This is the namespace for all functions and classes defined and used by the discontinuous Galerkin library.
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| struct | ABS |
| | \( f(x) = |x|\) More...
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| struct | AbsMax |
| | \( f(x,y) = \max(|x|,|y|)\) More...
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| struct | AbsMin |
| | \( f(x,y) = \min(|x|,|y|)\) More...
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| struct | Adaptive |
| | Driver class for adaptive timestep ODE integration. More...
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| struct | AdaptiveTimeloop |
| | Integrate using a while loop. More...
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| struct | Advection |
| | Upwind discretization of advection operator \( \vec v\cdot\nabla f\) More...
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| struct | AndersonAcceleration |
| | Anderson Acceleration of Fixed Point/Richardson Iteration for the nonlinear equation \( f(x) = b\). More...
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| struct | AnyMatrixTag |
| | tensor_category base class More...
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| struct | AnyPolicyTag |
| | Execution Policy base class. More...
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| struct | AnyScalarTag |
| | Scalar Tag base class. More...
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| struct | AnyVectorTag |
| | Vector Tag base class, indicates the basic Vector/container concept. More...
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| struct | ArakawaX |
| | Arakawa's scheme for Poisson bracket \( \{ f,g\} \). More...
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| struct | aRealGeometry2d |
| | This is the abstract interface class for a two-dimensional Geometry. More...
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| struct | aRealGeometry3d |
| | This is the abstract interface class for a three-dimensional Geometry. More...
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| struct | aRealGeometryX2d |
| | This is the abstract interface class for a two-dimensional RealGeometryX. More...
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| struct | aRealGeometryX3d |
| | This is the abstract interface class for a three-dimensional RealGeometryX. More...
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| struct | aRealMPIGeometry2d |
| | This is the abstract interface class for a two-dimensional Geometry. More...
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| struct | aRealMPIGeometry3d |
| | This is the abstract interface class for a three-dimensional MPIGeometry. More...
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| struct | aRealMPITopology |
| | An abstract base class for MPI distributed Nd-dimensional dG grids. More...
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| struct | aRealProductGeometry3d |
| | A 3d product space Geometry \( g_{2d} \otimes g_{1d}\). More...
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| struct | aRealProductMPIGeometry3d |
| | A 3d product space Geometry \( g_{2d} \otimes g_{1d}\). More...
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| struct | aRealRefinement1d |
| | Abstract base class for 1d grid refinement that increases the number of grid cells of a fixed basis grid. More...
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| struct | aRealRefinementX2d |
| | Abstract base class for 2d grid refinement that increases the number of grid cells of a fixed basis grid. More...
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| struct | aRealTopology |
| | An abstract base class for Nd-dimensional dG grids. More...
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| struct | aRealTopologyX2d |
| | A 2D grid class with X-point topology. More...
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| struct | aRealTopologyX3d |
| | A 3D grid class with X-point topology. More...
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| struct | ArithmeticTag |
| | Types where std::is_arithmetic is true. More...
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| struct | ARKStep |
| | Additive Runge Kutta (semi-implicit) time-step with error estimate following The ARKode library More...
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| struct | ArrayScalarTag |
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| struct | ArrayVectorTag |
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| struct | aTimeloop |
| | Abstract timeloop independent of stepper and ODE. More...
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| struct | Average |
| | Topological average computations in a Cartesian topology. More...
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| struct | BathRZ |
| | \(f(R,Z) = A B \sum_\vec{k} \sqrt{E_k} \alpha_k \cos{\left(k \kappa_k + \theta_k \right)}
\) More...
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| class | BICGSTABl |
| | Preconditioned BICGSTAB(l) method to solve \( Ax=b\). More...
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| struct | ButcherTableau |
| | Manage coefficients of a (extended) Butcher tableau. More...
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| 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...
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| 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...
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| class | ChebyshevIteration |
| | Preconditioned Chebyshev iteration for solving \( PAx=Pb\). More...
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| struct | ChebyshevPreconditioner |
| | Chebyshev Polynomial Preconditioner \( C( A)\). More...
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| struct | ClonePtr |
| | Manager class that invokes the clone() method on the managed ptr when copied. More...
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| struct | ComplexTag |
| | complex number type More...
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| struct | Composite |
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| struct | CONSTANT |
| | \( f(x,...) = c\) More...
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| struct | ConvertsToButcherTableau |
| | Convert identifiers to their corresponding dg::ButcherTableau. More...
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| struct | ConvertsToMultistepTableau |
| | Convert identifiers to their corresponding dg::MultistepTableau. More...
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| struct | ConvertsToShuOsherTableau |
| | Convert identifiers to their corresponding dg::ShuOsherTableau. More...
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| struct | CooSparseBlockMat |
| | Coo Sparse Block Matrix format. More...
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| struct | CosXCosY |
| | \( f(x,y) =B+ A \cos(k_x x) \cos(k_y y) \) More...
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| struct | CosY |
| | \( f(x,y) =B+ A \cos(k_y y) \) More...
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| struct | CSRAverageFilter |
| | Average filter that computes the average of all points in the stencil More...
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| struct | CSRMedianFilter |
| | Compute (lower) Median of input numbers. More...
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| struct | CSRSlopeLimiter |
| | Generalized slope limiter for dG methods. More...
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| struct | CSRSWMFilter |
| | Switching median filter. More...
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| struct | CSRSymvFilter |
| | Test filter that computes the symv csr matrix-vector product if used. More...
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| struct | CudaTag |
| | CUDA implementation. More...
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| struct | CuspMatrixTag |
| | One of cusp's matrices, for these only the blas2 transfer and the symv( m,x,y) are implemented. More...
