An abstract base class for MPI distributed Nd-dimensional dG grids. More...

Inheritance diagram for dg::aRealMPITopology< real_type, Nd >:

Public Types
using	value_type = real_type
	value type of abscissas and weights

using	host_vector = MPI_Vector<thrust::host_vector<real_type>>

using	host_grid = RealMPIGrid<real_type, Nd>

Public Member Functions
unsigned	shape (unsigned u=0) const
	\( n_u N_u\) the total number of points of an axis

host_vector	abscissas (unsigned u=0) const
	Get the grid abscissas of the `u` axis.

host_vector	weights (unsigned u=0) const
	Get the weights of the `u` axis.

std::array< unsigned, Nd >	get_shape () const
	\( n_u N_u\) the total number of points of an axis

std::array< host_vector, Nd >	get_abscissas () const
	Construct abscissas for all axes.

std::array< host_vector, Nd >	get_weights () const
	Construct weights for all axes.

std::array< real_type, Nd >	get_p () const
	Get left boundary point \( \vec p\).

std::array< real_type, Nd >	get_q () const
	Get right boundary point \( \vec q\).

std::array< real_type, Nd >	get_l () const
	Get grid length \( l_u = q_u - p_u\) for all axes.

std::array< real_type, Nd >	get_h () const
	Get grid constant \( h_u = \frac{q_u - p_u}{N_u}\) for all axes.

std::array< unsigned, Nd >	get_N () const
	Get number of cells \( N_u\) for all axes.

std::array< unsigned, Nd >	get_n () const
	Get number of polynomial coefficients \( n_u\) for all axes.

std::array< dg::bc, Nd >	get_bc () const
	Get boundary condition \( b_u\) for all axes.

std::array< MPI_Comm, Nd >	get_comms () const
	Get 1d Cartesian communicator \( c_u\) for all axes.

real_type	p (unsigned u=0) const
	Get left boundary point \( p_u\) for axis `u`.

real_type	q (unsigned u=0) const
	Get right boundary point \( q_u\) for axis `u`.

real_type	h (unsigned u=0) const
	Get grid constant \( h_u = \frac{q_u - p_u}{N_u}\) for axis `u`.

real_type	l (unsigned u=0) const
	Get grid length \( l_u = q_u - p_u\) for axis `u`.

unsigned	n (unsigned u=0) const
	Get number of polynomial coefficients \( n_u\) for axis `u`.

unsigned	N (unsigned u=0) const
	Get number of cells \( N_u\) for axis `u`.

dg::bc	bc (unsigned u=0) const
	Get boundary condition \( b_u\) for axis `u`.

MPI_Comm	comm (unsigned u) const
	Get 1d Cartesian communicator \( c_u\) for axis `u`.

template<size_t Md = Nd>
std::enable_if_t< Md==1, MPI_Comm >	comm () const
	Equivalent to `comm(0)`

MPI_Comm	communicator () const
	Return Nd dimensional MPI cartesian communicator that is used in this grid.

template<size_t Md = Nd>
std::enable_if_t<(Md >=2), MPI_Comm >	get_perp_comm () const
	MPI Cartesian communicator in the first two dimensions (x and y)

RealMPIGrid< real_type, 1 >	grid (unsigned u) const
	Get axis `u` as a 1d grid.

RealMPIGrid< real_type, 1 >	axis (unsigned u) const
	An alias for "grid".

const RealGrid< real_type, Nd > &	local () const
	The local grid as a shared memory grid.

const RealGrid< real_type, Nd > &	global () const
	The global grid as a shared memory grid.

