Method< TMethod > Class Template Reference

#include <Method.h>

Public Member Functions
virtual	~Method ()
double	operator() (const Vector3d &vec) const
	The pointwise weighting function \(w\).
double	bondFunction (const Vector3d &vec1, const Vector3d &vec2) const
	The bond function \(b(\boldsymbol v^1, \boldsymbol v^2)\) gives the weight associated to a bond formed by two atoms.
double	getAveragingDomainSize () const
	Gets the spatial size of the averaging domain, i.e. the support of the weighting function.

Protected Attributes
double	averagingDomainSize

Detailed Description

template<typename TMethod>
class Method< TMethod >

This class provides a polymorphic interface for defining a method, which constitutes a weighting function and its associated bond function, to compute atomistic stress. The pointwise weighting function is also used for Cauchy mass density, momentum density, and kinetic stress.

It is intended to be used as a CRTP (Curiously Recurring Template Pattern) base class: the actual implementation of the method should be provided in the derived class TMethod, which will override the weighting function call operator and bondFunction.

Template Parameters

TMethod

The derived class implementing specific method logic. Examples of derived classes include MethodSphere, MethodLdad<Constant>, and MethodLdad<Trigonometric>.

Definition at line 27 of file Method.h.

Constructor & Destructor Documentation

~Method()

template<typename TMethod >

Method< TMethod >::~Method ( )

virtual

Definition at line 45 of file Method.cpp.

Member Function Documentation

bondFunction()

template<typename TMethod >

double Method< TMethod >::bondFunction	(	const Vector3d &	vec1,
		const Vector3d &	vec2
	)		const

The bond function \(b(\boldsymbol v^1, \boldsymbol v^2)\) gives the weight associated to a bond formed by two atoms.

See also

calculateStress() to see how bondfunction is used in stress computation

The function delegates the actual implementation to TMethod::bondFunction(vec1, vec2).

The bond function is defined as

\[ \begin{equation} b(\boldsymbol v^1, \boldsymbol v^2)= \int_{s=0}^1 w((1-s)\boldsymbol v^1 + s\boldsymbol v^2) \, ds \end{equation} \]

The actual implementation of the bondFunction is delegated to TMethod::bondFunction(vec1, vec2).

Parameters

vec1	first atomic position vector relative to a grid point
vec2	second atomic position vector relative to a grid point

Returns

The scalar output of the bond function.

Definition at line 33 of file Method.cpp.

getAveragingDomainSize()

template<typename TMethod >

double Method< TMethod >::getAveragingDomainSize

(

)

const

Gets the spatial size of the averaging domain, i.e. the support of the weighting function.

Returns

Averaging domain radius or cutoff, as a double.

Definition at line 40 of file Method.cpp.

operator()()

template<typename TMethod >

double Method< TMethod >::operator()

(

const Vector3d &

vec

)

const

The pointwise weighting function \(w\).

The pointwise weight is used directly for kinetic Cauchy stress and for the continuum fields \(\rho(\mathbf x)=\sum_i m_i w(\mathbf x-\mathbf x_i)\) and \(\mathbf p(\mathbf x)=\sum_i m_i\mathbf v_i w(\mathbf x-\mathbf x_i)\). It must therefore be normalized so that \(\int w(\mathbf r)d\mathbf r=1\). Potential stress uses bondFunction().

This weighting function operator delegates the implementation to the derived TMethod class.

Parameters

vec	A 3D vector

Returns

The scalar (non-negative) output of the weighting function.

Definition at line 26 of file Method.cpp.

Member Data Documentation

averagingDomainSize

template<typename TMethod >

double Method< TMethod >::averagingDomainSize

protected

Definition at line 84 of file Method.h.

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

• include/MDStressLab++/Method.h
• include/MDStressLab++/Method.cpp