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| struct | CuspVectorTag |
| | special tag for cusp arrays More...
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| struct | DefaultSolver |
| | PCG Solver class for solving \( (y-\alpha\hat I(t,y)) = \rho\). More...
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| struct | DenseMatrixTag |
| | indicate our dense matrix format More...
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| 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...
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| struct | Distance |
| | \( f(x,y) = \sqrt{ (x-x_0)^2 + (y-y_0)^2} \) More...
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| struct | divides_equals |
| | \( y = y/x\) More...
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| struct | DLT |
| | Struct providing coefficients for Discrete Legendre Transformation (DLT) related operations. More...
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| 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...
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| class | Elliptic1d |
| | A 1d negative elliptic differential operator \( -\partial_x ( \chi \partial_x ) \). More...
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| class | Elliptic2d |
| | A 2d negative elliptic differential operator \( -\nabla \cdot ( \mathbf{\chi}\cdot \nabla ) \). More...
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| class | Elliptic3d |
| | A 3d negative elliptic differential operator \( -\nabla \cdot ( \mathbf{\chi}\cdot \nabla ) \). More...
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| struct | EllSparseBlockMat |
| | Ell Sparse Block Matrix format. More...
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| struct | EmbeddedPairSum |
| | \( y = \sum_i b_i x_i + b_0 y,\quad \tilde y = \sum_i \tilde b_i x_i + \tilde b_0 y \) More...
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| struct | EntireDomain |
| | The domain that contains all points. More...
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| struct | equals |
| | \( y=x\) More...
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| 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...
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| class | Error |
| | class intended for the use in throw statements More...
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| class | EVE |
| | The Eigen-Value-Estimator (EVE) finds largest Eigenvalue of \( M^{-1}Ax = \lambda_\max x\). More...
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| struct | EXP |
| | \( f(x) = \exp( x)\) More...
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| 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...
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| 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...
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| struct | ExpProfX |
| | \( f(x) = f(x,y) = f(x,y,z) = A\exp(-x/L_n) + B \) More...
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| struct | Extrapolation |
| | Extrapolate a polynomial passing through up to three points. More...
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| struct | Fail |
| | Indicate failure to converge. More...
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| 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...
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| 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...
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| struct | FloatingPointTag |
| | Types where std::is_floating_point is true. More...
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| 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...
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| 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...
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| 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...
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| struct | GaussianX |
| | \(
f(x,y) = Ae^{-\frac{(x-x_0)^2}{2\sigma_x^2} }
\) More...
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| struct | GaussianY |
| | \(
f(x,y) = Ae^{-\frac{(y-y_0)^2}{2\sigma_y^2}}
\) More...
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| struct | GaussianZ |
| | \(
f(x,y,z) = Ae^{-\frac{(z-z_0)^2}{2\sigma_z^2}}
\) More...
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| struct | GeneralHelmholtz |
| | A general Helmholtz-type operator \( (\chi-\alpha F) \). More...
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| struct | Heaviside |
| | \( f(x) = \begin{cases}
0 \text{ if } x < x_b \\
1 \text{ else}
\end{cases}\) More...
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| struct | Helmholtz2 |
| | DEPRECATED, Matrix class that represents a more general Helmholtz-type operator. More...
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| struct | Histogram |
| | Compute a histogram on a 1D grid. More...
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| struct | Histogram2D |
| | Compute a histogram on a 2D grid. More...
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| struct | Horner2d |
| | \( f(x,y) = \sum_{i=0}^{M-1} \sum_{j=0}^{N-1} c_{iN+j} x^i y^j \) More...
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| struct | IDENTITY |
| | \( f(x) = x\) More...
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| struct | IdentityFilter |
| | A filter that does nothing. More...
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| 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...
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| 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...
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| struct | IntegralTag |
| | Types where std::is_integral is true. More...
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| struct | InvCoshXsq |
| | \( f(x,y) =A/\cosh^2(k_x x) \) More...
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| struct | InverseKroneckerTriDiagonal2d |
| | Fast inverse tridiagonal sparse matrix in 2d \( T_y^{-1}\otimes T_x^{-1}\). More...
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| struct | InverseTriDiagonal |
| | DEPRECATED/UNTESTED Fast inverse tridiagonal sparse matrix. More...
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| struct | INVERT |
| | \( f(x) = 1/x \) More...
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| struct | InvSqrt |
| | \( f(x) = \frac{1}{\sqrt{x}}\) More...
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| 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...
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| struct | Iris |
| | \( f(\psi) = \begin{cases}
1 \text{ if } \psi_{\min} < \psi < \psi_{\max}\\
0 \text{ else}
\end{cases}\) More...
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| struct | IslandXY |
| | \( f(x,y) = \lambda \ln{(\cosh{(x/\lambda) } +\epsilon \cos(y/\lambda)) } \) More...
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| struct | ISNFINITE |
| | \( f(x) = \mathrm{!std::isfinite(x)}\) More...
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| struct | ISNSANE |
| | \( f(x) =\begin{cases} \mathrm{true\ if}\ |x| > 10^{100}\\
\mathrm{false\ else}
\end{cases}\) More...
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| struct | KroneckerTriDiagonal2d |
| | Fast tridiagonal sparse matrix in 2d \( T_y\otimes T_x\). More...
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| 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...
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| struct | LeastSquaresExtrapolation |
| | Evaluate a least squares fit More...
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| struct | LeastSquaresPreconditioner |
| | Least Squares Polynomial Preconditioner \( M^{-1} s( AM^{-1})\). More...
