This is the namespace for all functions and classes defined and used by the discontinuous Galerkin library. More...

Namespaces
namespace	blas1
	BLAS Level 1 routines.

namespace	blas2
	BLAS Level 2 routines.

namespace	create
	Contains functions used for matrix creation.

namespace	exblas

namespace	geo

namespace	mat

namespace	tensor
	Utility functions used in connection with the SparseTensor class.

namespace	x

Classes
struct	ABS
	\( f(x) = \|x\|\) More...

struct	AbsMax
	\( f(x,y) = \max(\|x\|,\|y\|)\) More...

struct	AbsMin
	\( f(x,y) = \min(\|x\|,\|y\|)\) More...

struct	aCommunicator
	Struct that performs collective scatter and gather operations across processes on distributed vectors using MPI. More...

struct	Adaptive
	Driver class for adaptive timestep ODE integration. More...

struct	AdaptiveTimeloop
	Integrate using a while loop. More...

struct	Advection
	Upwind discretization of advection operator \( \vec v\cdot\nabla f\) More...

struct	AndersonAcceleration
	Anderson Acceleration of Fixed Point/Richardson Iteration for the nonlinear equation \( f(x) = b\). More...

struct	AnyMatrixTag
	tensor_category base class More...

struct	AnyPolicyTag
	Execution Policy base class. More...

struct	AnyScalarTag
	Scalar Tag base class, indicates the basic Scalar Tensor concept. More...

struct	AnyVectorTag
	Vector Tag base class, indicates the basic Vector/container concept. More...

struct	ArakawaX
	Arakawa's scheme for Poisson bracket \( \{ f,g\} \). More...

struct	aRealGeometry2d
	This is the abstract interface class for a two-dimensional Geometry. More...

struct	aRealGeometry3d
	This is the abstract interface class for a three-dimensional Geometry. More...

struct	aRealGeometryX2d
	This is the abstract interface class for a two-dimensional RealGeometryX. More...

struct	aRealGeometryX3d
	This is the abstract interface class for a three-dimensional RealGeometryX. More...

struct	aRealMPIGeometry2d
	This is the abstract interface class for a two-dimensional Geometry. More...

struct	aRealMPIGeometry3d
	This is the abstract interface class for a three-dimensional MPIGeometry. More...

struct	aRealMPITopology2d
	2D MPI abstract grid class More...

struct	aRealMPITopology3d
	3D MPI Grid class More...

struct	aRealProductGeometry3d
	A 3d product space Geometry \( g_{2d} \otimes g_{1d}\). More...

struct	aRealProductMPIGeometry3d
	A 3d product space Geometry \( g_{2d} \otimes g_{1d}\). More...

struct	aRealRefinement1d
	Abstract base class for 1d grid refinement that increases the number of grid cells of a fixed basis grid. More...

struct	aRealRefinementX2d
	Abstract base class for 2d grid refinement that increases the number of grid cells of a fixed basis grid. More...

struct	aRealTopology2d
	An abstract base class for two-dimensional grids. More...

struct	aRealTopology3d
	An abstract base class for three-dimensional grids. More...

struct	aRealTopologyX2d
	A 2D grid class with X-point topology. More...

struct	aRealTopologyX3d
	A 3D grid class with X-point topology. More...

struct	ARKStep
	Additive Runge Kutta (semi-implicit) time-step with error estimate following The ARKode library More...

struct	ArrayScalarTag

struct	ArrayVectorTag

struct	aTimeloop
	Abstract timeloop independent of stepper and ODE. More...

struct	Average
	Topological average computations in a Cartesian topology. More...

struct	Average< MPI_Vector< container > >
	MPI specialized class for average computations. More...

struct	Axpby
	\( y\leftarrow ax+by \) More...

struct	Axpbypgz
	\( z\leftarrow ax+by+gz \) More...

struct	AxyPby
	\( y\leftarrow axy+by \) More...

struct	BathRZ
	\(f(R,Z) = A B \sum_\vec{k} \sqrt{E_k} \alpha_k \cos{\left(k \kappa_k + \theta_k \right)} \) More...

class	BICGSTABl
	Preconditioned BICGSTAB(l) method to solve \( Ax=b\). More...

struct	BijectiveComm
	Perform bijective gather and its transpose (scatter) operation across processes on distributed vectors using mpi. More...

struct	Buffer
	a manager class that invokes the copy constructor on the managed ptr when copied (deep copy) More...

struct	ButcherTableau
	Manage coefficients of a (extended) Butcher tableau. More...

struct	Cauchy
	\( f(x,y) = \begin{cases} Ae^{1 + \left(\frac{(x-x_0)^2}{\sigma_x^2} + \frac{(y-y_0)^2}{\sigma_y^2} - 1\right)^{-1}} \text{ if } \frac{(x-x_0)^2}{\sigma_x^2} + \frac{(y-y_0)^2}{\sigma_y^2} < 1\\ 0 \text{ else} \end{cases} \) More...

struct	CauchyX
	\( f(x,y) = \begin{cases} Ae^{1 + \left(\frac{(x-x_0)^2}{\sigma_x^2} - 1\right)^{-1}} \text{ if } \frac{(x-x_0)^2}{\sigma_x^2} < 1\\ 0 \text{ else} \end{cases} \) More...

class	ChebyshevIteration
	Preconditioned Chebyshev iteration for solving \( PAx=Pb\). More...

struct	ChebyshevPreconditioner
	Chebyshev Polynomial Preconditioner \( C( A)\). More...

struct	ClonePtr
	Manager class that invokes the `clone()` method on the managed ptr when copied. More...

struct	Composite

struct	CONSTANT
	\( f(x) = f(x,y) = f(x,y,z) = c\) More...

struct	ConvertsToButcherTableau
	Convert identifiers to their corresponding `dg::ButcherTableau`. More...

struct	ConvertsToMultistepTableau
	Convert identifiers to their corresponding `dg::MultistepTableau`. More...

struct	ConvertsToShuOsherTableau
	Convert identifiers to their corresponding `dg::ShuOsherTableau`. More...

struct	CooSparseBlockMat
	Coo Sparse Block Matrix format. More...

struct	CosXCosY
	\( f(x,y) =B+ A \cos(k_x x) \cos(k_y y) \) More...

struct	CosY
	\( f(x,y) =B+ A \cos(k_y y) \) More...

struct	CSRAverageFilter
	Average filter that computes the average of all points in the stencil More...

struct	CSRMedianFilter
	Compute (lower) Median of input numbers. More...

struct	CSRSlopeLimiter
	Generalized slope limiter for dG methods. More...

struct	CSRSWMFilter
	Switching median filter. More...

struct	CSRSymvFilter
	Test filter that computes the symv csr matrix-vector product if used. More...

struct	CudaTag
	CUDA implementation. More...

struct	CuspMatrixTag
	One of cusp's matrices, for these only the `blas2` transfer and the symv( m,x,y) are implemented. More...

struct	CuspVectorTag
	special tag for cusp arrays More...

struct	DefaultSolver
	PCG Solver class for solving \( (y-\alpha\hat I(t,y)) = \rho\). More...

struct	DenseMatrixTag
	indicate our dense matrix format More...

struct	DIRKStep
	Embedded diagonally implicit Runge Kutta time-step with error estimate \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \\ \tilde u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s \tilde b_j k_j \\ \delta^{n+1} = u^{n+1} - \tilde u^{n+1} = \Delta t\sum_{j=1}^s (b_j-\tilde b_j) k_j \end{align} \). More...

struct	Distance
	\( f(x,y) = \sqrt{ (x-x_0)^2 + (y-y_0)^2} \) More...

struct	divides
	\( y = x_1/x_2 \) More...

struct	divides_equals
	\( y = y/x\) More...

class	DLT
	Struct holding coefficients for Discrete Legendre Transformation (DLT) related operations. More...

struct	DPolynomialHeaviside
	\( f(x) = \begin{cases} 0 \text{ if } x < x_b-a \|\| x > x_b+a \\ (35 (a + x - x_b)^3 (a - x + x_b)^3)/(32 a^7) \text{ if } \|x-x_b\| < a \end{cases}\) The derivative of PolynomialHeaviside approximates delta(x) More...

class	Elliptic1d
	A 1d negative elliptic differential operator \( -\partial_x ( \chi \partial_x ) \). More...

class	Elliptic2d
	A 2d negative elliptic differential operator \( -\nabla \cdot ( \mathbf{\chi}\cdot \nabla ) \). More...

class	Elliptic3d
	A 3d negative elliptic differential operator \( -\nabla \cdot ( \mathbf{\chi}\cdot \nabla ) \). More...