template<size_t Md = Nd>
real_type	x0 () const
	Equivalent to `p(0)`

template<size_t Md = Nd>
real_type	x1 () const
	Equivalent to `p(1)`

template<size_t Md = Nd>
real_type	y0 () const
	Equivalent to `p(2)`

template<size_t Md = Nd>
real_type	y1 () const
	Equivalent to `q(0)`

template<size_t Md = Nd>
real_type	z0 () const
	Equivalent to `q(1)`

template<size_t Md = Nd>
real_type	z1 () const
	Equivalent to `q(2)`

template<size_t Md = Nd>
real_type	lx () const
	Equivalent to `l(0)`

template<size_t Md = Nd>
real_type	ly () const
	Equivalent to `l(1)`

template<size_t Md = Nd>
real_type	lz () const
	Equivalent to `l(2)`

template<size_t Md = Nd>
real_type	hx () const
	Equivalent to `h(0)`

template<size_t Md = Nd>
real_type	hy () const
	Equivalent to `h(1)`

template<size_t Md = Nd>
real_type	hz () const
	Equivalent to `h(2)`

template<size_t Md = Nd>
unsigned	nx () const
	Equivalent to `n(0)`

template<size_t Md = Nd>
unsigned	ny () const
	Equivalent to `n(1)`

template<size_t Md = Nd>
unsigned	nz () const
	Equivalent to `n(2)`

template<size_t Md = Nd>
unsigned	Nx () const
	Equivalent to `N(0)`

template<size_t Md = Nd>
unsigned	Ny () const
	Equivalent to `N(1)`

template<size_t Md = Nd>
unsigned	Nz () const
	Equivalent to `N(2)`

template<size_t Md = Nd>
dg::bc	bcx () const
	Equivalent to `bc(0)`

template<size_t Md = Nd>
dg::bc	bcy () const
	Equivalent to `bc(1)`

template<size_t Md = Nd>
dg::bc	bcz () const
	Equivalent to `bc(2)`

template<size_t Md = Nd>
RealMPIGrid< real_type, 1 >	gx () const
	Equivalent to `grid(0)`

template<size_t Md = Nd>
RealMPIGrid< real_type, 1 >	gy () const
	Equivalent to `grid(1)`

template<size_t Md = Nd>
RealMPIGrid< real_type, 1 >	gz () const
	Equivalent to `grid(2)`

template<size_t Md = Nd>
std::enable_if_t<(Md >=2), void >	multiplyCellNumbers (real_type fx, real_type fy)
	Multiply the number of cells in the first two dimensions with a given factor.

template<size_t Md = Nd>
std::enable_if_t<(Md==1), void >	set (unsigned new_n, unsigned new_Nx)
	Set n and N in a 1-dimensional grid.

template<size_t Md = Nd>
std::enable_if_t<(Md==2), void >	set (unsigned new_n, unsigned new_Nx, unsigned new_Ny)
	Set n and N in a 2-dimensional grid.

template<size_t Md = Nd>
std::enable_if_t<(Md==3), void >	set (unsigned new_n, unsigned new_Nx, unsigned new_Ny, unsigned new_Nz)
	Set n and N in a 3-dimensional grid.

void	set (unsigned new_n, std::array< unsigned, Nd > new_N)
	Same as `set( {new_n, new_n,...}, new_N);`

void	set_axis (unsigned coord, unsigned new_n, unsigned new_N)
	Set n and N for axis `coord`.

void	set (std::array< unsigned, Nd > new_n, std::array< unsigned, Nd > new_N)
	Set the number of polynomials and cells.

void	set_pq (std::array< real_type, Nd > new_p, std::array< real_type, Nd > new_q)
	Reset the boundaries of the grid.

void	set_bcs (std::array< dg::bc, Nd > new_bcs)
	Reset the boundary conditions of the grid.

unsigned	size () const
	The total global number of points.

unsigned	local_size () const
	The total local number of points.

void	display (std::ostream &os=std::cout) const
	Display global and local grid paramters.

template<size_t Md = Nd>
std::enable_if_t<(Md==1), bool >	contains (real_type x) const
	Check if the grid contains a point.

template<class Vector >
bool	contains (const Vector &x) const
	Check if the grid contains a point.

bool	local2globalIdx (int localIdx, int rank, int &globalIdx) const
	Convert the index of a local vector and the rank of the containing process to a global index.

bool	global2localIdx (int globalIdx, int &localIdx, int &rank) const
	Convert the global index of a vector to a local index and the rank of the containing process.

std::array< unsigned, Nd >	start () const
	The global start coordinate in C-order of `dg::file::MPINcHyperslab` that the local grid represents.

std::array< unsigned, Nd >	count () const
	Count vector in C-order for `dg::file::MPINcHyperslab`.

Static Public Member Functions
static constexpr unsigned	ndim ()
	Dimensionality == Nd.