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| class | LGMRES |
| | Functor class for the right preconditioned LGMRES method to solve \( Ax=b\). More...
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| 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...
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| struct | LinearX |
| | \( f(x) = f(x,y) = f(x,y,z) = ax+b \) More...
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| struct | LinearY |
| | \( f(x,y) = f(x,y,z) = ay+b \) More...
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| struct | LinearZ |
| | \( f(x,y,z) = az+b \) More...
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| struct | LN |
| | \( f(x) = \ln(x)\) More...
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| |
| class | Message |
| | small class holding a stringstream More...
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| |
| 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...
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| |
| struct | minus_equals |
| | \( y=y-x\) More...
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| struct | MOD |
| | \( f(x) = \) x mod m > 0 ? x mod m : x mod m + m More...
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| struct | ModifiedChebyshevPreconditioner |
| | Approximate inverse Chebyshev Polynomial Preconditioner \( A^{-1} = \frac{c_0}{2} I + \sum_{k=1}^{r}c_kT_k( Z)\). More...
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| |
| struct | MPI_Vector |
| | A simple wrapper around a container object and an MPI_Comm. More...
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| |
| struct | MPIDistMat |
| | Distributed memory matrix class, asynchronous communication. More...
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| |
| struct | MPIGather |
| | Optimized MPI Gather operation. More...
|
| |
| struct | MPIKroneckerGather |
| | Communicator for asynchronous communication of MPISparseBlockMat. More...
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| struct | MPIMatrixTag |
| | indicate one of our mpi matrices More...
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| struct | MPISparseBlockMat |
| | Distributed memory Sparse block matrix class, asynchronous communication. More...
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| struct | MPIVectorTag |
| | A distributed vector contains a data container and a MPI communicator. More...
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| struct | MultigridCG2d |
| | Solve. More...
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| |
| struct | MultiMatrix |
| | Struct that applies given matrices one after the other. More...
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| |
| struct | MultistepTableau |
| | Manage coefficients of Multistep methods. More...
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| |
| struct | MultistepTimeloop |
| | Integrate using a for loop and a fixed non-changeable time-step. More...
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| |
| struct | NestedGrids |
| | Hold nested grids and provide dg fast interpolation and projection matrices. More...
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| |
| struct | NoPolicyTag |
| | Indicate that a type does not have an execution policy. More...
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| |
| class | NoRoot1d |
| | Exception class, that stores boundaries for 1D root finding. More...
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| |
| struct | NotATensorTag |
| | Indicate that a type is not a tensor. More...
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| |
| struct | OmpTag |
| | OpenMP parallel execution. More...
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| |
| struct | ONE |
| | \( f(x,...) = 1\) More...
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| |
| struct | PairSum |
| | \( y = \sum_i a_i x_i \) More...
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| |
| class | PCG |
| | Preconditioned conjugate gradient method to solve \( Ax=b\). More...
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| |
| struct | PLUS |
| | \( f(x) = x + c\) More...
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| |
| struct | plus_equals |
| | \( y=y+x\) More...
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| |
| struct | Poisson |
| | Direct discretization of Poisson bracket \( \{ f,g\} \). More...
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| |
| 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...
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| |
| 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...
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| |
| struct | POSVALUE |
| | \( f(x) = \begin{cases}
x \text{ for } x>0 \\
0 \text{ else}
\end{cases}
\) More...
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| |
| struct | Product |
| | \( y = \prod_i x_i \) More...
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| |
| struct | PsiPupil |
| | \( f(\psi) = \begin{cases}
\psi_{\max} \text{ if } \psi > \psi_{\max} \\
\psi \text{ else}
\end{cases}\) More...
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| |
| 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 | RealGrid |
| | The simplest implementation of aRealTopology. 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 | RealMPIGrid |
| | The simplest implementation of aRealMPITopology3d. More...
|
| |
| struct | RecursiveVectorTag |
| | This tag indicates composition/recursion. More...
|
| |
| class | RefinedElliptic |
| | The refined version of Elliptic. More...
|
| |
| 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 | 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 | SparseMatrix |
| | A CSR formatted sparse matrix. More...
|
| |
| struct | SparseMatrixTag |
| | indicate our sparse 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...
|
| |
| class | SquareMatrix |
| | A square nxn matrix. More...
|
| |
| struct | StdMapTag |
| |
| struct | Sum |
| | \( y = \sum_i x_i \) More...
|
| |
| struct | TanhProfX |
| | \( f(x) = B + 0.5 A(1+ \text{sign} \tanh((x-x_b)/\alpha ) ) \) More...
|
| |
| struct | TensorTraits |
| | The vector traits. More...
|
| |
| struct | TensorTraits< CooSparseBlockMat< T, V > > |
| |
| 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, V > > |
| |
| struct | TensorTraits< mat::PolChargeN< G, M, V > > |
| |
| struct | TensorTraits< MPI_Vector< container > > |
| | prototypical MPI vector More...
|
| |
| struct | TensorTraits< MPIDistMat< V, LI, LO > > |
| |
| struct | TensorTraits< MPISparseBlockMat< V, LI, LO > > |
| |
| struct | TensorTraits< SparseMatrix< I, T, V > > |
| |
| struct | TensorTraits< SquareMatrix< T > > |
| |
| struct | TensorTraits< std::array< T, N >, std::enable_if_t< !dg::is_scalar< T >::value > > |
| |
| struct | TensorTraits< std::array< T, N >, std::enable_if_t< dg::is_scalar< T >::value > > |
| |
| struct | TensorTraits< std::complex< T > > |
| | Enable std::complex as a Scalar. More...
|
| |
| struct | TensorTraits< std::map< Key, T > > |
| | Behaves like a RecursiveVector. More...