struct	EllSparseBlockMat
	Ell Sparse Block Matrix format. More...

struct	EmbeddedPairSum
	\( y = \sum_i a_i x_i + b y,\quad \tilde y = \sum_i \tilde a_i x_i + \tilde b y \) More...

struct	EntireDomain
	The domain that contains all points. More...

struct	equals
	\( y=x\) More...

struct	ERKStep
	Embedded Runge Kutta explicit time-step with error estimate \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \\ \tilde u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s \tilde b_j k_j \\ \delta^{n+1} = u^{n+1} - \tilde u^{n+1} = \Delta t\sum_{j=1}^s (b_j - \tilde b_j) k_j \end{align} \). More...

class	Error
	class intended for the use in throw statements More...

struct	Evaluate
	\( f( y, g(x_0, ..., x_s)) \) More...

class	EVE
	The Eigen-Value-Estimator (EVE) finds largest Eigenvalue of \( M^{-1}Ax = \lambda_\max x\). More...

struct	EXP
	\( f(x) = \exp( x)\) More...

struct	ExplicitMultistep
	General explicit linear multistep ODE integrator \( \begin{align} v^{n+1} = \sum_{j=0}^{s-1} a_j v^{n-j} + \Delta t\left(\sum_{j=0}^{s-1}b_j \hat f\left(t^{n}-j\Delta t, v^{n-j}\right)\right) \end{align} \). More...

struct	ExponentialFilter
	\( f(i) = \begin{cases} 1 \text{ if } \eta < \eta_c \\ \exp\left( -\alpha \left(\frac{\eta-\eta_c}{1-\eta_c} \right)^{2s}\right) \text { if } \eta \geq \eta_c \\ 0 \text{ else} \\ \eta=\frac{i}{1-n} \end{cases}\) More...

struct	ExpProfX
	\( f(x) = f(x,y) = f(x,y,z) = A\exp(-x/L_n) + B \) More...

struct	Extrapolation
	Extrapolate a polynomial passing through up to three points. More...

struct	Fail
	Indicate failure to converge. More...

struct	FilteredERKStep
	EXPERIMENTAL: Filtered Embedded Runge Kutta explicit time-step with error estimate \( \begin{align} k_i = f\left( t^n + c_i \Delta t, \Lambda\Pi \left[u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right]\right) \\ u^{n+1} = \Lambda\Pi\left[u^{n} + \Delta t\sum_{j=1}^s b_j k_j\right] \\ \delta^{n+1} = \Delta t\sum_{j=1}^s (\tilde b_j - b_j) k_j \end{align} \). More...

struct	FilteredExplicitMultistep
	EXPERIMENTAL: General explicit linear multistep ODE integrator with Limiter / Filter \( \begin{align} \tilde v &= \sum_{j=0}^{s-1} a_j v^{n-j} + \Delta t\left(\sum_{j=0}^{s-1}b_j \hat f\left(t^{n}-j\Delta t, v^{n-j}\right)\right) \\ v^{n+1} &= \Lambda\Pi \left( \tilde v\right) \end{align} \). More...

struct	Gaussian
	\( f(x,y) = Ae^{-\left(\frac{(x-x_0)^2}{2\sigma_x^2} + \frac{(y-y_0)^2}{2\sigma_y^2}\right)} \) More...

struct	Gaussian3d
	\( f(x,y,z) = Ae^{-\left(\frac{(x-x_0)^2}{2\sigma_x^2} + \frac{(y-y_0)^2}{2\sigma_y^2} + \frac{(z-z_0)^2}{2\sigma_z^2}\right)} \) More...

struct	GaussianDamping
	\( f(\psi) = \begin{cases} 1 \text{ if } \psi < \psi_{\max}\\ 0 \text{ if } \psi > (\psi_{\max} + 4\alpha) \\ \exp\left( - \frac{(\psi - \psi_{\max})^2}{2\alpha^2}\right), \text{ else} \end{cases} \) More...

struct	GaussianX
	\( f(x,y) = Ae^{-\frac{(x-x_0)^2}{2\sigma_x^2} } \) More...

struct	GaussianY
	\( f(x,y) = Ae^{-\frac{(y-y_0)^2}{2\sigma_y^2}} \) More...

struct	GaussianZ
	\( f(x,y,z) = Ae^{-\frac{(z-z_0)^2}{2\sigma_z^2}} \) More...

struct	GeneralComm
	Perform general gather and its transpose (scatter) operation across processes on distributed vectors using mpi. More...

struct	GeneralHelmholtz
	A general Helmholtz-type operator \( (\chi-\alpha F) \). More...

struct	Heaviside
	\( f(x) = \begin{cases} 0 \text{ if } x < x_b \\ 1 \text{ else} \end{cases}\) More...

struct	Helmholtz2
	DEPRECATED, Matrix class that represents a more general Helmholtz-type operator. More...

struct	Histogram
	Compute a histogram on a 1D grid. More...

struct	Histogram2D
	Compute a histogram on a 2D grid. More...

struct	Horner2d
	\( f(x,y) = \sum_{i=0}^{M-1} \sum_{j=0}^{N-1} c_{iN+j} x^i y^j \) More...

struct	IDENTITY
	\( f(x) = x\) More...

struct	IdentityFilter
	A filter that does nothing. More...

struct	ImExMultistep
	Semi-implicit multistep ODE integrator \( \begin{align} v^{n+1} = \sum_{q=0}^{s-1} a_q v^{n-q} + \Delta t\left[\left(\sum_{q=0}^{s-1}b_q \hat E(t^{n}-q\Delta t, v^{n-q}) + \sum_{q=1}^{s} c_q \hat I( t^n - q\Delta t, v^{n-q})\right) + c_0\hat I(t^{n}+\Delta t, v^{n+1})\right] \end{align} \). More...

struct	ImplicitMultistep
	Implicit multistep ODE integrator \( \begin{align} v^{n+1} &= \sum_{i=0}^{s-1} a_i v^{n-i} + \Delta t \sum_{i=1}^{s} c_i\hat I(t^{n+1-i}, v^{n+1-i}) + \Delta t c_{0} \hat I (t + \Delta t, v^{n+1}) \\ \end{align} \). More...

struct	InvCoshXsq
	\( f(x,y) =A/\cosh^2(k_x x) \) More...

struct	InverseKroneckerTriDiagonal2d
	Fast inverse tridiagonal sparse matrix in 2d \( T_y^{-1}\otimes T_x^{-1}\). More...

struct	InverseTensorMultiply2d
	\( y_i \leftarrow \lambda T^{-1}_{ij} x_i + \mu y_i\) More...

struct	InverseTensorMultiply3d
	\( y_i \leftarrow \lambda T^{-1}_{ij} x_i + \mu y_i\) More...

struct	InverseTriDiagonal
	Fast inverse tridiagonal sparse matrix. More...

struct	INVERT
	\( f(x) = 1/x \) More...

struct	InvSqrt
	\( f(x) = \frac{1}{\sqrt{x}}\) More...

struct	IPolynomialHeaviside
	\( f(x) = \begin{cases} x_b \text{ if } x < x_b-a \\ x_b + ((35 a^3 - 47 a^2 (x - x_b) + 25 a (x - x_b)^2 - 5 (x - x_b)^3) (a + x - x_b)^5)/(256 a^7) \text{ if } \|x-x_b\| < a \\ x \text{ if } x > x_b + a \end{cases}\) The integral of PolynomialHeaviside approximates xH(x) More...

struct	Iris
	\( f(\psi) = \begin{cases} 1 \text{ if } \psi_{\min} < \psi < \psi_{\max}\\ 0 \text{ else} \end{cases}\) More...

struct	IslandXY
	\( f(x,y) = \lambda \ln{(\cosh{(x/\lambda) } +\epsilon \cos(y/\lambda)) } \) More...

struct	ISNFINITE
	\( f(x) = \mathrm{!std::isfinite(x)}\) More...

struct	ISNSANE
	\( f(x) =\begin{cases} \mathrm{true\ if}\ \|x\| > 10^{100}\\ \mathrm{false\ else} \end{cases}\) More...

struct	KroneckerTriDiagonal2d
	Fast tridiagonal sparse matrix in 2d \( T_y\otimes T_x\). More...

struct	Lamb
	\( f(x,y) = \begin{cases} 2\lambda U J_1(\lambda r) / J_0(\gamma)\cos(\theta) \text{ for } r<R \\ 0 \text{ else} \end{cases} \) More...

