Topics

Here is a list of all topics with brief descriptions:

[detail level 1234]

▼Level 1: Vectors, Matrices and basic operations
BLAS level 1 routines: Vector-Vector	\( f( x_{0i}, x_{1i}, x_{2i}, ...) \) and \( x^T y\)
BLAS level 2 routines: Matrix-Vector	\( \alpha M \cdot x + \beta y\) and \( x^T M y \)
►MPI backend
Distributed Matrix and Vector
MPI Distributed Gather and Scatter
►Utility
►The tag dispatch system
All TensorTraits specialisations
Sparse matrix formats
Dense matrix formats
Vector view
Typedefs for Vectors and Matrices
▼Level 2: Basic numerical algorithms
►ODE integration	\( \dot y = f(y,t) \)
Utilities for ODE integrators
Quadrature	\( \int_{t_0}^T u(t) dt \)
Extrapolation
Linear and nonlinear solvers	Linear \( Ax = b\) and non-linear \( f(x) = b\)
▼Level 3: Topology and Geometry
►Topological grids and operations
Discontinuous Galerkin Nd grid
Discontinuous Galerkin grids with X-point
Evaluate, integrate, weights	\( f_i = f(\vec x_i) \)
Create derivatives	\( D_x\), \( D_y\) and \( D_z \)
Create stencils
►Interpolation, Projection, Transformation
Fast interpolation
Averaging, prolongation and partial reductions	\( I \) and \( P = I^\dagger\)
Scatter and Gather
►Geometric grids and tensor operations
Geometry classes
Geometry classes with X-point
Grid refinement
Tensor-Vector operations	\( v^i = T^{ij} w_j\)
Pullback, pushforward, volume	\( f_i = f( x (\zeta_i,\eta_i), y(\zeta_i,\eta_i)) \), \( \sqrt{g} \)
Finite Element Methods
Grid Typedefs
▼Level 4: Advanced numerical schemes
Advection terms	\( \vec v \cdot \nabla u\) and \( \{ f,g\} \)
Elliptic operators	Elliptic \( -\nabla\cdot (\chi \nabla f)\) and Helmholtz \( (\chi + \alpha \Delta) f\)
Multigrid matrix inversion	\( A x = b\)
▼Level 99: Miscellaneous additions
Timer class	T.tic(); t.toc(); t.diff();
►Functions and functors
Simple	For the dg::evaluate and dg::blas1::evaluate functions
A large collection	For the dg::evaluate and dg::blas1::evaluate functions
Composition of two or more functors
dg::blas1::evaluate binary operators	Binary subroutines for the dg::blas1::evaluate function
dg::blas1::evaluate variadic functors	Functors to use in the dg::blas1::evaluate function
dg::blas1::subroutine subroutines	Functors to use in the dg::blas1::subroutine functions
dg::blas2::stencil subroutines	Functors to use in dg::blas2::stencil function
►MPI utility functions
Legacy MPI functions
Lowlevel helper functions and classes