|
| |
| struct | TensorTraits< std::vector< T >, std::enable_if_t< !dg::is_scalar< T >::value > > |
| | Prototypical Recursive Vector (unless vector of scalars) More...
|
| |
| struct | TensorTraits< std::vector< T >, std::enable_if_t< dg::is_scalar< T >::value > > |
| |
| struct | TensorTraits< T, std::enable_if_t< std::is_floating_point_v< T > > > |
| | Enable double and float as a floating point. More...
|
| |
| struct | TensorTraits< T, std::enable_if_t< std::is_integral_v< T > > > |
| | Enable integers and anything promotable to integer (such as bool and char) as integral. More...
|
| |
| struct | TensorTraits< thrust::complex< T > > |
| |
| 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 | ThrustVectorTag |
| | Indicate thrust/std - like behaviour. More...
|
| |
| struct | Timer |
| | Simple tool for performance measuring. More...
|
| |
| struct | times_equals |
| | \( y=xy\) More...
|
| |
| struct | TriDiagonal |
| | Fast (shared memory) tridiagonal sparse matrix. More...
|
| |
| struct | TripletSum |
| | \( y = \sum_i a_i x_i y_i \) 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 | WhichType |
| |
| struct | ZERO |
| | \( f(x, ...) = 0\) More...
|
| |
|
| template<class T , class Tag = AnyScalarTag> |
| using | is_scalar = typename std::is_base_of<Tag, get_tensor_category<T>>::type |
| | Does a type have a tensor_category derived from Tag.
|
| |
| template<class T , class Tag = AnyVectorTag> |
| using | is_vector = typename std::is_base_of<Tag, get_tensor_category<T>>::type |
| | Does a type have a tensor_category derived from Tag.
|
| |
| template<class T , class Tag = AnyMatrixTag> |
| using | is_matrix = typename std::is_base_of<Tag, get_tensor_category<T>>::type |
| | Does a type have a tensor_category derived from Tag.
|
| |
| template<class T , class Tag = AnyPolicyTag> |
| using | has_policy = std::is_same<Tag, get_execution_policy<T>> |
| | Does a type have an execution_policy equal to Tag.
|
| |
| 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.
|
| |
| using | HVec = thrust::host_vector<double> |
| | Host Vector.
|
| |
| using | cHVec = thrust::host_vector<thrust::complex<double>> |
| | complex Host Vector
|
| |
| using | iHVec = thrust::host_vector<int> |
| | integer Host Vector
|
| |
| using | fHVec = thrust::host_vector<float> |
| | Host Vector.
|
| |
| 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.
|
| |
| using | iDVec = thrust::device_vector<int> |
| | integer Device Vector
|
| |
| using | cDVec = thrust::device_vector<thrust::complex<double>> |
| | complex Device Vector
|
| |
| 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.
|
| |
| template<class T > |
| using | HMatrix_t = EllSparseBlockMat<T, thrust::host_vector> |
| |
| using | HMatrix = EllSparseBlockMat<double, thrust::host_vector> |
| | Host Matrix for derivatives.
|
| |
| using | fHMatrix = EllSparseBlockMat<float, thrust::host_vector> |
| | Host Matrix for derivatives.
|
| |
| using | DMatrix = EllSparseBlockMat<double, thrust::device_vector> |
| | Device Matrix for derivatives.
|
| |
| using | fDMatrix = EllSparseBlockMat<float, thrust::device_vector> |
| | Device Matrix for derivatives.
|
| |
| template<class real_type > |
| using | IHMatrix_t = dg::SparseMatrix<int, real_type, thrust::host_vector> |
| |
| template<class real_type > |
| using | IDMatrix_t = dg::SparseMatrix<int, real_type, thrust::device_vector> |
| |
| 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.
|
| |
| using | MHVec = dg::MPI_Vector<dg::HVec > |
| | MPI Host Vector s.a. dg::HVec.
|
| |
| using | cMHVec = dg::MPI_Vector<dg::cHVec > |
| | MPI Host Vector s.a. dg::cHVec.
|
| |
| using | fMHVec = dg::MPI_Vector<dg::fHVec > |
| | MPI Host Vector s.a. dg::fHVec.
|
| |
| using | MDVec = dg::MPI_Vector<dg::DVec > |
| | MPI Device Vector s.a. dg::DVec.
|
| |
| using | cMDVec = dg::MPI_Vector<dg::cDVec > |
| | MPI Device Vector s.a. dg::cDVec.
|
| |
| using | fMDVec = dg::MPI_Vector<dg::fDVec > |
| | MPI Device Vector s.a. dg::fDVec.
|
| |
| template<class T > |
| using | CooMat_t = dg::CooSparseBlockMat<T, thrust::host_vector> |
| |
| using | CooMat = dg::CooSparseBlockMat<double, thrust::host_vector> |
| |
| using | fCooMat = dg::CooSparseBlockMat<float, thrust::host_vector> |
| |
| using | DCooMat = dg::CooSparseBlockMat<double, thrust::device_vector> |
| |
| using | fDCooMat = dg::CooSparseBlockMat<float, thrust::device_vector> |
| |
| template<class T > |
| using | MHMatrix_t = dg::MPISparseBlockMat<thrust::host_vector, dg::HMatrix_t<T>, dg::CooMat_t<T>> |
| | MPI Host Matrix for derivatives.
|
| |
| using | MHMatrix = dg::MPISparseBlockMat<thrust::host_vector, dg::HMatrix, dg::CooMat> |
| | MPI Host Matrix for derivatives.
