dispersion::stiff< T, SAFE_MATH > Class Template Reference

Stiff dispersion function. More...

#include <dispersion.hpp>

Inheritance diagram for dispersion::stiff< T, SAFE_MATH >:

Public Member Functions
virtual graph::shared_leaf< T, SAFE_MATH >	D (graph::shared_leaf< T, SAFE_MATH > w, graph::shared_leaf< T, SAFE_MATH > kx, graph::shared_leaf< T, SAFE_MATH > ky, graph::shared_leaf< T, SAFE_MATH > kz, graph::shared_leaf< T, SAFE_MATH > x, graph::shared_leaf< T, SAFE_MATH > y, graph::shared_leaf< T, SAFE_MATH > z, graph::shared_leaf< T, SAFE_MATH > t, equilibrium::shared< T, SAFE_MATH > &eq)
	Stiff function.

Additional Inherited Members
Public Types inherited from dispersion::dispersion_function< T, SAFE_MATH >
typedef T	base
	Type def to retrieve the backend base type.
Static Public Attributes inherited from dispersion::dispersion_function< T, SAFE_MATH >
static constexpr bool	safe_math = SAFE_MATH
	Retrieve template parameter of safe math.

Detailed Description

template<jit::float_scalar T, bool SAFE_MATH = false>
class dispersion::stiff< T, SAFE_MATH >

Stiff dispersion function.

Template Parameters

T	Base type of the calculation.
SAFE_MATH	Use Safe Math operations.

Member Function Documentation

D()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual graph::shared_leaf< T, SAFE_MATH > dispersion::stiff< T, SAFE_MATH >::D ( graph::shared_leaf< T, SAFE_MATH >  w, graph::shared_leaf< T, SAFE_MATH >  kx, graph::shared_leaf< T, SAFE_MATH >  ky, graph::shared_leaf< T, SAFE_MATH >  kz, graph::shared_leaf< T, SAFE_MATH >  x, graph::shared_leaf< T, SAFE_MATH >  y, graph::shared_leaf< T, SAFE_MATH >  z, graph::shared_leaf< T, SAFE_MATH >  t, equilibrium::shared< T, SAFE_MATH > &  eq  )

inlinevirtual

Stiff function.

This is not really a dispersion function but is an example of a stiff system.

dx/dt = -1.0E3*(x - Exp(-t)) - Exp(-t) (1)

We need to figure out a disperison function D(w,k,x) such that

dx/dt = -(dD/dk)/(dD/dw) = -1.0E3*(x - Exp(-t)) - Exp(-t). (2)

If we assume,

D = (1.0E3*(x - Exp(-t)) - Exp(-t))*kx + w (3)

dD/dw = 1 (4)

dD/dkx = (1.0E3*(x - Exp(-t)) - Exp(-t)) (5)

This satisfies equations 1.

Parameters

[in]	w	Omega variable.
[in]	kx	Kx variable.
[in]	ky	Ky variable.
[in]	kz	Kz variable.
[in]	x	x variable.
[in]	y	y variable.
[in]	z	z variable.
[in]	t	Current time.
[in]	eq	The plasma equilibrium.

Implements dispersion::dispersion_function< T, SAFE_MATH >.

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

• graph_framework/dispersion.hpp