Kaskade::AdvectedFunctionView< Function, Velocity > Class Template Reference

A weak function view that defines an advected function. More...

#include <advect.hh>

Detailed Description

template<class Function, class Velocity>
class Kaskade::AdvectedFunctionView< Function, Velocity >

A weak function view that defines an advected function.

The function view's value is defined by advection along the velocity field \( v\) as \( \hat f(x) = f(y(\tau)) \), where \( y(t) \) satisfies

\[ \dot y = -v(y), \quad y(0) = x. \]

The integration is performed with \( n \) equidistant explicit Euler steps. The integration is stopped prematurely if the domain boundary is encountered.

Template Parameters

Function	a weak function view (e.g. a finite element function) type
Velocity	a vector-valued WeakFunctionView. The vector size has to be the spatial dimension of the grid.

Definition at line 121 of file advect.hh.

Public Types
using	GridView = typename Function::Space::GridView
using	Cell = Kaskade::Cell< GridView >
using	Position = GlobalPosition< GridView >

Public Member Functions
	AdvectedFunctionView (Function const &f_, Velocity const &v_, double tau_, int n_=1)
	Constructor. More...
Function::ValueType	value (Cell const &cell, Position const &xi) const

Related Functions
(Note that these are not member functions.)
template<class Function , class Velocity >
auto	makeAdvectedFunctionView (Function const &f, Velocity const &v, double tau, int n=1)
	Creates a weak function view for advecting FE functions. More...

Member Typedef Documentation

Cell

template<class Function , class Velocity >

using Kaskade::AdvectedFunctionView< Function, Velocity >::Cell = Kaskade::Cell<GridView>

Definition at line 125 of file advect.hh.

GridView

template<class Function , class Velocity >

using Kaskade::AdvectedFunctionView< Function, Velocity >::GridView = typename Function::Space::GridView

Definition at line 124 of file advect.hh.

Position

template<class Function , class Velocity >

using Kaskade::AdvectedFunctionView< Function, Velocity >::Position = GlobalPosition<GridView>

Definition at line 126 of file advect.hh.

Constructor & Destructor Documentation

AdvectedFunctionView()

template<class Function , class Velocity >

Kaskade::AdvectedFunctionView< Function, Velocity >::AdvectedFunctionView ( Function const &  f_, Velocity const &  v_, double  tau_, int  n_ = 1  )

inline

Constructor.

Parameters

f	the function to be advected
v	the velocity field
tau	the integration length
n	the number of Euler integration steps (>= 1)

Definition at line 140 of file advect.hh.

Member Function Documentation

value()

template<class Function , class Velocity >

Function::ValueType Kaskade::AdvectedFunctionView< Function, Velocity >::value ( Cell const &  cell, Position const &  xi  ) const

inline

Definition at line 145 of file advect.hh.

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

• advect.hh