struct	LeastSquaresExtrapolation
	Evaluate a least squares fit More...

struct	LeastSquaresPreconditioner
	Least Squares Polynomial Preconditioner \( M^{-1} s( AM^{-1})\). More...

class	LGMRES
	Functor class for the right preconditioned LGMRES method to solve \( Ax=b\). More...

struct	Line
	\( f(x) = y_1\frac{x-x_0}{x_1-x_0} + y_0\frac{x-x_1}{x_0-x_1}\) More...

struct	LinearX
	\( f(x) = f(x,y) = f(x,y,z) = ax+b \) More...

struct	LinearY
	\( f(x,y) = f(x,y,z) = ay+b \) More...

struct	LinearZ
	\( f(x,y,z) = az+b \) More...

struct	LN
	\( f(x) = \ln(x)\) More...

class	Message
	small class holding a stringstream More...

struct	MinMod
	\( f(x_1, x_2, ...) = \begin{cases} \min(x_1, x_2, ...) &\text{ for } x_1, x_2, ... >0 \\ \max(x_1, x_2, ...) &\text{ for } x_1, x_2, ... <0 \\ 0 &\text{ else} \end{cases} \) More...

struct	minus_equals
	\( y=y-x\) More...

struct	MOD
	\( f(x) = \) `x` mod m > 0 ? x mod m : x mod m + m More...

struct	ModifiedChebyshevPreconditioner
	Approximate inverse Chebyshev Polynomial Preconditioner \( A^{-1} = \frac{c_0}{2} I + \sum_{k=1}^{r}c_kT_k( Z)\). More...

struct	MPI_Vector
	mpi Vector class More...

struct	MPIDistMat
	Distributed memory matrix class. More...

struct	MPIMatrixTag
	indicate one of our mpi matrices More...

struct	MPITag
	distributed memory system More...

struct	MPIVectorTag
	A distributed vector contains a data container and a MPI communicator. More...

struct	MultigridCG2d
	Solve. More...

struct	MultiMatrix
	Struct that applies given matrices one after the other. More...

struct	MultistepTableau
	Manage coefficients of Multistep methods. More...

struct	MultistepTimeloop
	Integrate using a for loop and a fixed non-changeable time-step. More...

struct	NearestNeighborComm
	Communicator for asynchronous nearest neighbor communication. More...

struct	NestedGrids
	Hold nested grids and provide dg fast interpolation and projection matrices. More...

struct	NoPolicyTag
	Indicate that a type does not have an execution policy. More...

class	NoRoot1d
	Exception class, that stores boundaries for 1D root finding. More...

struct	NotATensorTag
	Indicate that a type is not a tensor. More...

struct	OmpTag
	OpenMP parallel execution. More...

struct	ONE
	\( f(x) = f(x,y) = f(x,y,z) = 1\) More...

struct	OneDimensionalTag
	1d More...

class	Operator
	A square nxn matrix. More...

struct	PairSum
	\( y = \sum_i a_i x_i \) More...

class	PCG
	Preconditioned conjugate gradient method to solve \( Ax=b\). More...

struct	Plus
	\( y\leftarrow y+a \) More...

struct	PLUS
	\( f(x) = x + c\) More...

struct	plus_equals
	\( y=y+x\) More...

struct	PointwiseDivide
	\( z\leftarrow ax/y + bz \) More...

struct	PointwiseDot
	\( z\leftarrow ax_1y_1+bx_2y_2+gz \) More...

struct	Poisson
	Direct discretization of Poisson bracket \( \{ f,g\} \). More...

struct	PolynomialHeaviside
	\( f(x) = \begin{cases} 0 \text{ if } x < x_b-a \\ ((16 a^3 - 29 a^2 (x - x_b) + 20 a (x - x_b)^2 - 5 (x - x_b)^3) (a + x - x_b)^4)/(32 a^7) \text{ if } \|x-x_b\| < a \\ 1 \text{ if } x > x_b + a \end{cases}\) More...

struct	PolynomialRectangle
	\( f(x) = \begin{cases} 0 \text{ if } x < x_l-a_l \\ ((16 a_l^3 - 29 a_l^2 (x - x_l) + 20 a_l (x - x_l)^2 - 5 (x - x_l)^3) (a_l + x - x_l)^4)/(32 a_l^7) \text{ if } \|x-x_l\| < a_l \\ 1 \text{ if } x_l + a_l < x < x_r-a_r \\ ((16 a_r^3 - 29 a_r^2 (x - x_r) + 20 a_r (x - x_r)^2 - 5 (x - x_r)^3) (a_r + x - x_l)^4)/(32 a_r^7) \text{ if } \|x-x_r\| < a_r \\ 0 \text{ if } x > x_r + a_r \end{cases}\) More...

struct	POSVALUE
	\( f(x) = \begin{cases} x \text{ for } x>0 \\ 0 \text{ else} \end{cases} \) More...

struct	PsiPupil
	\( f(\psi) = \begin{cases} \psi_{\max} \text{ if } \psi > \psi_{\max} \\ \psi \text{ else} \end{cases}\) More...

struct	Pupil
	\( f(\psi) = \begin{cases} 0 \text{ if } \psi > \psi_{\max} \\ 1 \text{ else} \end{cases}\) More...

struct	RealCartesianGrid2d
	two-dimensional Grid with Cartesian metric More...

struct	RealCartesianGrid3d
	three-dimensional Grid with Cartesian metric More...

struct	RealCartesianGridX2d
	two-dimensional GridX with RealCartesian metric More...

struct	RealCartesianGridX3d
	three-dimensional GridX with RealCartesian metric More...

struct	RealCartesianMPIGrid2d
	The mpi version of RealCartesianGrid2d. More...

struct	RealCartesianMPIGrid3d
	The mpi version of RealCartesianGrid3d. More...

struct	RealCartesianRefinedGrid2d
	Refined RealCartesian grid. More...

struct	RealCartesianRefinedGrid3d
	Refined RealCartesian grid. More...

struct	RealCartesianRefinedGridX2d
	Refined X-point grid. More...

struct	RealCartesianRefinedGridX3d
	Refined X-point grid. More...

struct	RealCylindricalGrid3d
	three-dimensional Grid with Cylindrical metric More...

struct	RealCylindricalMPIGrid3d
	the mpi version of RealCylindricalGrid3d More...

struct	RealEquidistRefinement
	Cell refinement around a given node. More...

struct	RealEquidistXRefinement
	RealEquidistant cell refinement around the X-point. More...

struct	RealExponentialRefinement
	The exponential refinement around a node. More...

struct	RealExponentialXRefinement
	The exponential refinement around the X-point. More...

struct	RealFemRefinement
	Insert equidistant points in between dG nodes. More...

struct	RealGrid1d
	1D grid More...

struct	RealGrid2d
	The simplest implementation of aRealTopology2d. More...

struct	RealGrid3d
	The simplest implementation of aRealTopology3d. More...

struct	RealGridX1d
	1D grid for X-point topology More...

struct	RealGridX2d
	The simplest implementation of aRealTopologyX2d. More...

struct	RealGridX3d
	The simplest implementation of aRealTopologyX3d. More...

struct	RealIdentityRefinement
	No refinement. More...

struct	RealIdentityXRefinement
	No refinement. More...

struct	RealLinearRefinement
	Multiply every cell in the grid by a factor. More...

struct	RealMPIGrid2d
	The simplest implementation of aRealMPITopology2d. More...

struct	RealMPIGrid3d
	The simplest implementation of aRealMPITopology3d. More...

struct	RecursiveVectorTag
	This tag indicates composition/recursion. More...

class	RefinedElliptic
	The refined version of `Elliptic`. More...

struct	RowColDistMat
	Distributed memory matrix class, asynchronous communication. More...

struct	Scal
	\( y\leftarrow ay \) More...

struct	ScalarTag

struct	SelfMadeMatrixTag
	Indicates that the type has a member function with the same name and interface (up to the matrix itself of course) as the corresponding `blas2` member function, for example `void symv( const ContainerType1&, ContainerType2& );` More...

struct	SerialTag
	Indicate sequential execution. More...

struct	SharedTag
	shared memory system More...

struct	SharedVectorTag
	Indicate a contiguous chunk of shared memory. More...

struct	ShuOsher
	Shu-Osher fixed-step explicit ODE integrator with Slope Limiter / Filter \( \begin{align} u_0 &= u_n \\ u_i &= \Lambda\Pi \left(\sum_{j=0}^{i-1}\left[ \alpha_{ij} u_j + \Delta t \beta_{ij} f( t_j, u_j)\right]\right)\\ u^{n+1} &= u_s \end{align} \). More...