Protected Member Functions
	~aRealMPITopology ()=default
	disallow deletion through base class pointer

	aRealMPITopology ()=default
	default constructor

	aRealMPITopology (std::array< real_type, Nd > p, std::array< real_type, Nd > q, std::array< unsigned, Nd > n, std::array< unsigned, Nd > N, std::array< dg::bc, Nd > bcs, std::array< MPI_Comm, Nd > comms)
	Construct a topology directly from points and dimensions.

	aRealMPITopology (const std::array< RealMPIGrid< real_type, 1 >, Nd > &axes)
	Construct a topology as the product of 1d axes grids.

	aRealMPITopology (const aRealMPITopology &src)=default

aRealMPITopology &	operator= (const aRealMPITopology &src)=default

virtual void	do_set (std::array< unsigned, Nd > new_n, std::array< unsigned, Nd > new_N)=0
	Set the number of polynomials and cells.

virtual void	do_set_pq (std::array< real_type, Nd > new_p, std::array< real_type, Nd > new_q)=0
	Reset the boundaries of the grid.

virtual void	do_set (std::array< dg::bc, Nd > new_bcs)=0
	Reset the boundary conditions of the grid.

Detailed Description

template<class real_type, size_t Nd>
struct dg::aRealMPITopology< real_type, Nd >

An abstract base class for MPI distributed Nd-dimensional dG grids.

grids vs MPI grids

In the dg library we have MPI grids as a separate type from shared memory grids. The design goal is that MPI grids generally can be used the same way as just a single global shared memory grid. A notable exception is the constructor, when MPI grids depend on a Cartesian MPI communicator (that has to be constructed beforehand with e.g. dg::mpi_cart_create)

Shared memory considerations

This grid defines a discretization of the \(N_d\) dimensional hypercube given by

\[ [\vec p, \vec q] = [p_0, p_1] \times [p_1,q_1] \times ... \times [p_{N_d-1}, q_{N_d-1}]\]

Each axis \( [p_i, q_i] \) is discretized using \( N_i\) equidistant cells. Each cells is then further discretized using \( n_i\) Gauss-Legendre nodes. The Gauss-Legendre nodes are tabulated by the dg::DLT class for \( 1\leq n_i \leq 20\). Each axis further can have a boundary condition \( b_i \) that is given by dg::bc For more information dG methods see

See also: Introduction to dg methods

Distributed memory considerations

In MPI we want to distribute the above hypercube among processes in a Cartesian communicator of same dimensionality \( N_d\). This is done by evenly distributing the global number of cells \( N_u\) in each dimension among the processes in the corresponding dimension in the Cartesian communicator. Each process gets a local number of cells \( N_{ur} \approx N_u / s_u\), where \( s_u \) is the size of the Cartesian communicator in direction \( u\). The approximation becomes an equality if \( s_u\) evenly divides \( N_u\) otherwise the remainder is distributed among the participating processes (such that some have one cell more or less than others). We have

\[ N_u = \sum_{r=0}^{s-1} N_{ur}\]

The number of polynomial coefficients and the boundary condition is the same for all processes of an axis. Each axis among processes is thus

\[ [p_u,q_u] = [p_{u0}, q_{u0}],[p_{u1}, q_{u1}],...,[p_{us-1}, q_{us-1}] \]

The local boundaries are determined such that the local \( h_{ur} = \frac{q_{ur}-p_{ur}}{N_{ur}} = \frac{q_u-p_u}{N_u}\)

Overview

This class in essence provides a collection of getters and setters for the aforementioned parameters together with the abscissas and weights members that are necessary for dg::evaluate and dg::create::weights.

For code readability in many physical contexts the first 3 dimensions get special names \( x,\ y,\ z\) i.e. \( \vec p = (x_0, y_0, z_0)\) and \( \vec q = (x_1, y_1, z_1)\). The class provides coresponding getters and setters like e.g. x0() or Nx() for p(0) and N(0)

Note: Unless otherwise indicate the getters and setters refer to the global grid quantities. If access to local quantities is needed we have the local() function, which provides a grid with all local quantities

Lastly, we provide start and count members such that the grid can be used as a dg::file::MPINcHyperslab in NetCDF output in dg::file

Template Parameters

real_type	Determines value type of abscissas and weights
Nd	The number of dimensions \( N_d\)

Member Typedef Documentation

◆ host_grid

template<class real_type , size_t Nd>

using dg::aRealMPITopology< real_type, Nd >::host_grid = RealMPIGrid<real_type, Nd>

◆ host_vector

template<class real_type , size_t Nd>

using dg::aRealMPITopology< real_type, Nd >::host_vector = MPI_Vector<thrust::host_vector<real_type>>

vector type of abscissas and weights; Can be used to recognize MPI grid via: dg::is_vector_v< typename Topology::host_vector, MPIVectorTag>