|
| |
| using | fMHMatrix = dg::MPISparseBlockMat<thrust::host_vector, dg::fHMatrix, dg::fCooMat> |
| | MPI Host Matrix for derivatives.
|
| |
| using | MDMatrix = dg::MPISparseBlockMat<thrust::device_vector, dg::DMatrix, dg::DCooMat> |
| | MPI Device Matrix for derivatives.
|
| |
| using | fMDMatrix = dg::MPISparseBlockMat<thrust::device_vector, dg::fDMatrix, dg::fDCooMat> |
| | MPI Device Matrix for derivatives.
|
| |
| template<class real_type > |
| using | MIHMatrix_t = MPIDistMat< thrust::host_vector, IHMatrix_t<real_type> > |
| |
| template<class real_type > |
| using | MIDMatrix_t = MPIDistMat< thrust::device_vector, IDMatrix_t<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 | Grid0d = dg::RealGrid<double,0> |
| |
| using | Grid1d = dg::RealGrid<double,1> |
| |
| using | Grid2d = dg::RealGrid<double,2> |
| |
| using | Grid3d = dg::RealGrid<double,3> |
| |
| template<size_t Nd> |
| using | Grid = dg::RealGrid<double,Nd> |
| |
| using | aTopology2d = dg::aRealTopology<double,2> |
| |
| using | aTopology3d = dg::aRealTopology<double,3> |
| |
| template<class T > |
| using | aRealTopology2d = dg::aRealTopology<T,2> |
| |
| template<class T > |
| using | aRealTopology3d = dg::aRealTopology<T,3> |
| |
| template<class T > |
| using | RealGrid0d = dg::RealGrid<T,0> |
| |
| template<class T > |
| using | RealGrid1d = dg::RealGrid<T,1> |
| |
| template<class T > |
| using | RealGrid2d = dg::RealGrid<T,2> |
| |
| template<class T > |
| using | RealGrid3d = dg::RealGrid<T,3> |
| |
| 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 | MPIGrid0d = dg::RealMPIGrid<double,0> |
| |
| using | MPIGrid1d = dg::RealMPIGrid<double,1> |
| |
| using | MPIGrid2d = dg::RealMPIGrid<double,2> |
| |
| using | MPIGrid3d = dg::RealMPIGrid<double,3> |
| |
| template<size_t Nd> |
| using | MPIGrid = dg::RealMPIGrid<double,Nd> |
| |
| using | aMPITopology2d = dg::aRealMPITopology<double,2> |
| |
| using | aMPITopology3d = dg::aRealMPITopology<double,3> |
| |
| template<class T > |
| using | aRealMPITopology2d = dg::aRealMPITopology<T,2> |
| |
| template<class T > |
| using | aRealMPITopology3d = dg::aRealMPITopology<T,3> |
| |
| template<class T > |
| using | RealMPIGrid0d = dg::RealMPIGrid<T,0> |
| |
| template<class T > |
| using | RealMPIGrid1d = dg::RealMPIGrid<T,1> |
| |
| template<class T > |
| using | RealMPIGrid2d = dg::RealMPIGrid<T,2> |
| |
| template<class T > |
| using | RealMPIGrid3d = dg::RealMPIGrid<T,3> |
| |
| template<class T > |
| using | Operator = SquareMatrix<T> |
| | The old name for SquareMatrix was Operator.
|
| |
| 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 |
| |
| template<class ContainerType > |
| using | FixedPointIteration = AndersonAcceleration<ContainerType> |
| | If you are looking for fixed point iteration: it is a special case of Anderson Acceleration.
|
| |
| template<class Geometry , class Matrix , class Container > |
| using | Elliptic = Elliptic2d<Geometry, Matrix, Container> |
| | A 2d negative elliptic differential operator \( -\nabla \cdot ( \mathbf{\chi}\cdot \nabla ) \).
|
| |
| template<class Geometry , class Matrix , class Container > |
| using | Helmholtz = GeneralHelmholtz<dg::Elliptic2d<Geometry,Matrix,Container>, Container> |
| | a 2d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\Delta\)
|
| |
| template<class Geometry , class Matrix , class Container > |
| using | Helmholtz1d = GeneralHelmholtz<dg::Elliptic1d<Geometry,Matrix,Container>, Container> |
| | a 1d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\partial_x^2\)
|
| |
| template<class Geometry , class Matrix , class Container > |
| using | Helmholtz2d = GeneralHelmholtz<dg::Elliptic2d<Geometry,Matrix,Container>, Container> |
| | a 2d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\Delta\)
|
| |
| template<class Geometry , class Matrix , class Container > |
| using | Helmholtz3d = GeneralHelmholtz<dg::Elliptic3d<Geometry,Matrix,Container>, Container> |
| | a 3d Helmholtz opereator \( (\chi - \alpha F)\) with \( F = -\Delta\)
|
| |
| template<class ContainerType > |
| using | RungeKutta = ERKStep<ContainerType> |
| | Runge-Kutta fixed-step explicit ODE integrator \(
\begin{align}
k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right) \\
u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j
\end{align}
\).
|
| |
| template<class ContainerType > |
| using | FilteredRungeKutta = FilteredERKStep<ContainerType> |
| | Filtered Runge-Kutta fixed-step explicit ODE integrator \(
\begin{align}
k_i = f\left( t^n + c_i \Delta t, \Lambda\Pi \left[u^n + \Delta t \sum_{j=1}^{i-1} a_{ij} k_j\right]\right) \\
u^{n+1} = \Lambda\Pi\left[u^{n} + \Delta t\sum_{j=1}^s b_j k_j\right]
\end{align}
\).