struct	ShuOsherTableau
	Manage coefficients in Shu-Osher form. More...

struct	Sign
	\( f(x) = \text{sgn}(x) = \begin{cases} -1 \text{ for } x < 0 \\ 0 \text{ for } x = 0 \\ +1 \text{ for } x > 0 \end{cases}\) More...

struct	Simpsons
	Time integration based on Simpson's rule. More...

struct	SinglestepTimeloop
	Integrate using a for loop and a fixed time-step. More...

struct	SinProfX
	\( f(x) = f(x,y) = f(x,y,z) = B + A(1 - \sin(k_xx )) \) More...

struct	SinX
	\( f(x) = f(x,y) = f(x,y,z) =B+ A \sin(k_x x) \) More...

struct	SinXCosY
	\( f(x,y) =B+ A \sin(k_x x) \cos(k_y y) \) More...

struct	SinXSinY
	\( f(x,y) =B+ A \sin(k_x x) \sin(k_y y) \) More...

struct	SinY
	\( f(x,y) =B+ A \sin(k_y y) \) More...

struct	SlopeLimiter
	\( \text{up}(v, g_m, g_0, g_p, h_m, h_p ) = \begin{cases} +h_m \Lambda( g_0, g_m) &\text{ if } v \geq 0 \\ -h_p \Lambda( g_p, g_0) &\text{ else} \end{cases} \) More...

struct	SlopeLimiterProduct
	\( \text{up}(v, g_m, g_0, g_p, h_m, h_p ) = v \begin{cases} +h_m \Lambda( g_0, g_m) &\text{ if } v \geq 0 \\ -h_p \Lambda( g_p, g_0) &\text{ else} \end{cases} \) More...

struct	SparseBlockMatrixTag
	indicate our sparse block matrix format More...

struct	SparseTensor
	Class for 2x2 and 3x3 matrices sharing elements. More...

struct	SQRT
	\( f(x) = \sqrt{x}\) More...

struct	Square
	\( f(x) = x^2\) More...

struct	StdMapTag

struct	Sum
	\( y = \sum_i x_i \) More...

struct	SurjectiveComm
	Perform surjective gather and its transpose (scatter) operation across processes on distributed vectors using mpi. More...

struct	TanhProfX
	\( f(x) = B + 0.5 A(1+ \text{sign} \tanh((x-x_b)/\alpha ) ) \) More...

struct	TensorDeterminant2d
	\( y = t_{00} t_{11} - t_{10}t_{01} \) More...

struct	TensorDeterminant3d
	\( y = t_{00} t_{11}t_{22} + t_{01}t_{12}t_{20} + t_{02}t_{10}t_{21} - t_{02}t_{11}t_{20} - t_{01}t_{10}t_{22} - t_{00}t_{12}t_{21} \) More...

struct	TensorDot2d
	\( y = \lambda\mu v_i T_{ij} w_j \) More...

struct	TensorDot3d
	\( y = \lambda \mu v_i T_{ij} w_j \) More...

struct	TensorMultiply2d
	\( y_i \leftarrow \lambda T_{ij} x_i + \mu y_i\) More...

struct	TensorMultiply3d
	\( y_i \leftarrow \lambda T_{ij} x_i + \mu y_i\) More...

struct	TensorTraits
	The vector traits. More...

struct	TensorTraits< CooSparseBlockMat< T > >

struct	TensorTraits< cusp::coo_matrix< I, V, M > >

struct	TensorTraits< cusp::csr_matrix< I, V, M > >

struct	TensorTraits< cusp::dia_matrix< I, V, M > >

struct	TensorTraits< cusp::ell_matrix< I, V, M > >

struct	TensorTraits< cusp::hyb_matrix< I, V, M > >

struct	TensorTraits< EllSparseBlockMat< T > >

struct	TensorTraits< mat::PolChargeN< G, M, V > >

struct	TensorTraits< MPI_Vector< container > >
	prototypical MPI vector More...

struct	TensorTraits< MPIDistMat< L, C > >

struct	TensorTraits< RowColDistMat< LI, LO, C > >

struct	TensorTraits< std::array< T, N >, std::enable_if_t< !std::is_arithmetic< T >::value > >

struct	TensorTraits< std::array< T, N >, std::enable_if_t< std::is_arithmetic< T >::value > >

struct	TensorTraits< std::map< Key, T > >
	Behaves like a RecursiveVector. More...

struct	TensorTraits< std::vector< T >, std::enable_if_t< !std::is_arithmetic< T >::value > >
	Prototypical Recursive Vector. More...

struct	TensorTraits< std::vector< T >, std::enable_if_t< std::is_arithmetic< T >::value > >

struct	TensorTraits< T, std::enable_if_t< std::is_arithmetic< T >::value > >
	Recognize arithmetic types as scalars. More...

struct	TensorTraits< thrust::device_vector< T > >
	prototypical Shared Vector with Cuda or Omp Tag More...

struct	TensorTraits< thrust::host_vector< T > >
	prototypical Shared Vector with Serial Tag More...

struct	TensorTraits< View< ThrustVector > >
	A View has identical value_type and execution_policy as the underlying container. More...

struct	ThreeDimensionalTag
	3d More...

struct	ThrustVectorTag
	Indicate thrust/std - like behaviour. More...

struct	Timer
	Simple tool for performance measuring. More...

struct	times_equals
	\( y=xy\) More...

struct	TopologyTraits

struct	TriDiagonal
	Fast (shared memory) tridiagonal sparse matrix. More...

struct	TripletSum
	\( y = \sum_i a_i x_i y_i \) More...

struct	TwoDimensionalTag
	2d More...

struct	Upwind
	\( \text{up}(v, b, f ) = \begin{cases} b &\text{ if } v \geq 0 \\ f &\text{ else} \end{cases} \) More...

struct	UpwindProduct
	\( \text{up}(v, b, f ) = v \begin{cases} b &\text{ if } v \geq 0 \\ f &\text{ else} \end{cases} \) More...

struct	VanLeer
	\( f(x_1,x_2) = 2\begin{cases} \frac{x_1x_2}{x_1+x_2} &\text{ if } x_1x_2 > 0 \\ 0 & \text { else } \end{cases} \) More...

struct	View
	A vector view class, usable in `dg` functions. More...

struct	Vortex
	\(f(x,y) =\begin{cases} \frac{u_d}{1.2965125} \left( r\left(1+\frac{\beta_i^2}{g_i^2}\right) - R \frac{\beta_i^2}{g_i^2} \frac{J_1(g_ir/R)}{J_1(g_i)}\right)\cos(\theta) \text{ if } r < R \\ \frac{u_d}{1.2965125} R \frac{K_1(\beta_i {r}/{R})}{K_1(\beta)} \cos(\theta) \text{ else } \end{cases} \) More...

struct	WallDistance
	Shortest Distance to a collection of vertical and horizontal lines. More...

struct	ZERO
	\( f(x) = f(x,y) = f(x,y,z) = 0\) More...

Typedefs
template<class value_type >
using	EllSparseBlockMatDevice = EllSparseBlockMat< value_type >

template<class value_type >
using	CooSparseBlockMatDevice = CooSparseBlockMat< value_type >

template<class Vector >
using	get_value_type = typename TensorTraits< std::decay_t< Vector > >::value_type

template<class Vector >
using	get_tensor_category = typename TensorTraits< std::decay_t< Vector > >::tensor_category

template<class Vector >
using	get_execution_policy = typename TensorTraits< std::decay_t< Vector > >::execution_policy

template<class T >
using	HVec_t = thrust::host_vector< T >
	Host Vector. More...

using	HVec = thrust::host_vector< double >
	Host Vector. More...

using	iHVec = thrust::host_vector< int >
	integer Host Vector More...

using	fHVec = thrust::host_vector< float >
	Host Vector. More...

using	DVec = thrust::device_vector< double >
	Device Vector. The device can be an OpenMP parallelized cpu or a gpu. This depends on the value of the macro THRUST_DEVICE_SYSTEM, which can be either THRUST_DEVICE_SYSTEM_OMP for openMP or THRUST_DEVICE_SYSTEM_CUDA for a gpu or THRUST_DEVICE_SYSTEM_CPP for a cpu. More...

using	iDVec = thrust::device_vector< int >
	integer Device Vector More...

using	fDVec = thrust::device_vector< float >
	Device Vector. The device can be an OpenMP parallelized cpu or a gpu. This depends on the value of the macro THRUST_DEVICE_SYSTEM, which can be either THRUST_DEVICE_SYSTEM_OMP for openMP or THRUST_DEVICE_SYSTEM_CUDA for a gpu or THRUST_DEVICE_SYSTEM_CPP for a cpu. More...