◆ value_type

template<class real_type , size_t Nd>

using dg::aRealMPITopology< real_type, Nd >::value_type = real_type

value type of abscissas and weights

Constructor & Destructor Documentation

◆ ~aRealMPITopology()

template<class real_type , size_t Nd>

dg::aRealMPITopology< real_type, Nd >::~aRealMPITopology ( )

protecteddefault

disallow deletion through base class pointer

◆ aRealMPITopology() [1/4]

template<class real_type , size_t Nd>

dg::aRealMPITopology< real_type, Nd >::aRealMPITopology ( )

protecteddefault

default constructor

◆ aRealMPITopology() [2/4]

template<class real_type , size_t Nd>

dg::aRealMPITopology< real_type, Nd >::aRealMPITopology	(	std::array< real_type, Nd >	p,
		std::array< real_type, Nd >	q,
		std::array< unsigned, Nd >	n,
		std::array< unsigned, Nd >	N,
		std::array< dg::bc, Nd >	bcs,
		std::array< MPI_Comm, Nd >	comms )

inlineprotected

Construct a topology directly from points and dimensions.

Parameters

p	left boundary point
q	right boundary point
n	number of polynomial coefficients for each axis
N	number of cells for each axis
bcs	boundary condition for each axis
comms	The 1d MPI Cartesian communicators for each axis that make up an Nd dimensional Cartesian communicator (see `dg::mpi_cart_split`, `dg::mpi_cart_kron`)

◆ aRealMPITopology() [3/4]

template<class real_type , size_t Nd>

dg::aRealMPITopology< real_type, Nd >::aRealMPITopology ( const std::array< RealMPIGrid< real_type, 1 >, Nd > & axes )

inlineprotected

Construct a topology as the product of 1d axes grids.

Parameters

axes	One-dimensional grids for each dimension

◆ aRealMPITopology() [4/4]

template<class real_type , size_t Nd>

dg::aRealMPITopology< real_type, Nd >::aRealMPITopology ( const aRealMPITopology< real_type, Nd > & src )

protecteddefault

explicit copy constructor (default)

Parameters

src source

Member Function Documentation

◆ abscissas()

template<class real_type , size_t Nd>

host_vector dg::aRealMPITopology< real_type, Nd >::abscissas ( unsigned u = 0 ) const

inline

Get the grid abscissas of the u axis.

Note: In MPI there is a strong guarantee that the returned abscissas correspond binary exactly to the shared memory abscissas returned by global() grid.

Parameters

u	Axis number `u<Nd`

Returns: Vector containing abscissas

See also: dg::evaluate

◆ axis()

template<class real_type , size_t Nd>

RealMPIGrid< real_type, 1 > dg::aRealMPITopology< real_type, Nd >::axis ( unsigned u ) const

inline

An alias for "grid".

Parameters

u	Axis number `u<Nd`

Returns: One dimensional grid

◆ bc()

template<class real_type , size_t Nd>

dg::bc dg::aRealMPITopology< real_type, Nd >::bc ( unsigned u = 0 ) const

inline

Get boundary condition \( b_u\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: Value for axis u

◆ bcx()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::bc dg::aRealMPITopology< real_type, Nd >::bcx ( ) const

inline

Equivalent to bc(0)

◆ bcy()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::bc dg::aRealMPITopology< real_type, Nd >::bcy ( ) const

inline

Equivalent to bc(1)

◆ bcz()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

dg::bc dg::aRealMPITopology< real_type, Nd >::bcz ( ) const

inline

Equivalent to bc(2)

◆ comm() [1/2]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

std::enable_if_t< Md==1, MPI_Comm > dg::aRealMPITopology< real_type, Nd >::comm ( ) const

inline

Equivalent to comm(0)

◆ comm() [2/2]

template<class real_type , size_t Nd>

MPI_Comm dg::aRealMPITopology< real_type, Nd >::comm ( unsigned u ) const

inline

Get 1d Cartesian communicator \( c_u\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: MPI Cartesian communicator

◆ communicator()

template<class real_type , size_t Nd>

MPI_Comm dg::aRealMPITopology< real_type, Nd >::communicator ( ) const

inline

Return Nd dimensional MPI cartesian communicator that is used in this grid.

Returns: Communicator

◆ contains() [1/2]

template<class real_type , size_t Nd>

template<class Vector >

bool dg::aRealMPITopology< real_type, Nd >::contains ( const Vector & x ) const

inline

Check if the grid contains a point.

Used for example in integrate_in_domain method of dg::AdaptiveTimeloop

Note: doesn't check periodicity!!

