A functor to handle Axilrod-Teller(-Muto) interactions between three particles (molecules). More...

#include <AxilrodTellerFunctor.h>

Inheritance diagram for mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >:

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Collaboration diagram for mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >:

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Public Member Functions
	AxilrodTellerFunctor ()=delete
	Deleted default constructor.

	AxilrodTellerFunctor (double cutoff)
	Constructor for Functor with mixing disabled.

	AxilrodTellerFunctor (double cutoff, ParticlePropertiesLibrary< double, size_t > &particlePropertiesLibrary)
	Constructor for Functor with mixing active.

std::string	getName () final
	Returns name of functor.

bool	isRelevantForTuning () final
	Specifies whether the functor should be considered for the auto-tuning process.

bool	allowsNewton3 () final
	Specifies whether the functor is capable of Newton3-like functors.

bool	allowsNonNewton3 () final
	Specifies whether the functor is capable of non-Newton3-like functors.

void	AoSFunctor (Particle_T &i, Particle_T &j, Particle_T &k, bool newton3) final
	TriwiseFunctor for arrays of structures (AoS).

void	setParticleProperties (SoAFloatPrecision nu)
	Sets the particle properties constants for this functor.

void	initTraversal () final
	Reset the global values.

void	endTraversal (bool newton3) final
	Accumulates global values, e.g.

double	getPotentialEnergy ()
	Get the potential Energy.

double	getVirial ()
	Get the virial.

size_t	getNumFLOPs () const override
	Gets the number of useful FLOPs.

double	getHitRate () const override
	Get the hit rate.

Public Member Functions inherited from autopas::TriwiseFunctor< Particle_T, CRTP_T >
	TriwiseFunctor (double cutoff)
	Constructor.

virtual void	AoSFunctor (Particle_T &i, Particle_T &j, Particle_T &k, bool newton3)
	TriwiseFunctor for arrays of structures (AoS).

virtual void	SoAFunctorSingle (SoAView< SoAArraysType > soa, bool newton3)
	TriwiseFunctor for structure of arrays (SoA)

virtual void	SoAFunctorPair (SoAView< SoAArraysType > soa1, SoAView< SoAArraysType > soa2, bool newton3)
	TriwiseFunctor for structure of arrays (SoA)

virtual void	SoAFunctorTriple (SoAView< SoAArraysType > soa1, SoAView< SoAArraysType > soa2, SoAView< SoAArraysType > soa3, bool newton3)
	TriwiseFunctor for structure of arrays (SoA)

virtual void	SoAFunctorVerlet (SoAView< SoAArraysType > soa, const size_t indexFirst, const std::vector< size_t, AlignedAllocator< size_t > > &neighborList, bool newton3)
	TriwiseFunctor for structure of arrays (SoA) for neighbor lists.

Public Member Functions inherited from autopas::Functor< Particle_T, CRTP_T >
	Functor (double cutoff)
	Constructor.

virtual void	initTraversal ()
	This function is called at the start of each traversal.

virtual void	endTraversal (bool newton3)
	This function is called at the end of each traversal.

template<class ParticleCell >
void	SoALoader (ParticleCell &cell, SoA< SoAArraysType > &soa, size_t offset, bool skipSoAResize)
	Copies the AoS data of the given cell in the given soa.

template<typename ParticleCell >
void	SoAExtractor (ParticleCell &cell, SoA< SoAArraysType > &soa, size_t offset)
	Copies the data stored in the soa back into the cell.

virtual bool	allowsNewton3 ()=0
	Specifies whether the functor is capable of Newton3-like functors.

virtual bool	allowsNonNewton3 ()=0
	Specifies whether the functor is capable of non-Newton3-like functors.

virtual bool	isRelevantForTuning ()=0
	Specifies whether the functor should be considered for the auto-tuning process.

virtual std::string	getName ()=0
	Returns name of functor.

double	getCutoff () const
	Getter for the functor's cutoff.

virtual size_t	getNumFLOPs () const
	Get the number of FLOPs.

virtual double	getHitRate () const
	Get the hit rate.