template<class T >
using	HMatrix_t = EllSparseBlockMat< T >

using	HMatrix = EllSparseBlockMat< double >
	Host Matrix for derivatives. More...

using	fHMatrix = EllSparseBlockMat< float >
	Host Matrix for derivatives. More...

using	DMatrix = EllSparseBlockMatDevice< double >
	Device Matrix for derivatives. More...

using	fDMatrix = EllSparseBlockMatDevice< float >
	Device Matrix for derivatives. More...

template<class real_type >
using	IHMatrix_t = cusp::csr_matrix< int, real_type, cusp::host_memory >

template<class real_type >
using	IDMatrix_t = cusp::csr_matrix< int, real_type, cusp::device_memory >

using	IHMatrix = IHMatrix_t< double >

using	IDMatrix = IDMatrix_t< double >

template<class T >
using	MHVec_t = dg::MPI_Vector< dg::HVec_t< T > >
	MPI Host Vector s.a. dg::HVec_t. More...

using	MHVec = dg::MPI_Vector< dg::HVec >
	MPI Host Vector s.a. dg::HVec. More...

using	fMHVec = dg::MPI_Vector< dg::fHVec >
	MPI Host Vector s.a. dg::fHVec. More...

using	MDVec = dg::MPI_Vector< dg::DVec >
	MPI Device Vector s.a. dg::DVec. More...

using	fMDVec = dg::MPI_Vector< dg::fDVec >
	MPI Device Vector s.a. dg::fDVec. More...

template<class T >
using	NNCH = dg::NearestNeighborComm< dg::iHVec, thrust::host_vector< const T * >, thrust::host_vector< T > >
	host Communicator for the use in an mpi matrix for derivatives More...

template<class T >
using	NNCD = dg::NearestNeighborComm< dg::iDVec, thrust::device_vector< const T * >, thrust::device_vector< T > >
	host Communicator for the use in an mpi matrix for derivatives More...

using	dNNCH = dg::NNCH< double >
	host Communicator for the use in an mpi matrix for derivatives More...

using	fNNCH = dg::NNCH< float >
	host Communicator for the use in an mpi matrix for derivatives More...

using	dNNCD = dg::NNCD< double >
	device Communicator for the use in an mpi matrix for derivatives More...

using	fNNCD = dg::NNCD< float >
	device Communicator for the use in an mpi matrix for derivatives More...

template<class T >
using	CooMat_t = dg::CooSparseBlockMat< T >

using	CooMat = dg::CooSparseBlockMat< double >

using	fCooMat = dg::CooSparseBlockMat< float >

using	DCooMat = dg::CooSparseBlockMatDevice< double >

using	fDCooMat = dg::CooSparseBlockMatDevice< float >

template<class T >
using	MHMatrix_t = dg::RowColDistMat< dg::HMatrix_t< T >, dg::CooMat_t< T >, dg::NNCH< T > >
	MPI Host Matrix for derivatives. More...

using	MHMatrix = dg::RowColDistMat< dg::HMatrix, dg::CooMat, dg::dNNCH >
	MPI Host Matrix for derivatives. More...

using	fMHMatrix = dg::RowColDistMat< dg::fHMatrix, dg::fCooMat, dg::fNNCH >
	MPI Host Matrix for derivatives. More...

using	MDMatrix = dg::RowColDistMat< dg::DMatrix, dg::DCooMat, dg::dNNCD >
	MPI Device Matrix for derivatives. More...

using	fMDMatrix = dg::RowColDistMat< dg::fDMatrix, dg::fDCooMat, dg::fNNCD >
	MPI Device Matrix for derivatives. More...

template<class real_type >
using	MIHMatrix_t = MPIDistMat< IHMatrix_t< real_type >, GeneralComm< dg::iHVec, thrust::host_vector< real_type > > >

template<class real_type >
using	MIDMatrix_t = MPIDistMat< IDMatrix_t< real_type >, GeneralComm< dg::iDVec, thrust::device_vector< real_type > > >

using	MIHMatrix = MIHMatrix_t< double >

using	MIDMatrix = MIDMatrix_t< double >

using	aGeometry2d = dg::aRealGeometry2d< double >

using	aGeometry3d = dg::aRealGeometry3d< double >

using	aProductGeometry3d = dg::aRealProductGeometry3d< double >

using	CartesianGrid2d = dg::RealCartesianGrid2d< double >

using	CartesianGrid3d = dg::RealCartesianGrid3d< double >

using	CylindricalGrid3d = dg::RealCylindricalGrid3d< double >

using	CartesianGridX2d = dg::RealCartesianGridX2d< double >

using	CartesianGridX3d = dg::RealCartesianGridX3d< double >

using	aGeometryX2d = dg::aRealGeometryX2d< double >

using	aGeometryX3d = dg::aRealGeometryX3d< double >

using	Grid1d = dg::RealGrid1d< double >

using	Grid2d = dg::RealGrid2d< double >

using	Grid3d = dg::RealGrid3d< double >

using	aTopology2d = dg::aRealTopology2d< double >

using	aTopology3d = dg::aRealTopology3d< double >

using	GridX1d = dg::RealGridX1d< double >

using	GridX2d = dg::RealGridX2d< double >

using	GridX3d = dg::RealGridX3d< double >

using	aTopologyX2d = dg::aRealTopologyX2d< double >

using	aTopologyX3d = dg::aRealTopologyX3d< double >

using	aMPIGeometry2d = dg::aRealMPIGeometry2d< double >

using	aMPIGeometry3d = dg::aRealMPIGeometry3d< double >

using	aProductMPIGeometry3d = dg::aRealProductMPIGeometry3d< double >

using	CartesianMPIGrid2d = dg::RealCartesianMPIGrid2d< double >

using	CartesianMPIGrid3d = dg::RealCartesianMPIGrid3d< double >

using	CylindricalMPIGrid3d = dg::RealCylindricalMPIGrid3d< double >

using	MPIGrid2d = dg::RealMPIGrid2d< double >

using	MPIGrid3d = dg::RealMPIGrid3d< double >

using	aMPITopology2d = dg::aRealMPITopology2d< double >

using	aMPITopology3d = dg::aRealMPITopology3d< double >

using	aRefinement1d = dg::aRealRefinement1d< double >

using	IdentityRefinement = dg::RealIdentityRefinement< double >

using	FemRefinement = dg::RealFemRefinement< double >

using	LinearRefinement = dg::RealLinearRefinement< double >

using	EquidistRefinement = dg::RealEquidistRefinement< double >

using	ExponentialRefinement = dg::RealExponentialRefinement< double >

using	CartesianRefinedGrid2d = dg::RealCartesianRefinedGrid2d< double >

using	CartesianRefinedGrid3d = dg::RealCartesianRefinedGrid3d< double >

using	aRefinementX2d = dg::aRealRefinementX2d< double >

using	IdentityXRefinement = dg::RealIdentityXRefinement< double >

using	EquidistXRefinement = dg::RealEquidistXRefinement< double >

using	ExponentialXRefinement = dg::RealExponentialXRefinement< double >

using	CartesianRefinedGridX2d = dg::RealCartesianRefinedGridX2d< double >

using	CartesianRefinedGridX3d = dg::RealCartesianRefinedGridX3d< double >

template<class MPIContainer >
using	get_mpi_view_type = std::conditional_t< std::is_const< MPIContainer >::value, MPI_Vector< View< const typename MPIContainer::container_type > >, MPI_Vector< View< typename MPIContainer::container_type > > >

template<class ContainerType >
using	FixedPointIteration = AndersonAcceleration< ContainerType >
	If you are looking for fixed point iteration: it is a special case of Anderson Acceleration. More...

template<class Geometry , class Matrix , class Container >
using	Elliptic = Elliptic2d< Geometry, Matrix, Container >
	A 2d negative elliptic differential operator \( -\nabla \cdot ( \mathbf{\chi}\cdot \nabla ) \). More...

template<class Geometry , class Matrix , class Container >
using	Helmholtz = GeneralHelmholtz< dg::Elliptic2d< Geometry, Matrix, Container >, Container >
	a 2d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\Delta\) More...

template<class Geometry , class Matrix , class Container >
using	Helmholtz1d = GeneralHelmholtz< dg::Elliptic1d< Geometry, Matrix, Container >, Container >
	a 1d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\partial_x^2\) More...

template<class Geometry , class Matrix , class Container >
using	Helmholtz2d = GeneralHelmholtz< dg::Elliptic2d< Geometry, Matrix, Container >, Container >
	a 2d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\Delta\) More...

template<class Geometry , class Matrix , class Container >
using	Helmholtz3d = GeneralHelmholtz< dg::Elliptic3d< Geometry, Matrix, Container >, Container >
	a 3d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\Delta\) More...

template<class ContainerType >
using	RungeKutta = ERKStep< ContainerType >
	Runge-Kutta fixed-step explicit ODE integrator \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \end{align} \). More...

template<class ContainerType >
using	FilteredRungeKutta = FilteredERKStep< ContainerType >
	Filtered Runge-Kutta fixed-step explicit ODE integrator \( \begin{align} k_i = f\left( t^n + c_i \Delta t, \Lambda\Pi \left[u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right]\right) \\ u^{n+1} = \Lambda\Pi\left[u^{n} + \Delta t\sum_{j=1}^s b_j k_j\right] \end{align} \). More...

template<class ContainerType >
using	ImplicitRungeKutta = DIRKStep< ContainerType >
	Runge-Kutta fixed-step implicit ODE integrator \( \begin{align} k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{s} a_{ij} k_j\right) \\ u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j \end{align} \). More...