Parameters

x	point to check

Returns: true if p0[u]<=x[u]<=p1[u] for all u, false else

Attention: returns false if x[u] is NaN or INF

◆ contains() [2/2]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

std::enable_if_t<(Md==1), bool > dg::aRealMPITopology< real_type, Nd >::contains ( real_type x ) const

inline

Check if the grid contains a point.

Used for example in integrate_in_domain method of dg::AdaptiveTimeloop

Note: doesn't check periodicity!!

Parameters

x	point to check

Returns: true if p0[u]<=x[u]<=p1[u] for all u, false else

Attention: returns false if x[u] is NaN or INF

◆ count()

template<class real_type , size_t Nd>

std::array< unsigned, Nd > dg::aRealMPITopology< real_type, Nd >::count ( ) const

inline

Count vector in C-order for dg::file::MPINcHyperslab.

Used to construct dg::file::MPINcHyperslab together with start()

Returns: local().count()

Note: In C-order the fastest dimension is the last one while our dg::evaluate and dg::kronecker make the 0 dimension/ 1st argument the fastest varying, so we return the reverse order of local().get_shape()

◆ display()

template<class real_type , size_t Nd>

void dg::aRealMPITopology< real_type, Nd >::display ( std::ostream & os = std::cout ) const

inline

Display global and local grid paramters.

Parameters

os	output stream

◆ do_set() [1/2]

template<class real_type , size_t Nd>

virtual void dg::aRealMPITopology< real_type, Nd >::do_set ( std::array< dg::bc, Nd > new_bcs )

protectedpure virtual

Reset the boundary conditions of the grid.

Parameters

new_bcs new boundary condition

◆ do_set() [2/2]

template<class real_type , size_t Nd>

virtual void dg::aRealMPITopology< real_type, Nd >::do_set	(	std::array< unsigned, Nd >	new_n,
		std::array< unsigned, Nd >	new_N )

protectedpure virtual

Set the number of polynomials and cells.

Parameters

new_n	new number of Gaussian nodes in each dimension
new_N	new number of cells in each dimension

◆ do_set_pq()

template<class real_type , size_t Nd>

virtual void dg::aRealMPITopology< real_type, Nd >::do_set_pq	(	std::array< real_type, Nd >	new_p,
		std::array< real_type, Nd >	new_q )

protectedpure virtual

Reset the boundaries of the grid.

Parameters

new_p	new left boundary
new_q	new right boundary ( > x0)

◆ get_abscissas()

template<class real_type , size_t Nd>

std::array< host_vector, Nd > dg::aRealMPITopology< real_type, Nd >::get_abscissas ( ) const

inline

Construct abscissas for all axes.

Returns: \( \vec a_u\) for all \( u < N_d\)

◆ get_bc()

template<class real_type , size_t Nd>

std::array< dg::bc, Nd > dg::aRealMPITopology< real_type, Nd >::get_bc ( ) const

inline

Get boundary condition \( b_u\) for all axes.

Returns: Boundary condition \( b_u\) for all u

◆ get_comms()

template<class real_type , size_t Nd>

std::array< MPI_Comm, Nd > dg::aRealMPITopology< real_type, Nd >::get_comms ( ) const

inline

Get 1d Cartesian communicator \( c_u\) for all axes.

Returns: 1d Cartesian communicator \( c_u\) for all u

◆ get_h()

template<class real_type , size_t Nd>

std::array< real_type, Nd > dg::aRealMPITopology< real_type, Nd >::get_h ( ) const

inline

Get grid constant \( h_u = \frac{q_u - p_u}{N_u}\) for all axes.

Returns: Grid constant \( h_u\) for all u

◆ get_l()

template<class real_type , size_t Nd>

std::array< real_type, Nd > dg::aRealMPITopology< real_type, Nd >::get_l ( ) const

inline

Get grid length \( l_u = q_u - p_u\) for all axes.

Returns: Grid length \( l_u\) for all u

◆ get_N()

template<class real_type , size_t Nd>

std::array< unsigned, Nd > dg::aRealMPITopology< real_type, Nd >::get_N ( ) const

inline

Get number of cells \( N_u\) for all axes.

Returns: Number of cells \( N_u\) for all u

◆ get_n()

template<class real_type , size_t Nd>

std::array< unsigned, Nd > dg::aRealMPITopology< real_type, Nd >::get_n ( ) const

inline

Get number of polynomial coefficients \( n_u\) for all axes.