Static Public Member Functions
static constexpr auto	getNeededAttr ()
	Get attributes needed for computation.

static constexpr auto	getNeededAttr (std::false_type)
	Get attributes needed for computation without N3 optimization.

static constexpr auto	getComputedAttr ()
	Get attributes computed by this functor.

static constexpr bool	getMixing ()

Static Public Member Functions inherited from autopas::Functor< Particle_T, CRTP_T >
static constexpr std::array< typename Particle_T::AttributeNames, 0 >	getNeededAttr ()
	Get attributes needed for computation.

static constexpr std::array< typename Particle_T::AttributeNames, 0 >	getNeededAttr (std::false_type)
	Get attributes needed for computation without N3 optimization.

static constexpr std::array< typename Particle_T::AttributeNames, 0 >	getComputedAttr ()
	Get attributes computed by this functor.

Additional Inherited Members
Public Types inherited from autopas::TriwiseFunctor< Particle_T, CRTP_T >
using	SoAArraysType = typename Particle_T::SoAArraysType
	Structure of the SoAs defined by the particle.

Public Types inherited from autopas::Functor< Particle_T, CRTP_T >
using	SoAArraysType = typename Particle_T::SoAArraysType
	Structure of the SoAs defined by the particle.

using	Functor_T = CRTP_T
	Make the Implementation type template publicly available.

Detailed Description

template<class Particle_T, bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>
class mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >

A functor to handle Axilrod-Teller(-Muto) interactions between three particles (molecules).

The Axilrod-Teller potential

The reference paper of Axilrod and Teller can be found here: https://doi.org/10.1063/1.1723844

Sketch of three particles that are used in the Axilrod-Teller Functor

The Axilrod-Teller potential is a model for the interactions of three molecules which appear when the van der Waals forces are approximated to the third order. It is usually combined with a model for pairwise interaction as e.g. the Lennard-Jones potential.

\[ U_{AT} = \nu \frac{3 \cos\gamma_1 \cos\gamma_2 \cos\gamma_3 + 1}{r_{12}^3 r_{23}^3 r_{31}^3} \]

, where \(r_{ij}\) is the distance between particles \(i\) and \(j\) and \(\gamma_i\) is the angle between the sides \(r_{ij}\) and \(r_{ik}\). \(\nu\) is a material dependent parameter of the order \(V\alpha^3\), where \(V\) is the ionization energy and \(\alpha\) the polarizability.

The cosines can also be expressed as:

\[ \cos\gamma_1 = \frac{ \vec{r}_{12} \cdot \vec{r}_{13}}{|\vec{r}_{12}||\vec{r}_{13}|} \]

, where \(\vec{r}_{ij}\) is the vector from particle \(i\) to particle \(j\) ( \(i \longrightarrow j\) ). It is calculated as \(\vec{x}_j - \vec{x}_i\), where \(\vec{x}_i\) is the position of particle \(i\).

Therefore, the potential can also be expressed as:

\[ U_{AT} = \nu\frac{-3 (\vec{r}_{12} \cdot \vec{r}_{31}) (\vec{r}_{12} \cdot \vec{r}_{23}) (\vec{r}_{31} \cdot \vec{r}_{23}) + r_{12}^2 r_{23}^2 r_{31}^2}{r_{12}^5 r_{23}^5 r_{31}^5} \]

Note that we have \(-3\) because we use the circular vectors \(\vec{r}_ {12}, \vec{r}_ {23}, \vec{r}_ {31}\).

The derivative can be calculated by applying the chain rule and leads to a resulting Force exerted on particle \(1\):

\[ \vec{F}_ {1} = - \frac{\partial U_ {AT}}{\partial \vec{x}_ 1} \]

\[ \vec{F}_ {1} = \frac{3}{r_ {12}^5 r_ {23}^5 r_ {31}^5}\cdot \left[ \left( -5\frac{<>_ 1<>_ 2<>_ 3}{r_ {12}^2} - <>_ 1<>_ 3 + r_ {23}^2r_ {31}^2\right)\cdot \vec{r}_ {12} +\left( 5\frac{<>_ 1<>_ 2<>_ 3}{r_ {23}^2} + <>_ 1<>_ 3 - r_ {12}^2r_ {31}^2\right)\cdot\vec{r}_ {23} +\left( <>_ 2<>_ 3 - <>_ 2<>_ 1 \right)\cdot \vec{r}_ {31} \right] \]

, where \(<>_ 1=\vec{r}_ {12}\cdot\vec{r}_ {31}\) and so on. The terms are already ordered to show the contribution from all three distance vectors.