Enumerations
enum	dist_type { row_dist =0 , col_dist =1 }
	Type of distribution of MPI distributed matrices. More...

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

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

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

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

enum class	coo3d : char { coo3d::x = 'x' , coo3d::y = 'y' , coo3d::z = 'z' , coo3d::xy = 'a' , coo3d::yz = 'b' , coo3d::xz = 'c' }
	3d contra- and covariant coordinates More...

enum	multistep_identifier { IMEX_EULER_1_1 , IMEX_ADAMS_2_2 , IMEX_ADAMS_3_3 , IMEX_KOTO_2_2 , IMEX_BDF_2_2 , IMEX_BDF_3_3 , IMEX_BDF_4_4 , IMEX_BDF_5_5 , IMEX_BDF_6_6 , IMEX_TVB_3_3 , IMEX_TVB_4_4 , IMEX_TVB_5_5 , AB_1_1 , AB_2_2 , AB_3_3 , AB_4_4 , AB_5_5 , eBDF_1_1 , eBDF_2_2 , eBDF_3_3 , eBDF_4_4 , eBDF_5_5 , eBDF_6_6 , TVB_1_1 , TVB_2_2 , TVB_3_3 , TVB_4_4 , TVB_5_5 , TVB_6_6 , SSP_1_1 , SSP_2_2 , SSP_3_2 , SSP_4_2 , SSP_5_3 , SSP_6_3 , BDF_1_1 , BDF_2_2 , BDF_3_3 , BDF_4_4 , BDF_5_5 , BDF_6_6 }
	Identifiers for Multistep Tableaus. More...

enum class	to { to::exact , to::at_least }
	Switch for the Timeloop integrate function. More...

enum	tableau_identifier { EXPLICIT_EULER_1_1 , MIDPOINT_2_2 , KUTTA_3_3 , CLASSIC_4_4 , HEUN_EULER_2_1_2 , CAVAGLIERI_3_1_2 , FEHLBERG_3_2_3 , FEHLBERG_4_2_3 , BOGACKI_SHAMPINE_4_2_3 , CAVAGLIERI_4_2_3 , ARK324L2SA_ERK_4_2_3 , ZONNEVELD_5_3_4 , ARK436L2SA_ERK_6_3_4 , SAYFY_ABURUB_6_3_4 , CASH_KARP_6_4_5 , FEHLBERG_6_4_5 , DORMAND_PRINCE_7_4_5 , TSITOURAS09_7_4_5 , TSITOURAS11_7_4_5 , ARK548L2SA_ERK_8_4_5 , VERNER_9_5_6 , VERNER_10_6_7 , FEHLBERG_13_7_8 , DORMAND_PRINCE_13_7_8 , FEAGIN_17_8_10 , IMPLICIT_EULER_1_1 , IMPLICIT_MIDPOINT_1_2 , TRAPEZOIDAL_2_2 , SDIRK_2_1_2 , CAVAGLIERI_IMPLICIT_3_1_2 , BILLINGTON_3_3_2 , TRBDF2_3_3_2 , SANCHEZ_3_3 , KVAERNO_4_2_3 , SDIRK_4_2_3 , CAVAGLIERI_IMPLICIT_4_2_3 , ARK324L2SA_DIRK_4_2_3 , SANCHEZ_3_4 , CASH_5_2_4 , CASH_5_3_4 , SDIRK_5_3_4 , KVAERNO_5_3_4 , ARK436L2SA_DIRK_6_3_4 , KVAERNO_7_4_5 , SANCHEZ_6_5 , ARK548L2SA_DIRK_8_4_5 , SANCHEZ_7_6 , SSPRK_2_2 , SSPRK_3_2 , SSPRK_3_3 , SSPRK_5_3 , SSPRK_5_4 }
	Identifiers for Butcher Tableaus. More...

Functions
template<class ContainerType >
void	transpose (unsigned nx, unsigned ny, const ContainerType &in, ContainerType &out)
	Transpose vector. More...

template<class ContainerType >
void	extend_line (unsigned nx, unsigned ny, const ContainerType &in, ContainerType &out)
	Copy a line into rows of output vector. More...

template<class ContainerType >
void	extend_column (unsigned nx, unsigned ny, const ContainerType &in, ContainerType &out)
	Copy a line into columns of output vector. More...

template<class ContainerType >
auto	asDenseMatrix (const std::vector< const ContainerType * > &in)
	Lightweight DenseMatrix for `dg::blas2::gemv`. More...

template<class ContainerType >
auto	asDenseMatrix (const std::vector< const ContainerType * > &in, unsigned size)
	Lightweight DenseMatrix for `dg::blas2::gemv`. More...

template<class ContainerType >
std::vector< const ContainerType * >	asPointers (const std::vector< ContainerType > &in)
	Convert a vector of vectors to a vector of pointers. More...

static void	abort_program (int code=-1)
	Abort program (both MPI and non-MPI) More...

static void	mpi_init (int argc, char *argv[])
	Convencience shortcut: Calls MPI_Init or MPI_Init_thread. More...

static void	mpi_init2d (dg::bc bcx, dg::bc bcy, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true)
	Read in number of processses and create Cartesian MPI communicator. More...

static void	mpi_init2d (unsigned &n, unsigned &Nx, unsigned &Ny, MPI_Comm comm, std::istream &is=std::cin, bool verbose=true)
	Read in number of processes and broadcast to process group. More...

static void	mpi_init2d (dg::bc bcx, dg::bc bcy, unsigned &n, unsigned &Nx, unsigned &Ny, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true)
	Read in number of processses and grid size and create Cartesian MPI communicator. More...

static void	mpi_init3d (dg::bc bcx, dg::bc bcy, dg::bc bcz, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true)
	Read in number of processses and create Cartesian MPI communicator. More...

static void	mpi_init3d (unsigned &n, unsigned &Nx, unsigned &Ny, unsigned &Nz, MPI_Comm comm, std::istream &is=std::cin, bool verbose=true)
	Read in number of processes and broadcast to process group. More...

static void	mpi_init3d (dg::bc bcx, dg::bc bcy, dg::bc bcz, unsigned &n, unsigned &Nx, unsigned &Ny, unsigned &Nz, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true)
	Read in number of processses and grid size and create Cartesian MPI communicator. More...

template<class Matrix >
Matrix	transpose (const Matrix &src)
	Generic matrix transpose method. More...

template<class Functor , class real_type >
thrust::host_vector< real_type >	pullback (const Functor &f, const aRealGeometryX2d< real_type > &g)
	\( f_i = f( x(\zeta_i, \eta_i), y(\zeta_i, \eta_i))\) More...

template<class Functor , class real_type >
thrust::host_vector< real_type >	pullback (const Functor &f, const aRealGeometryX3d< real_type > &g)
	\( f_i = f( x(\zeta_i, \eta_i, \nu_i), y(\zeta_i, \eta_i, \nu_i), z(\zeta_i,\eta_i,\nu_i))\) More...

template<class UnaryOp , class real_type >
thrust::host_vector< real_type >	evaluate (UnaryOp f, const RealGrid1d< real_type > &g)
	Evaluate a 1d function on grid coordinates. More...

template<class BinaryOp , class real_type >
thrust::host_vector< real_type >	evaluate (const BinaryOp &f, const aRealTopology2d< real_type > &g)
	Evaluate a 2d function on grid coordinates. More...