Returns: Number of polynomial coefficients \( n_u\) for all u

◆ get_p()

template<class real_type , size_t Nd>

std::array< real_type, Nd > dg::aRealMPITopology< real_type, Nd >::get_p ( ) const

inline

Get left boundary point \( \vec p\).

Returns: Left boundary \( \vec p\)

◆ get_perp_comm()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

std::enable_if_t<(Md >=2), MPI_Comm > dg::aRealMPITopology< real_type, Nd >::get_perp_comm ( ) const

inline

MPI Cartesian communicator in the first two dimensions (x and y)

Returns: 2d Cartesian Communicator

◆ get_q()

template<class real_type , size_t Nd>

std::array< real_type, Nd > dg::aRealMPITopology< real_type, Nd >::get_q ( ) const

inline

Get right boundary point \( \vec q\).

Returns: right boundary \( \vec q\)

◆ get_shape()

template<class real_type , size_t Nd>

std::array< unsigned, Nd > dg::aRealMPITopology< real_type, Nd >::get_shape ( ) const

inline

\( n_u N_u\) the total number of points of an axis

Returns: \( n_u N_u\) for all \( u < N_d\)

◆ get_weights()

template<class real_type , size_t Nd>

std::array< host_vector, Nd > dg::aRealMPITopology< real_type, Nd >::get_weights ( ) const

inline

Construct weights for all axes.

Returns: \( \vec w_u\) for all \( u < N_d\)

◆ global()

template<class real_type , size_t Nd>

const RealGrid< real_type, Nd > & dg::aRealMPITopology< real_type, Nd >::global ( ) const

inline

The global grid as a shared memory grid.

Returns: Global grid

◆ global2localIdx()

template<class real_type , size_t Nd>

bool dg::aRealMPITopology< real_type, Nd >::global2localIdx	(	int	globalIdx,
		int &	localIdx,
		int &	rank ) const

inline

Convert the global index of a vector to a local index and the rank of the containing process.

Note: All calling processes will get the same result

Parameters

globalIdx	Global index of the element
localIdx	(write only) Index in a local chunk of a vector
rank	(write only) Rank of the process that contains the globalIdx

See also: The main usage of this function is dg::make_mpi_matrix and dg::global2local

◆ grid()

template<class real_type , size_t Nd>

RealMPIGrid< real_type, 1 > dg::aRealMPITopology< real_type, Nd >::grid ( unsigned u ) const

inline

Get axis u as a 1d grid.

Parameters

u	Axis number `u<Nd`

Returns: One dimensional grid

◆ gx()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

RealMPIGrid< real_type, 1 > dg::aRealMPITopology< real_type, Nd >::gx ( ) const

inline

Equivalent to grid(0)

◆ gy()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

RealMPIGrid< real_type, 1 > dg::aRealMPITopology< real_type, Nd >::gy ( ) const

inline

Equivalent to grid(1)

◆ gz()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

RealMPIGrid< real_type, 1 > dg::aRealMPITopology< real_type, Nd >::gz ( ) const

inline

Equivalent to grid(2)

◆ h()

template<class real_type , size_t Nd>

real_type dg::aRealMPITopology< real_type, Nd >::h ( unsigned u = 0 ) const

inline

Get grid constant \( h_u = \frac{q_u - p_u}{N_u}\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: Value for axis u

◆ hx()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

real_type dg::aRealMPITopology< real_type, Nd >::hx ( ) const

inline

Equivalent to h(0)

◆ hy()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

real_type dg::aRealMPITopology< real_type, Nd >::hy ( ) const

inline

Equivalent to h(1)

◆ hz()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

real_type dg::aRealMPITopology< real_type, Nd >::hz ( ) const

inline

Equivalent to h(2)

◆ l()

template<class real_type , size_t Nd>

real_type dg::aRealMPITopology< real_type, Nd >::l ( unsigned u = 0 ) const

inline

Get grid length \( l_u = q_u - p_u\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: Value for axis u

◆ local()

template<class real_type , size_t Nd>

const RealGrid< real_type, Nd > & dg::aRealMPITopology< real_type, Nd >::local ( ) const

inline

The local grid as a shared memory grid.

Returns: Local grid

◆ local2globalIdx()

template<class real_type , size_t Nd>

bool dg::aRealMPITopology< real_type, Nd >::local2globalIdx	(	int	localIdx,
		int	rank,
		int &	globalIdx ) const

inline

Convert the index of a local vector and the rank of the containing process to a global index.