Newton's third law

To apply Newton's third law, the force on particle \(2\) needs to be calculated in a similar fashion as for particle \(1\). The force on particle \(3\) can then be written as the negative sum of the other two forces:

\[ \vec{F}_3 = -(\vec{F}_1 + \vec{F}_2) \]

This functor assumes that duplicated calculations are always happening, which is characteristic for a Full-Shell scheme.

Template Parameters

Particle_T	The type of particle.
useMixing	Switch for the functor to be used with multiple particle types. If set to false, _epsilon and _sigma need to be set and the constructor with PPL can be omitted.
useNewton3	Switch for the functor to support newton3 on, off or both. See FunctorN3Modes for possible values.
calculateGlobals	Defines whether the global values are to be calculated (energy, virial).
countFLOPs	counts FLOPs and hitrate

Constructor & Destructor Documentation

◆ AxilrodTellerFunctor() [1/2]

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::AxilrodTellerFunctor ( double cutoff )

inlineexplicit

Constructor for Functor with mixing disabled.

When using this functor it is necessary to call setParticleProperties() to set internal constants because it does not use a particle properties library.

Note: Only to be used with mixing == false.

Parameters

cutoff

◆ AxilrodTellerFunctor() [2/2]

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::AxilrodTellerFunctor	(	double	cutoff,
		ParticlePropertiesLibrary< double, size_t > &	particlePropertiesLibrary
	)

inlineexplicit

Constructor for Functor with mixing active.

This functor takes a ParticlePropertiesLibrary to look up (mixed) properties like nu.

Parameters

cutoff
particlePropertiesLibrary

Member Function Documentation

◆ allowsNewton3()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

bool mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::allowsNewton3 ( )

inlinefinalvirtual

Specifies whether the functor is capable of Newton3-like functors.

If the functor provides an interface to soa or aos functions that utilize Newton's third law of motion (actio = reactio) to reduce the computational complexity this function should return true. If this is not the case this function should return false.

Returns: true if and only if this functor provides an interface to Newton3-like functions.

Implements autopas::Functor< Particle_T, CRTP_T >.

◆ allowsNonNewton3()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

bool mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::allowsNonNewton3 ( )

inlinefinalvirtual

Specifies whether the functor is capable of non-Newton3-like functors.

If the functor provides an interface to soa or aos functions that do not utilize Newton's third law of motion (actio = reactio) this function should return true. If this is not the case this function should return false.

Returns: true if and only if this functor provides an interface to functions that do not utilize Newton3.

Implements autopas::Functor< Particle_T, CRTP_T >.

◆ AoSFunctor()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

void mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::AoSFunctor	(	Particle_T &	i,
		Particle_T &	j,
		Particle_T &	k,
		bool	newton3
	)

inlinefinalvirtual

TriwiseFunctor for arrays of structures (AoS).

This functor should calculate the forces or any triwise interaction between three particles. This should include a cutoff check if needed!

Parameters

i	Particle i
j	Particle j
k	Particle k
newton3	defines whether or whether not to use newton 3

Reimplemented from autopas::TriwiseFunctor< Particle_T, CRTP_T >.

◆ endTraversal()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

void mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::endTraversal ( bool newton3 )

inlinefinalvirtual

Accumulates global values, e.g.

potential energy and virial.

Parameters

newton3

Reimplemented from autopas::Functor< Particle_T, CRTP_T >.

◆ getComputedAttr()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

static constexpr auto mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getComputedAttr ( )

inlinestaticconstexpr

Get attributes computed by this functor.

Returns: Attributes computed by this functor.

Todo:: C++20: make this function virtual

◆ getHitRate()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

double mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getHitRate ( ) const

inlineoverridevirtual

Get the hit rate.

Implementation required if FLOPLogger used.

If derived class provides no implementation, the FLOPLogger interprets the default NaN output as invalid and leaves "Not Implemented" in the log.

Returns: (number of kernel calls) / (number of distance calculations)

Reimplemented from autopas::Functor< Particle_T, CRTP_T >.

