MethodSphere Class Reference

Implements radially symmetric weighting functions (Hardy, Virial) and its associated bond function for atomistic stress computation. More...

#include <MethodSphere.h>

Inheritance diagram for MethodSphere:

Collaboration diagram for MethodSphere:

Public Member Functions
	MethodSphere (double, const std::string &type="virial")
	Constructs a MethodSphere using a named weighting type.
	MethodSphere (double, std::map< double, double >)
	Constructs a MethodSphere using a user-defined piecewise-linear weight function.
	MethodSphere (const MethodSphere &)
virtual	~MethodSphere ()
Public Member Functions inherited from Method< MethodSphere >
virtual	~Method ()
double	operator() (const Vector3d &vec) const
	The weighting function \(w\) used to compute stress.
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 Member Functions
double	operator() (const Vector3d &vec) const
	Evaluate the weighting function at a vector.
double	bondFunction (const Vector3d &vec1, const Vector3d &vec2) const
	Computes the bond function for a pair of atomic positions.

Friends
class	Method< MethodSphere >

Additional Inherited Members
Protected Attributes inherited from Method< MethodSphere >
double	averagingDomainSize

Detailed Description

Implements radially symmetric weighting functions (Hardy, Virial) and its associated bond function for atomistic stress computation.

This class defines a weighting function \(w\) over a spherical domain of radius \(R\) (the averaging domain size). Two common forms are supported:

• Hardy-type weighting
• Virial-type (uniform) weighting

Additionally, users can supply a custom radial weighting function as a piecewise linear map.

Examples

crack/main.cpp, and testLJ.cpp.

Definition at line 28 of file MethodSphere.h.

Constructor & Destructor Documentation

MethodSphere() [1/3]

MethodSphere::MethodSphere ( double  averagingDomainSize, const std::string &  type = "virial"  )

explicit

Constructs a MethodSphere using a named weighting type.

Parameters

averagingDomainSize	The diameter \(R\) of the spherical averaging domain.
type	The type of weighting function: "hardy" or "virial".

For "hardy", the radial weighting function \(w(r)\) is defined as:

\[ w(r) = \begin{cases} c, & \text{if } 0 \le r \le R/2 \\ 2c\left(1 - \frac{r}{R}\right), & \text{if } R/2 < r \le R \\ 0, & \text{otherwise} \end{cases} \]

where \(c = \frac{8}{5\pi R^3}\) ensures normalization.

For "virial", the weighting function is:

\[ w(r) = \begin{cases} c, & \text{if } 0 \le r \le R \\ 0, & \text{otherwise} \end{cases} \]

where \(c = \frac{3}{4 \pi R^3}\).

Definition at line 15 of file MethodSphere.cpp.

MethodSphere() [2/3]

MethodSphere::MethodSphere	(	double	averagingDomainSize,
		std::map< double, double >	map
	)

Constructs a MethodSphere using a user-defined piecewise-linear weight function.

Parameters

averagingDomainSize	The diameter \(R\) of the spherical domain.
map	A map from normalized radius values in \([0,1]\) to non-negative weight values.

The keys of the map (in \([0, 1]\)) are rescaled by \(R\) to get the real radii. For each interval \([x_i, x_{i+1}]\), a linear segment is fitted:

\[ w(r) = y_i + \frac{y_{i+1} - y_i}{x_{i+1} - x_i} (r - x_i R), \quad r \in [x_i R, x_{i+1} R] \]

The resulting piecewise linear function is then normalized, i.e.

\[ 4 \pi \int_{0}^{R} w(r) \cdot r^2 \, dr = 1 \]

This allows users to define arbitrary, smooth weight profiles that are zero outside the domain.

Definition at line 63 of file MethodSphere.cpp.

MethodSphere() [3/3]

MethodSphere::MethodSphere

(

const MethodSphere &

_hardy

)

Definition at line 115 of file MethodSphere.cpp.

~MethodSphere()

MethodSphere::~MethodSphere ( )

virtual

Definition at line 120 of file MethodSphere.cpp.

Member Function Documentation

bondFunction()

double MethodSphere::bondFunction ( const Vector3d &  vec1, const Vector3d &  vec2  ) const

protected

Computes the bond function for a pair of atomic positions.

Parameters

vec1	Vector from grid point to atom 1.
vec2	Vector from grid point to atom 2.

Returns

This function evaluates the line integral of the radially symmetric weighting function along the bond.

Definition at line 168 of file MethodSphere.cpp.

operator()()

double MethodSphere::operator() ( const Vector3d &  vec ) const

protected

Evaluate the weighting function at a vector.

Parameters

vec	Position vector relative to center of the averaging domain.

Returns

Weight value.

Definition at line 154 of file MethodSphere.cpp.

Friends And Related Symbol Documentation

Method< MethodSphere >

friend class Method< MethodSphere >

friend

Definition at line 1 of file MethodSphere.h.

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

• include/MDStressLab++/MethodSphere.h
• src/MethodSphere.cpp