Note: All calling processes will get the same result

Parameters

localIdx	Index in a local chunk of a vector
rank	Rank of the process that contains the localIdx
globalIdx	(write only) Global index of the element

See also: The main usage of this function is dg::make_mpi_matrix and dg::global2local

◆ local_size()

template<class real_type , size_t Nd>

unsigned dg::aRealMPITopology< real_type, Nd >::local_size ( ) const

inline

The total local number of points.

Returns: local().size()

◆ lx()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

real_type dg::aRealMPITopology< real_type, Nd >::lx ( ) const

inline

Equivalent to l(0)

◆ ly()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

real_type dg::aRealMPITopology< real_type, Nd >::ly ( ) const

inline

Equivalent to l(1)

◆ lz()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

real_type dg::aRealMPITopology< real_type, Nd >::lz ( ) const

inline

Equivalent to l(2)

◆ multiplyCellNumbers()

template<class real_type , size_t Nd>

template<size_t Md = Nd>

std::enable_if_t<(Md >=2), void > dg::aRealMPITopology< real_type, Nd >::multiplyCellNumbers	(	real_type	fx,
		real_type	fy )

inline

Multiply the number of cells in the first two dimensions with a given factor.

With this function you can resize the grid ignorantly of its current size

Parameters

fx	new global number of cells is fx*Nx()
fy	new global number of cells is fy*Ny() The remaining dimensions are left unchanged

◆ N()

template<class real_type , size_t Nd>

unsigned dg::aRealMPITopology< real_type, Nd >::N ( unsigned u = 0 ) const

inline

Get number of cells \( N_u\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: Value for axis u

◆ n()

template<class real_type , size_t Nd>

unsigned dg::aRealMPITopology< real_type, Nd >::n ( unsigned u = 0 ) const

inline

Get number of polynomial coefficients \( n_u\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: Value for axis u

template<class real_type , size_t Nd>

aRealMPITopology & dg::aRealMPITopology< real_type, Nd >::operator= ( const aRealMPITopology< real_type, Nd > & src )

protecteddefault

explicit assignment operator (default)

Parameters

src source

◆ p()

template<class real_type , size_t Nd>

real_type dg::aRealMPITopology< real_type, Nd >::p ( unsigned u = 0 ) const

inline

Get left boundary point \( p_u\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: Value for axis u

◆ q()

template<class real_type , size_t Nd>

real_type dg::aRealMPITopology< real_type, Nd >::q ( unsigned u = 0 ) const

inline

Get right boundary point \( q_u\) for axis u.

Parameters

u	Axis number `u<Nd`

Returns: Value for axis u

◆ set() [1/5]

template<class real_type , size_t Nd>

void dg::aRealMPITopology< real_type, Nd >::set	(	std::array< unsigned, Nd >	new_n,
		std::array< unsigned, Nd >	new_N )

inline

Set the number of polynomials and cells.

Parameters

new_n	new number of Gaussian nodes in each dimension
new_N	new number of cells in each dimension

◆ set() [2/5]

template<class real_type , size_t Nd>

void dg::aRealMPITopology< real_type, Nd >::set	(	unsigned	new_n,
		std::array< unsigned, Nd >	new_N )

inline

Same as set( {new_n, new_n,...}, new_N);

◆ set() [3/5]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

std::enable_if_t<(Md==1), void > dg::aRealMPITopology< real_type, Nd >::set	(	unsigned	new_n,
		unsigned	new_Nx )

inline

Set n and N in a 1-dimensional grid.

Parameters

new_n	new number of Gaussian nodes
new_Nx	new number of cells

◆ set() [4/5]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

std::enable_if_t<(Md==2), void > dg::aRealMPITopology< real_type, Nd >::set	(	unsigned	new_n,
		unsigned	new_Nx,
		unsigned	new_Ny )

inline

Set n and N in a 2-dimensional grid.

Parameters

new_n	new number of Gaussian nodes in x and y
new_Nx	new number of cells
new_Ny	new number of cells

◆ set() [5/5]

template<class real_type , size_t Nd>

template<size_t Md = Nd>

std::enable_if_t<(Md==3), void > dg::aRealMPITopology< real_type, Nd >::set	(	unsigned	new_n,
		unsigned	new_Nx,
		unsigned	new_Ny,
		unsigned	new_Nz )

inline

Set n and N in a 3-dimensional grid.