template<class TernaryOp , class real_type >
thrust::host_vector< real_type >	evaluate (const TernaryOp &f, const aRealTopology3d< real_type > &g)
	Evaluate a 3d function on grid coordinates. More...

template<class real_type >
thrust::host_vector< real_type >	integrate (const thrust::host_vector< real_type > &in, const RealGrid1d< real_type > &g, dg::direction dir=dg::forward)
	Indefinite integral of a function on a grid. More...

template<class UnaryOp , class real_type >
thrust::host_vector< real_type >	integrate (UnaryOp f, const RealGrid1d< real_type > &g, dg::direction dir=dg::forward)
	Indefinite integral of a function on a grid. More...

template<class UnaryOp , class real_type >
thrust::host_vector< real_type >	evaluate (UnaryOp f, const RealGridX1d< real_type > &g)
	Evaluate a 1d function on grid coordinates. More...

template<class BinaryOp , class real_type >
thrust::host_vector< real_type >	evaluate (const BinaryOp &f, const aRealTopologyX2d< real_type > &g)
	Evaluate a 2d function on grid coordinates. More...

template<class TernaryOp , class real_type >
thrust::host_vector< real_type >	evaluate (const TernaryOp &f, const aRealTopologyX3d< real_type > &g)
	Evaluate a 3d function on grid coordinates. More...

template<class real_type >
thrust::host_vector< real_type >	forward_transform (const thrust::host_vector< real_type > &in, const aRealTopology2d< real_type > &g)
	Transform a vector from dg::xspace (nodal values) to dg::lspace (modal values) More...

static DG_DEVICE double	one (double x)
	\( f(x) = 1\) More...

static DG_DEVICE double	one (double x, double y)
	\( f(x,y) = 1\) More...

static DG_DEVICE double	one (double x, double y, double z)
	\( f(x,y,z) = 1\) More...

static DG_DEVICE double	zero (double x)
	\( f(x) = 0\) More...

static DG_DEVICE double	zero (double x, double y)
	\( f(x,y) = 0\) More...

static DG_DEVICE double	zero (double x, double y, double z)
	\( f(x,y,z) = 0\) More...

static DG_DEVICE double	cooX1d (double x)
	\( f(x) = x\) More...

static DG_DEVICE double	cooX2d (double x, double y)
	\( f(x,y) = x\) More...

static DG_DEVICE double	cooX3d (double x, double y, double z)
	\( f(x,y,z) = x\) More...

static DG_DEVICE double	cooY2d (double x, double y)
	\( f(x,y) = y\) More...

static DG_DEVICE double	cooY3d (double x, double y, double z)
	\( f(x,y,z) = y\) More...

static DG_DEVICE double	cooZ3d (double x, double y, double z)
	\( f(x,y,z) = z\) More...

static DG_DEVICE double	cooRZP2X (double R, double Z, double P)
	\( x = R\sin(\varphi)\) More...

static DG_DEVICE double	cooRZP2Y (double R, double Z, double P)
	\( y = R\cos(\varphi)\) More...

static DG_DEVICE double	cooRZP2Z (double R, double Z, double P)
	\( z = Z\) More...

static DG_DEVICE float	one (float x)
	\( f(x) = 1\) More...

static DG_DEVICE float	one (float x, float y)
	\( f(x,y) = 1\) More...

static DG_DEVICE float	one (float x, float y, float z)
	\( f(x,y,z) = 1\) More...

static DG_DEVICE float	zero (float x)
	\( f(x) = 0\) More...

static DG_DEVICE float	zero (float x, float y)
	\( f(x,y) = 0\) More...

static DG_DEVICE float	zero (float x, float y, float z)
	\( f(x,y,z) = 0\) More...

template<class real_type >
real_type	interpolate (dg::space sp, const thrust::host_vector< real_type > &v, real_type x, const RealGrid1d< real_type > &g, dg::bc bcx=dg::NEU)
	Interpolate a vector on a single point on a 1d Grid. More...

template<class real_type >
real_type	interpolate (dg::space sp, const thrust::host_vector< real_type > &v, real_type x, real_type y, const aRealTopology2d< real_type > &g, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU)
	Interpolate a vector on a single point on a 2d Grid. More...

template<class real_type >
real_type	interpolate (dg::space sp, const thrust::host_vector< real_type > &v, real_type x, real_type y, const aRealTopologyX2d< real_type > &g, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU)
	Interpolate a vector on a single point on a 2d Grid. More...

template<class BinaryOp , class real_type >
MPI_Vector< thrust::host_vector< real_type > >	evaluate (const BinaryOp &f, const aRealMPITopology2d< real_type > &g)
	Evaluate a 2d function on mpi distributed grid coordinates. More...

template<class TernaryOp , class real_type >
MPI_Vector< thrust::host_vector< real_type > >	evaluate (const TernaryOp &f, const aRealMPITopology3d< real_type > &g)
	Evaluate a 3d function on mpi distributed grid coordinates. More...

template<class real_type >
MPI_Vector< thrust::host_vector< real_type > >	global2local (const thrust::host_vector< real_type > &global, const aRealMPITopology3d< real_type > &g)
	Take the relevant local part of a global vector. More...

template<class real_type >
MPI_Vector< thrust::host_vector< real_type > >	global2local (const thrust::host_vector< real_type > &global, const aRealMPITopology2d< real_type > &g)
	Take the relevant local part of a global vector. More...

template<class ConversionPolicy , class real_type >
dg::MIHMatrix_t< real_type >	convert (const dg::IHMatrix_t< real_type > &global, const ConversionPolicy &policy)
	Convert a (row-distributed) matrix with local row and global column indices to a row distributed MPI matrix. More...

template<class ConversionPolicy , class real_type >
dg::IHMatrix_t< real_type >	convertGlobal2LocalRows (const dg::IHMatrix_t< real_type > &global, const ConversionPolicy &policy)
	Convert a (column-distributed) matrix with global row and column indices to a row distributed matrix. More...

template<class ConversionPolicy , class real_type >
void	convertLocal2GlobalCols (dg::IHMatrix_t< real_type > &local, const ConversionPolicy &policy)
	Convert a matrix with local column indices to a matrix with global column indices. More...

template<class T >
dg::Operator< T >	invert (const dg::Operator< T > &in)
	Alias for `dg::create::inverse`. Compute inverse of square matrix. More...

template<class T >
Operator< T >	tensorproduct (const Operator< T > &op1, const Operator< T > &op2)
	Form the tensor product between two operators. More...

template<class T >
cusp::coo_matrix< int, T, cusp::host_memory >	tensorproduct (unsigned N, const Operator< T > &op)
	Tensor product between Identity matrix and an operator. More...

template<class T >
cusp::coo_matrix< int, T, cusp::host_memory >	sandwich (const Operator< T > &left, const cusp::coo_matrix< int, T, cusp::host_memory > &m, const Operator< T > &right)
	Multiply 1d matrices by diagonal block matrices from left and right. More...

template<class T >
T	gcd (T a, T b)
	Greatest common divisor. More...

template<class T >
T	lcm (T a, T b)
	Least common multiple. More...

template<class SharedContainer , class real_type >
void	split (SharedContainer &in, std::vector< View< SharedContainer > > &out, const aRealTopology3d< real_type > &grid)
	Split a vector into planes along the last dimension (fast version) More...

template<class SharedContainer , class real_type >
std::vector< View< SharedContainer > >	split (SharedContainer &in, const aRealTopology3d< real_type > &grid)
	Split a vector into planes along the last dimension (construct version) More...

template<class Container , class real_type >
void	assign3dfrom2d (const thrust::host_vector< real_type > &in2d, Container &out, const aRealTopology3d< real_type > &grid)
	Construct a 3d vector given a 2d host vector. More...

template<class MPIContainer , class real_type >
void	split (MPIContainer &in, std::vector< get_mpi_view_type< MPIContainer > > &out, const aRealMPITopology3d< real_type > &grid)
	MPI Version of split (fast version) More...

template<class MPIContainer , class real_type >
std::vector< get_mpi_view_type< MPIContainer > >	split (MPIContainer &in, const aRealMPITopology3d< real_type > &grid)
	MPI Version of split (construct version) More...

template<class LocalContainer , class real_type >
void	assign3dfrom2d (const MPI_Vector< thrust::host_vector< real_type > > &in2d, MPI_Vector< LocalContainer > &out, const aRealMPITopology3d< real_type > &grid)
	MPI Version of assign3dfrom2d. More...