|
| |
| template<class ContainerType > |
| using | ImplicitRungeKutta = DIRKStep<ContainerType> |
| | Runge-Kutta fixed-step implicit ODE integrator \(
\begin{align}
k_i = f\left( t^n + c_i \Delta t, u^n + \Delta t \sum_{j=1}^{s} a_{ij} k_j\right) \\
u^{n+1} = u^{n} + \Delta t\sum_{j=1}^s b_j k_j
\end{align}
\).
|
| |
|
| template<class ContainerType > |
| auto | asDenseMatrix (const std::vector< const ContainerType * > &in) |
| | Lightweight DenseMatrix for dg::blas2::gemv.
|
| |
| template<class ContainerType > |
| auto | asDenseMatrix (const std::vector< const ContainerType * > &in, unsigned size) |
| | Lightweight DenseMatrix for dg::blas2::gemv.
|
| |
| template<class ContainerType > |
| std::vector< const ContainerType * > | asPointers (const std::vector< ContainerType > &in) |
| | Convert a vector of vectors to a vector of pointers.
|
| |
| void | abort_program (int code=-1) |
| | Abort program (both MPI and non-MPI)
|
| |
| void | mpi_init (int argc, char *argv[]) |
| | Convencience shortcut: Calls MPI_Init or MPI_Init_thread and inits CUDA devices.
|
| |
| template<class T > |
| std::vector< T > | mpi_read_as (unsigned num, MPI_Comm comm, std::istream &is=std::cin) |
| | Read num values from is and broadcast to all processes as type T.
|
| |
| void | mpi_read_grid (unsigned &n, std::vector< unsigned > &N, MPI_Comm comm, std::istream &is=std::cin, bool verbose=true, std::ostream &os=std::cout) |
| | Read in grid sizes from is.
|
| |
| void | mpi_read_grid (unsigned &n, std::vector< unsigned * > N, MPI_Comm comm, std::istream &is=std::cin, bool verbose=true, std::ostream &os=std::cout) |
| | Convenience shortcut allowing a call like.
|
| |
| MPI_Comm | mpi_cart_create (MPI_Comm comm_old, std::vector< int > dims, std::vector< int > periods, bool reorder=true) |
| | Convenience call to MPI_Cart_create preceded by MPI_Dims_create.
|
| |
| MPI_Comm | mpi_cart_create (std::vector< dg::bc > bcs, std::istream &is=std::cin, MPI_Comm comm_old=MPI_COMM_WORLD, bool reorder=true, bool verbose=true, std::ostream &os=std::cout) |
| | Convenience call: read in number of processses from istream and create Cartesian MPI communicator.
|
| |
| void | mpi_init1d (dg::bc bcx, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true) |
| | DEPRECATED: Short for.
|
| |
| void | mpi_init2d (dg::bc bcx, dg::bc bcy, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true) |
| | DEPRECATED: Short for.
|
| |
| void | mpi_init3d (dg::bc bcx, dg::bc bcy, dg::bc bcz, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true) |
| | DEPRECATED: Short for.
|
| |
| void | mpi_init1d (dg::bc bcx, unsigned &n, unsigned &N, MPI_Comm &comm, std::istream &is=std::cin, bool verbose=true) |
| | DEPRECATED.
|
| |
| 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) |
| | DEPRECATED.
|
| |
| 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) |
| | DEPRECATED.
|
| |
| MPI_Comm | mpi_cart_sub (MPI_Comm comm, std::vector< int > remain_dims, bool duplicate=false) |
| | Call and register a call to MPI_Cart_sub with the dg library.
|
| |
| MPI_Comm | mpi_cart_kron (std::vector< MPI_Comm > comms) |
| | Form a Kronecker product among Cartesian communicators.
|
| |
| template<class Vector > |
| MPI_Comm | mpi_cart_kron (Vector comms) |
| | Convenience shortcut for return mpi_cart_kron( std::vector<MPI_Comm>(comms.begin(), comms.end()));
|
| |
| std::vector< MPI_Comm > | mpi_cart_split (MPI_Comm comm) |
| | Split a Cartesian communicator along each dimensions.
|
| |
| template<size_t Nd> |
| std::array< MPI_Comm, Nd > | mpi_cart_split_as (MPI_Comm comm) |
| | Same as mpi_cart_split but differen return type.
|
| |
| template<class real_type , class ConversionPolicyRows , class ConversionPolicyCols > |
| auto | make_mpi_sparseblockmat (const EllSparseBlockMat< real_type, thrust::host_vector > &src, const ConversionPolicyRows &g_rows, const ConversionPolicyCols &g_cols) |
| | Split given EllSparseBlockMat into computation and communication part.
|
| |
| template<class MessageType > |
| std::map< int, MessageType > | mpi_permute (const std::map< int, MessageType > &messages, MPI_Comm comm) |
| | Exchange messages between processes in a communicator.
|
| |
| template<class ContainerType > |
| void | mpi_gather (const thrust::host_vector< std::array< int, 2 > > &gather_map, const ContainerType &gatherFrom, ContainerType &result, MPI_Comm comm) |
| | Un-optimized distributed gather operation.
|
| |
| template<class ContainerType > |
| void | mpi_scatter (const thrust::host_vector< std::array< int, 2 > > &scatter_map, const ContainerType &toScatter, ContainerType &result, MPI_Comm comm, bool resize_result=false) |
| | Un-optimized distributed scatter operation.
|
| |
| template<class Integer > |
| thrust::host_vector< std::array< Integer, 2 > > | mpi_invert_permutation (const thrust::host_vector< std::array< Integer, 2 > > &p, MPI_Comm comm) |
| | Invert a globally bijective index map.