◆ getMixing()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

static constexpr bool mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getMixing ( )

inlinestaticconstexpr

Returns: useMixing

◆ getName()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

std::string mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getName ( )

inlinefinalvirtual

Returns name of functor.

Intended for use with the iteration logger, to differentiate between calls to computeInteractions using different functors in the logs.

Returns: name of functor.

Implements autopas::Functor< Particle_T, CRTP_T >.

◆ getNeededAttr() [1/2]

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

static constexpr auto mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getNeededAttr ( )

inlinestaticconstexpr

Get attributes needed for computation.

Returns: Attributes needed for computation.

Todo:: C++20: make this function virtual

◆ getNeededAttr() [2/2]

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

static constexpr auto mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getNeededAttr ( std::false_type )

inlinestaticconstexpr

Get attributes needed for computation without N3 optimization.

Returns: Attributes needed for computation.

Todo:: C++20: make this function virtual

◆ getNumFLOPs()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

size_t mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getNumFLOPs ( ) const

inlineoverridevirtual

Gets the number of useful FLOPs.

For the three distance squared calculations, this is:

Displacement: 3
DistanceSquared: 5
Total: 8 * 3 = 24

For the force kernel, this is:

calculation of prefactor: 7
dot products: 3 * 5 = 15
all dot products: 2
forceIDirectionJK: 5
forceIDirectionIJ: 9
forceIDirectionKI: 9
add force vectors and multiply: 9
add force to mol i: 3
If N3:
forceJDirectionKI: 5
forceJDirectionIJ: 9
forceJDirectionJK: 9
add force vectors and multiply: 9
add force to mol j: 3
sum forceK: 3 (don't count multiplication with -1.0)
add force to mol k: 3
Total: 59 without n3, 100 with n3

For the globals calculation, this is:

potential: 3
virial: 3 without n3, 9 with n3
accumulation: 4 without n3, 12 with n3
Total: 10 without n3, 24 with n3

Returns: number of FLOPs since initTraversal() is called.

Reimplemented from autopas::Functor< Particle_T, CRTP_T >.

◆ getPotentialEnergy()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

double mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getPotentialEnergy ( )

inline

Get the potential Energy.

Returns: the potential Energy

◆ getVirial()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

double mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::getVirial ( )

inline

Get the virial.

Returns

◆ initTraversal()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

void mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::initTraversal ( )

inlinefinalvirtual

Reset the global values.

Will set the global values to zero to prepare for the next iteration.

Reimplemented from autopas::Functor< Particle_T, CRTP_T >.

◆ isRelevantForTuning()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

bool mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::isRelevantForTuning ( )

inlinefinalvirtual

Specifies whether the functor should be considered for the auto-tuning process.

Returns: true if and only if this functor is relevant for auto-tuning.

Implements autopas::Functor< Particle_T, CRTP_T >.

◆ setParticleProperties()

template<class Particle_T , bool useMixing = false, autopas::FunctorN3Modes useNewton3 = autopas::FunctorN3Modes::Both, bool calculateGlobals = false, bool countFLOPs = false>

void mdLib::AxilrodTellerFunctor< Particle_T, useMixing, useNewton3, calculateGlobals, countFLOPs >::setParticleProperties ( SoAFloatPrecision nu )

inline

Sets the particle properties constants for this functor.

This is only necessary if no particlePropertiesLibrary is used.

Parameters

nu	The Axilrod-Teller potential parameter

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

/github/workspace/applicationLibrary/molecularDynamics/molecularDynamicsLibrary/AxilrodTellerFunctor.h

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

The Axilrod-Teller potential

Constructor & Destructor Documentation

◆ AxilrodTellerFunctor() [1/2]

◆ AxilrodTellerFunctor() [2/2]

Member Function Documentation

◆ allowsNewton3()

◆ allowsNonNewton3()

◆ AoSFunctor()

◆ endTraversal()

◆ getComputedAttr()

◆ getHitRate()

◆ getMixing()

◆ getName()

◆ getNeededAttr() [1/2]

◆ getNeededAttr() [2/2]

◆ getNumFLOPs()

◆ getPotentialEnergy()

◆ getVirial()

◆ initTraversal()

◆ isRelevantForTuning()

◆ setParticleProperties()