template<class ContainerType>
struct dg::Average< ContainerType >
Topological average computations in a Cartesian topology.
\[ \langle f \rangle_x := \frac{1}{L_x}\int_0^{L_x}dx f \quad \langle f \rangle_y := \frac{1}{L_y}\int_0^{L_y}dy f \quad \langle f \rangle_z := \frac{1}{L_z}\int_0^{L_z}dz f \\ \langle f \rangle_{xy} := \frac{1}{L_xL_y}\int_0^{L_x}\int_0^{L_y}dxdy f \quad \langle f \rangle_{xz} := \frac{1}{L_xL_z}\int_0^{L_x}\int_0^{L_z}dxdz f \quad \langle f \rangle_{yz} := \frac{1}{L_yL_z}\int_0^{L_y}\int_0^{L_z}dydz f \quad \]
Given a Cartesian topology it is possible to define a partial reduction of a given vector. In two dimensions for example we can define a reduction over all points that are neighbors in the x (or y) direction. We are then left with Ny (Nx) points. In three dimensions we can define the reduction along the x, y, z directions but also over all points in the xy (xz or yz) planes. We are left with two- (respectively three-)dimensional vectors.
- Note
- The integrals include the dG weights but not the volume element (does not know about geometry)
std::cout << "Averaging y ... \n";
pol( vector, average_y, false);
thrust::host_vector< real_type > evaluate(UnaryOp f, const RealGrid1d< real_type > &g)
Evaluate a 1d function on grid coordinates.
Definition: evaluation.h:67
thrust::device_vector< double > DVec
Device Vector. The device can be an OpenMP parallelized cpu or a gpu. This depends on the value of th...
Definition: typedefs.h:23
Topological average computations in a Cartesian topology.
Definition: average.h:53
1.9.3