpY	(	const Topology &	g,
		bc	bc )

Short for dg::create::jump( 1, g, bc);

◆ jumpZ() [1/2]

template<class Topology >

auto dg::create::jumpZ ( const Topology & g )

Short for dg::create::jump( 2, g, g.bcz());

◆ jumpZ() [2/2]

template<class Topology >

auto dg::create::jumpZ	(	const Topology &	g,
		bc	bc )

Short for dg::create::jump( 2, g, bc);

◆ str2bc()

bc dg::str2bc ( std::string s )

inline

convert a string to a bc

converts

PER, per, periodic, PERIODIC and Periodic to dg::PER
DIR, dir, dirichlet, DIRICHLET and Dirichlet to dg::DIR
NEU, neu, neumann, NEUMANN and Neumann to dg::NEU
NEU_DIR and neu_dir to dg::NEU_DIR
DIR_NEU and dir_neu to dg::DIR_NEU

Parameters

s	the input string

Returns: a valid boundary condition

Exceptions

std::runtime_error if string doesn't match any of the above

◆ str2direction()

direction dg::str2direction ( std::string s )

inline

convert a string to a direction

converts

"forward" to forward
"backward" to backward
"centered" to centered

Parameters

s	the input string

Returns: a valid direction

Exceptions

std::runtime_error if string doesn't match any of the above

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ bc

◆ coo2d

◆ coo3d

◆ direction

◆ space

Function Documentation

◆ bc2str()

◆ derivative() [1/5]

◆ derivative() [2/5]

◆ derivative() [3/5]

◆ derivative() [4/5]

◆ derivative() [5/5]

◆ direction2str()

◆ dx() [1/4]

◆ dx() [2/4]

◆ dx() [3/4]

◆ dx() [4/4]

◆ dy() [1/2]

◆ dy() [2/2]

◆ dz() [1/2]

◆ dz() [2/2]

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ jump() [1/7]

◆ jump() [2/7]

◆ jump() [3/7]

◆ jump() [4/7]

◆ jump() [5/7]

◆ jump() [6/7]

◆ jump() [7/7]

◆ jumpX() [1/2]

◆ jumpX() [2/2]

◆ jumpY() [1/2]

◆ jumpY() [2/2]

◆ jumpZ() [1/2]

◆ jumpZ() [2/2]

◆ str2bc()

◆ str2direction()