template<class Functor , class real_type >
thrust::host_vector< real_type >	pullback (const Functor &f, const aRealGeometry2d< real_type > &g)
	\( f_i = f( x(\zeta_i, \eta_i), y(\zeta_i, \eta_i))\) More...

template<class Functor , class real_type >
thrust::host_vector< real_type >	pullback (const Functor &f, const aRealGeometry3d< real_type > &g)
	\( f_i = f( x(\zeta_i, \eta_i, \nu_i), y(\zeta_i, \eta_i, \nu_i), z(\zeta_i,\eta_i,\nu_i))\) More...

template<class Functor , class real_type >
MPI_Vector< thrust::host_vector< real_type > >	pullback (const Functor &f, const aRealMPIGeometry2d< real_type > &g)
	\( f_i = f( x(\zeta_i, \eta_i), y(\zeta_i, \eta_i))\) More...

template<class Functor , class real_type >
MPI_Vector< thrust::host_vector< real_type > >	pullback (const Functor &f, const aRealMPIGeometry3d< real_type > &g)
	\( f_i = f( x(\zeta_i, \eta_i, \nu_i), y(\zeta_i, \eta_i, \nu_i), z(\zeta_i,\eta_i,\nu_i))\) More...

template<class Functor1 , class Functor2 , class container , class Geometry >
void	pushForwardPerp (const Functor1 &vR, const Functor2 &vZ, container &vx, container &vy, const Geometry &g)
	\( \bar v = J v\) More...

template<class Functor1 , class Functor2 , class Functor3 , class container , class Geometry >
void	pushForward (const Functor1 &vR, const Functor2 &vZ, const Functor3 &vPhi, container &vx, container &vy, container &vz, const Geometry &g)
	\( {\bar v} = J v\) More...

template<class FunctorRR , class FunctorRZ , class FunctorZZ , class container , class Geometry >
void	pushForwardPerp (const FunctorRR &chiRR, const FunctorRZ &chiRZ, const FunctorZZ &chiZZ, SparseTensor< container > &chi, const Geometry &g)
	\( \bar \chi = J \chi J^T\) More...

template<class T >
cusp::csr_matrix< int, T, cusp::host_memory >	tensorproduct (const cusp::csr_matrix< int, T, cusp::host_memory > &lhs, const cusp::csr_matrix< int, T, cusp::host_memory > &rhs)
	\( L\otimes R\) Form the tensor (Kronecker) product between two matrices More...

template<class from_ContainerType , class ContainerType , class ... Params>
void	assign (const from_ContainerType &from, ContainerType &to, Params &&... ps)
	Generic way to assign the contents of a `from_ContainerType` object to a `ContainerType` object optionally given additional parameters. More...

template<class ContainerType , class from_ContainerType , class ... Params>
ContainerType	construct (const from_ContainerType &from, Params &&... ps)
	Generic way to construct an object of `ContainerType` given a `from_ContainerType` object and optional additional parameters. More...

template<class MatrixType , class ContainerType1 , class ContainerType2 >
void	apply (get_value_type< ContainerType1 > alpha, MatrixType &&M, const ContainerType1 &x, get_value_type< ContainerType1 > beta, ContainerType2 &y)
	\( y = \alpha M(x) + \beta y \); (alias for `dg::blas2::symv`) More...

template<class MatrixType , class ContainerType1 , class ContainerType2 >
void	apply (MatrixType &&M, const ContainerType1 &x, ContainerType2 &y)
	\( y = M( x)\); (alias for `dg::blas2::symv`) More...

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

static bc	str2bc (std::string s)
	convert a string to a bc More...

static bc	inverse (bc bound)
	invert boundary condition More...

static direction	str2direction (std::string s)
	convert a string to a direction More...

static std::string	direction2str (enum direction dir)
	convert a direciton to string More...

static direction	inverse (direction dir)
	invert direction More...

template<class ContainerType0 , class ContainerType1 >
std::vector< double >	least_squares (const std::vector< ContainerType0 > &bs, const ContainerType1 &b)
	Compute \( a = (B^T B)^{-1} B^T b\) for given \( B\) and \( a\). More...

template<class MatrixType0 , class ContainerType0 , class ContainerType1 , class MatrixType1 , class NestedGrids >
void	nested_iterations (std::vector< MatrixType0 > &ops, ContainerType0 &x, const ContainerType1 &b, std::vector< MatrixType1 > &inverse_ops, NestedGrids &nested_grids)
	Full approximation nested iterations. More...

template<class NestedGrids , class MatrixType0 , class MatrixType1 , class MatrixType2 >
void	multigrid_cycle (std::vector< MatrixType0 > &ops, std::vector< MatrixType1 > &inverse_ops_down, std::vector< MatrixType2 > &inverse_ops_up, NestedGrids &nested_grids, unsigned gamma, unsigned p)
	EXPERIMENTAL Full approximation multigrid cycle. More...

template<class MatrixType0 , class MatrixType1 , class MatrixType2 , class NestedGrids , class ContainerType0 , class ContainerType1 >
void	full_multigrid (std::vector< MatrixType0 > &ops, ContainerType0 &x, const ContainerType1 &b, std::vector< MatrixType1 > &inverse_ops_down, std::vector< MatrixType2 > &inverse_ops_up, NestedGrids &nested_grids, unsigned gamma, unsigned mu)
	EXPERIMENTAL One Full multigrid cycle. More...

template<class NestedGrids , class MatrixType0 , class MatrixType1 , class MatrixType2 , class ContainerType0 , class ContainerType1 , class ContainerType2 >
void	fmg_solve (std::vector< MatrixType0 > &ops, ContainerType0 &x, const ContainerType1 &b, std::vector< MatrixType1 > &inverse_ops_down, std::vector< MatrixType2 > &inverse_ops_up, NestedGrids &nested_grids, const ContainerType2 &weights, double eps, unsigned gamma)
	EXPERIMENTAL Full multigrid cycles. More...

template<typename UnaryOp >
int	bisection1d (UnaryOp &op, double &x_min, double &x_max, const double eps)
	Find a root of a 1d function \( f(x) = 0\). More...

static std::string	to2str (enum to mode)
	Convert integration mode to string. More...

bool	is_same (double x, double y, double eps=1e-15)

bool	is_same (float x, float y, float eps=1e-6)

bool	is_divisable (double a, double b, double eps=1e-15)

bool	is_divisable (float a, float b, float eps=1e-6)

template<class UnaryOp , class Functor >
auto	compose (UnaryOp f, Functor g)
	Create Composition functor \( f(g(x_0,x_1,...)) \). More...

template<class UnaryOp , typename... Functors>
auto	compose (UnaryOp f0, Functors... fs)
	Create Composition funtor of an arbitrary number of functions \( f_0(f_1(f_2( ... f_s(x_0, x_1, ...)))\). More...

Variables
static auto	l2norm = [] ( const auto& x){ return sqrt( dg::blas1::dot(x,x));}
	Compute \( \sqrt{\sum_i x_i^2}\) using `dg::blas1::dot`. More...

static auto	fast_l2norm
	Compute \( \sqrt{\sum_i x_i^2}\) using naive summation. More...

static auto	i_control
	\( h_{n+1}= h_n \epsilon_n^{-1/p}\) More...

static auto	pi_control
	\( h_{n+1}= h_n \epsilon_n^{-0.8/p}\epsilon_{n-1}^{0.31/p}\) More...

static auto	pid_control
	\( h_{n+1}= h_n \epsilon_n^{-0.58/p}\epsilon_{n-1}^{0.21/p}\epsilon_{n-2}^{-0.1/p}\) More...

static auto	ex_control
	\( h_{n+1} = h_n \epsilon_n^{-0.367/p}(\epsilon_n/\epsilon_{n-1})^{0.268/p} \) More...

static auto	im_control
	\( h_{n+1} = h_n (h_n/h_{n-1}) \epsilon_n^{-0.98/p}(\epsilon_n/\epsilon_{n-1})^{-0.95/p} \) More...

static auto	imex_control
	h_{n+1} = \|ex_control\| < \|im_control\| ? ex_control : im_control More...

Detailed Description

This is the namespace for all functions and classes defined and used by the discontinuous Galerkin library.

Typedef Documentation

◆ CooSparseBlockMatDevice

template<class value_type >

using dg::CooSparseBlockMatDevice = typedef CooSparseBlockMat<value_type>

◆ EllSparseBlockMatDevice

template<class value_type >

using dg::EllSparseBlockMatDevice = typedef EllSparseBlockMat<value_type>

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ CooSparseBlockMatDevice

◆ EllSparseBlockMatDevice