|
| |
| template<class real_type , class value_type > |
| void | ell_cpu_multiply_kernel (value_type alpha, value_type beta, const real_type *RESTRICT data, const int *RESTRICT cols_idx, const int *RESTRICT data_idx, const int num_rows, const int num_cols, const int blocks_per_line, const int n, const int left_size, const int right_size, const int *RESTRICT right_range, const value_type *RESTRICT x, value_type *RESTRICT y) |
| |
| template<class real_type , class value_type , int n, int blocks_per_line> |
| void | ell_cpu_multiply_kernel (value_type alpha, value_type beta, const real_type *RESTRICT data, const int *RESTRICT cols_idx, const int *RESTRICT data_idx, const int num_rows, const int num_cols, const int left_size, const int right_size, const int *RESTRICT right_range, const value_type *RESTRICT x, value_type *RESTRICT y) |
| |
| template<class real_type , class value_type , int n> |
| void | call_ell_cpu_multiply_kernel (value_type alpha, value_type beta, const real_type *RESTRICT data_ptr, const int *RESTRICT cols_ptr, const int *RESTRICT block_ptr, const int num_rows, const int num_cols, const int blocks_per_line, const int left_size, const int right_size, const int *RESTRICT right_range_ptr, const value_type *RESTRICT x_ptr, value_type *RESTRICT y_ptr) |
| |
| template<class real_type , class value_type , template< class > class Vector> |
| void | coo_cpu_multiply_kernel (value_type alpha, const value_type **x, value_type, value_type *RESTRICT y, const CooSparseBlockMat< real_type, Vector > &m) |
| |
| template<class real_type , class value_type , int n, template< class > class Vector> |
| void | coo_cpu_multiply_kernel (value_type alpha, const value_type **x, value_type, value_type *RESTRICT y, const CooSparseBlockMat< real_type, Vector > &m) |
| |
| template<class Functor , class Topology > |
| auto | evaluate (Functor &&f, const Topology &g) |
| | Evaluate a function on grid coordinates
|
| |
| template<class real_type > |
| thrust::host_vector< real_type > | integrate (const thrust::host_vector< real_type > &in, const RealGrid< real_type, 1 > &g, dg::direction dir=dg::forward) |
| | Indefinite integral of a function on a grid.
|
| |
| template<class UnaryOp , class real_type > |
| thrust::host_vector< real_type > | integrate (UnaryOp f, const RealGrid< real_type, 1 > &g, dg::direction dir=dg::forward) |
| | Untility shortcut.
|
| |
| template<class Topology > |
| Topology::host_vector | forward_transform (const typename Topology::host_vector &in, const Topology &g) |
| | Transform a vector from dg::xspace (nodal values) to dg::lspace (modal values)
|
| |
| template<class T , class ... Ts> |
| DG_DEVICE T | zero (T, Ts ...) |
| | This enum can be used in dg::evaluate.
|
| |
| template<class T , class ... Ts> |
| DG_DEVICE T | one (T, Ts ...) |
| | \( f(x, ...) = 1\)
|
| |
| DG_DEVICE double | cooX1d (double x) |
| | \( f(x) = x\)
|
| |
| DG_DEVICE double | cooX2d (double x, double) |
| | \( f(x,y) = x\)
|
| |
| DG_DEVICE double | cooX3d (double x, double, double) |
| | \( f(x,y,z) = x\)
|
| |
| DG_DEVICE double | cooY2d (double, double y) |
| | \( f(x,y) = y\)
|
| |
| DG_DEVICE double | cooY3d (double, double y, double) |
| | \( f(x,y,z) = y\)
|
| |
| DG_DEVICE double | cooZ3d (double, double, double z) |
| | \( f(x,y,z) = z\)
|
| |
| DG_DEVICE double | cooRZP2X (double R, double, double P) |
| | \( x = R\sin(\varphi)\)
|
| |
| DG_DEVICE double | cooRZP2Y (double R, double, double P) |
| | \( y = R\cos(\varphi)\)
|
| |
| DG_DEVICE double | cooRZP2Z (double, double Z, double) |
| | \( z = Z\)
|
| |
| template<class host_vector , class real_type > |
| real_type | interpolate (dg::space sp, const host_vector &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.
|
| |
| template<class host_vector , class real_type > |
| real_type | interpolate (dg::space sp, const host_vector &v, real_type x, real_type y, const aRealTopology< real_type, 2 > &g, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU) |
| | Interpolate a vector on a single point on a 2d Grid.
|
| |
| 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.
|
| |
| template<class real_type , class MPITopology > |
| MPI_Vector< thrust::host_vector< real_type > > | global2local (const thrust::host_vector< real_type > &global, const MPITopology &g) |
| | Take the relevant local part of a global vector.
|
| |
| template<class ConversionPolicy , class real_type > |
| dg::MIHMatrix_t< real_type > | make_mpi_matrix (const dg::IHMatrix_t< real_type > &global_cols, const ConversionPolicy &col_policy) |
| | Convert a (row-distributed) matrix with local row and global column indices to a row distributed MPI matrix.
|
| |
| template<class ConversionPolicy , class real_type > |
| dg::IHMatrix_t< real_type > | convertGlobal2LocalRows (const dg::IHMatrix_t< real_type > &global, const ConversionPolicy &row_policy) |
| | Convert a (column-distributed) matrix with global row and column indices to a row distributed matrix.
|
| |
| 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.
|
| |
| template<class T > |
| void | lu_solve (const dg::SquareMatrix< T > &lu, const std::vector< unsigned > &p, std::vector< T > &b) |
| | Solve the linear system with the LU decomposition.