Same as set({new_n,new_n,1}, {new_Nx,new_Ny,new_Nz})

Parameters

new_n new number of Gaussian nodes in x and y

Attention: Set nz to 1

Parameters

new_Nx	new number of cells in x
new_Ny	new number of cells in y
new_Nz	new number of cells in z

◆ set_axis()

template<class real_type , size_t Nd>

void dg::aRealMPITopology< real_type, Nd >::set_axis	(	unsigned	coord,
		unsigned	new_n,
		unsigned	new_N )

inline

Set n and N for axis coord.

Parameters

coord	Axis `coord<Nd`
new_n	new number of Gaussian nodes of axis `coord`
new_N	new number of cells

◆ set_bcs()

template<class real_type , size_t Nd>

void dg::aRealMPITopology< real_type, Nd >::set_bcs ( std::array< dg::bc, Nd > new_bcs )

inline

Reset the boundary conditions of the grid.

Parameters

new_bcs new boundary condition

◆ set_pq()

template<class real_type , size_t Nd>

void dg::aRealMPITopology< real_type, Nd >::set_pq	(	std::array< real_type, Nd >	new_p,
		std::array< real_type, Nd >	new_q )

inline

Reset the boundaries of the grid.

Parameters

new_p	new left boundary
new_q	new right boundary ( > x0)

◆ shape()

template<class real_type , size_t Nd>

unsigned dg::aRealMPITopology< real_type, Nd >::shape ( unsigned u = 0 ) const

inline

\( n_u N_u\) the total number of points of an axis

Parameters

u	Axis number `u<Nd`

Returns: \( n_u N_u\)

◆ size()

template<class real_type , size_t Nd>

unsigned dg::aRealMPITopology< real_type, Nd >::size ( ) const

inline

The total global number of points.

Returns: \( \prod_{i=0}^{N-1} n_i N_i\)

◆ start()

template<class real_type , size_t Nd>

std::array< unsigned, Nd > dg::aRealMPITopology< real_type, Nd >::start ( ) const

inline

The global start coordinate in C-order of dg::file::MPINcHyperslab that the local grid represents.

Used to construct dg::file::MPINcHyperslab together with count()

Returns: global start coordinates of the local grid in C-order

Note: In C-order the fastest dimension is the last one while our dg::evaluate and dg::kronecker make the 0 dimension/ 1st argument the fastest varying.

◆ weights()

template<class real_type , size_t Nd>

host_vector dg::aRealMPITopology< real_type, Nd >::weights ( unsigned u = 0 ) const

inline

Get the weights of the u axis.

Note: In MPI there is a strong guarantee that the returned weights correspond binary exactly to the shared memory weights returned by global() grid.

Parameters

u	Axis number `u<Nd`

Returns: Vector containing weights

See also: dg::create::weights dg::DLT

The documentation for this struct was generated from the following file:

topology/mpi_grid.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

grids vs MPI grids

Shared memory considerations

Distributed memory considerations

Overview

Member Typedef Documentation

◆ host_grid

◆ host_vector

◆ value_type

Constructor & Destructor Documentation

◆ ~aRealMPITopology()

◆ aRealMPITopology() [1/4]

◆ aRealMPITopology() [2/4]

◆ aRealMPITopology() [3/4]

◆ aRealMPITopology() [4/4]

Member Function Documentation

◆ abscissas()

◆ axis()

◆ bc()

◆ bcx()

◆ bcy()

◆ bcz()

◆ comm() [1/2]

◆ comm() [2/2]

◆ communicator()

◆ contains() [1/2]

◆ contains() [2/2]

◆ count()

◆ display()

◆ do_set() [1/2]

◆ do_set() [2/2]

◆ do_set_pq()

◆ get_abscissas()

◆ get_bc()

◆ get_comms()

◆ get_h()

◆ get_l()

◆ get_N()

◆ get_n()

◆ get_p()

◆ get_perp_comm()

◆ get_q()

◆ get_shape()

◆ get_weights()

◆ global()

◆ global2localIdx()

◆ grid()

◆ gx()

◆ gy()

◆ gz()

◆ h()

◆ hx()

◆ hy()

◆ hz()

◆ l()

◆ local()

◆ local2globalIdx()

◆ local_size()

◆ lx()

◆ ly()

◆ lz()

◆ multiplyCellNumbers()

◆ N()

◆ n()

◆ ndim()

◆ Nx()

◆ nx()

◆ Ny()

◆ ny()

◆ Nz()

◆ nz()

◆ operator=()

◆ p()

◆ q()

◆ set() [1/5]

◆ set() [2/5]