|
| |
| template<class T > |
| dg::SquareMatrix< T > | invert (const dg::SquareMatrix< T > &in) |
| | Compute inverse of square matrix (alias for dg::create::inverse)
|
| |
| template<class T > |
| SquareMatrix< T > | tensorproduct (const SquareMatrix< T > &op1, const SquareMatrix< T > &op2) |
| | Form the tensor product between two operators.
|
| |
| template<class T > |
| dg::SparseMatrix< int, T, thrust::host_vector > | tensorproduct (unsigned N, const SquareMatrix< T > &op) |
| | Tensor product between Identity matrix and an operator.
|
| |
| template<class T > |
| dg::SparseMatrix< int, T, thrust::host_vector > | sandwich (const SquareMatrix< T > &left, const dg::SparseMatrix< int, T, thrust::host_vector > &m, const SquareMatrix< T > &right) |
| | Multiply 1d matrices by diagonal block matrices from left and right.
|
| |
| template<class T > |
| T | gcd (T a, T b) |
| | Greatest common divisor.
|
| |
| template<class T > |
| T | lcm (T a, T b) |
| | Least common multiple.
|
| |
| 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)
|
| |
| 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)
|
| |
| template<class Container , class host_vector , class Topology > |
| void | assign3dfrom2d (const host_vector &in2d, Container &out, const Topology &grid) |
| | Construct a 3d vector given a 2d host vector.
|
| |
| 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)
|
| |
| 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)
|
| |
| template<class Functor , class Geometry > |
| Geometry::host_vector | pullback (const Functor &f, const Geometry &g) |
| | \( f_i = f( x(\zeta_i, \eta_i), y(\zeta_i, \eta_i))\)
|
| |
| template<class Functor1 , class Functor2 , class container , class Geometry > |
| void | pushForwardPerp (const Functor1 &vR, const Functor2 &vZ, container &vx, container &vy, const Geometry &g) |
| | \( \bar v = J v\)
|
| |
| 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) |
| | \( {\bar v} = J v\)
|
| |
| 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) |
| | \( \bar \chi = J \chi J^T\)
|
| |
| template<class T > |
| dg::SparseMatrix< int, T, thrust::host_vector > | tensorproduct (const dg::SparseMatrix< int, T, thrust::host_vector > &lhs, const dg::SparseMatrix< int, T, thrust::host_vector > &rhs) |
| | \( L\otimes R\) Form the tensor (Kronecker) product between two matrices
|
| |
| template<class T > |
| dg::SparseMatrix< int, T, thrust::host_vector > | tensorproduct_cols (const dg::SparseMatrix< int, T, thrust::host_vector > &lhs, const dg::SparseMatrix< int, T, thrust::host_vector > &rhs) |
| | \( L\otimes R\) Form the tensor (Kronecker) product between two matrices in the column index
|
| |
| 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.
|
| |
| 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.
|
| |
| template<class ContainerType , class Functor , class ... ContainerTypes> |
| auto | kronecker (Functor &&f, const ContainerType &x0, const ContainerTypes &... xs) |
| | \( y_I = f(x_{0i_0}, x_{1i_1}, ...) \) Memory allocating version of dg::blas1::kronecker
|
| |
| 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) |
| | Alias for dg::blas2::symv \( y = \alpha M(x) + \beta y \);.
|
| |
| template<class MatrixType , class ContainerType1 , class ContainerType2 > |
| void | apply (MatrixType &&M, const ContainerType1 &x, ContainerType2 &y) |
| | Alias for dg::blas2::symv \( y = M( x)\);.
|
| |
| std::string | bc2str (bc bcx) |
| | write a string describing boundary condition to an output stream
|
| |
| bc | str2bc (std::string s) |
| | convert a string to a bc
|
| |
| bc | inverse (bc bound) |
| | invert boundary condition
|
| |
| direction | str2direction (std::string s) |
| | convert a string to a direction
|
| |
| std::string | direction2str (enum direction dir) |
| | convert a direciton to string
|
| |
| direction | inverse (direction dir) |
| | invert direction
|
| |
| template<class ContainerType0 , class ContainerType1 , class ContainerType2 > |
| std::vector< double > | least_squares (const std::vector< ContainerType0 > &bs, const ContainerType1 &b, const ContainerType2 &weights) |
| | Compute \( a = (B^T W B)^{-1} WB^T b\) for given \( B\), weights \( W\) and right hand side \( b\).
|
| |
| template<class ContainerType0 , class ContainerType1 > |
| std::vector< double > | least_squares (const std::vector< ContainerType0 > &bs, const ContainerType1 &b) |
| | An alias for least_squares( bs, b, 1.)
|
| |
| 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.
|
| |
| 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.
|
| |
| 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.
|
| |
| 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.
|
| |
| template<typename UnaryOp > |
| int | bisection1d (UnaryOp &&op, double &x_min, double &x_max, const double eps) |
| | Find a root of a 1d function \( f(x) = 0\).
|
| |
| std::string | to2str (enum to mode) |
| | Convert integration mode to string.
|
| |
| bool | is_same (double x, double y, double eps=1e-15) |
| |
| bool | is_same (float x, float y, float eps=1e-6) |
| |
| template<class T > |
| bool | is_same (T x, T y) |
| |
| 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 \( f(g(x_0,x_1,...)) \).
|
| |
| template<class UnaryOp , typename... Functors> |
| auto | compose (UnaryOp f0, Functors... fs) |
| | Create Composition funtor of an arbitrary number of functions \( f_0(f_1(f_2( ... f_s(x_0, x_1, ...)))\).
|
| |
1.12.0