Six degree of freedom motion for a rigid body. More...

Collaboration diagram for sixDoFRigidBodyMotion:

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Public Member Functions
	sixDoFRigidBodyMotion ()
	Construct null. More...

	sixDoFRigidBodyMotion (const dictionary &dict, const dictionary &stateDict)
	Construct from constant and state dictionaries. More...

	sixDoFRigidBodyMotion (const sixDoFRigidBodyMotion &)
	Construct as copy. More...

	~sixDoFRigidBodyMotion ()
	Destructor. More...

scalar	mass () const
	Return the mass. More...

const diagTensor &	momentOfInertia () const
	Return the inertia tensor. More...

const sixDoFRigidBodyMotionState &	state () const
	Return the motion state. More...

const point &	centreOfRotation () const
	Return the current centre of rotation. More...

const point &	initialCentreOfMass () const
	Return the initial centre of mass. More...

point	centreOfMass () const
	Return the current centre of mass. More...

const tensor &	orientation () const
	Return the orientation tensor, Q. More...

vector	omega () const
	Return the angular velocity in the global frame. More...

const vector &	v () const
	Return the current velocity. More...

vector	momentArm () const

bool	report () const
	Return the report Switch. More...

void	newTime ()
	Store the motion state at the beginning of the time-step. More...

point &	centreOfRotation ()
	Return non-const access to the centre of rotation. More...

void	addRestraints (const dictionary &dict)
	Add restraints to the motion, public to allow external. More...

void	addConstraints (const dictionary &dict)
	Add restraints to the motion, public to allow external. More...

void	update (bool firstIter, const vector &fGlobal, const vector &tauGlobal, scalar deltaT, scalar deltaT0)
	Symplectic integration of velocities, orientation and position. More...

void	status () const
	Report the status of the motion. More...

point	velocity (const point &pt) const
	Return the velocity of a position. More...

point	transform (const point &initialPoints) const
	Transform the given initial state point by the current motion. More...

tmp< pointField >	transform (const pointField &initialPoints) const
	Transform the given initial state pointField by the current. More...

tmp< pointField >	transform (const pointField &initialPoints, const scalarField &scale) const
	Transform the given initial state pointField by the current. More...

void	write (Ostream &) const
	Write. More...

bool	read (const dictionary &dict)
	Read coefficients dictionary and update system parameters,. More...

Private Member Functions
tensor	rotationTensorX (scalar deltaT) const
	Calculate the rotation tensor around the body reference. More...

tensor	rotationTensorY (scalar deltaT) const
	Calculate the rotation tensor around the body reference. More...

tensor	rotationTensorZ (scalar deltaT) const
	Calculate the rotation tensor around the body reference. More...

Tuple2< tensor, vector >	rotate (const tensor &Q0, const vector &pi, const scalar deltaT) const
	Apply rotation tensors to Q0 for the given torque (pi) and deltaT. More...

void	applyRestraints ()
	Apply the restraints to the object. More...

void	updateAcceleration (const vector &fGlobal, const vector &tauGlobal)
	Update and relax accelerations from the force and torque. More...

const PtrList< sixDoFRigidBodyMotionRestraint > &	restraints () const
	Return the restraints. More...

const PtrList< sixDoFRigidBodyMotionConstraint > &	constraints () const
	Return the constraints. More...

const point &	initialCentreOfRotation () const
	Return the initial centre of rotation. More...

const tensor &	initialQ () const
	Return the initial orientation. More...

const tensor &	Q () const
	Return the orientation. More...

const vector &	a () const
	Return the current acceleration. More...

const vector &	pi () const
	Return the current angular momentum. More...

const vector &	tau () const
	Return the current torque. More...

point &	initialCentreOfRotation ()
	Return the centre of rotation. More...

tensor &	initialQ ()
	Return initial orientation. More...

tensor &	Q ()
	Return non-const access to the orientation. More...

vector &	v ()
	Return non-const access to vector. More...

vector &	a ()
	Return non-const access to acceleration. More...

vector &	pi ()
	Return non-const access to angular momentum. More...

vector &	tau ()
	Return non-const access to torque. More...

Private Attributes
sixDoFRigidBodyMotionState	motionState_
	Motion state data object. More...

sixDoFRigidBodyMotionState	motionState0_
	Motion state data object for previous time-step. More...

PtrList< sixDoFRigidBodyMotionRestraint >	restraints_
	Motion restraints. More...

PtrList< sixDoFRigidBodyMotionConstraint >	constraints_
	Motion constaints. More...

tensor	tConstraints_
	Translational constraint tensor. More...

tensor	rConstraints_
	Rotational constraint tensor. More...

point	initialCentreOfMass_
	Centre of mass of initial state. More...

point	initialCentreOfRotation_
	Centre of rotation of initial state. More...

tensor	initialQ_
	Orientation of initial state. More...

scalar	mass_
	Mass of the body. More...

diagTensor	momentOfInertia_
	Moment of inertia of the body in reference configuration. More...

scalar	aRelax_
	Acceleration relaxation coefficient. More...

scalar	aDamp_
	Acceleration damping coefficient (for steady-state simulations) More...

Switch	report_
	Switch to turn reporting of motion data on and off. More...

autoPtr< sixDoFSolver >	solver_
	Motion solver. More...

Friends
class	sixDoFSolver

Detailed Description

Six degree of freedom motion for a rigid body.

Angular momentum stored in body fixed reference frame. Reference orientation of the body (where Q = I) must align with the cartesian axes such that the Inertia tensor is in principle component form. Can add restraints (e.g. a spring) and constraints (e.g. motion may only be on a plane).

The time-integrator for the motion is run-time selectable with options for symplectic (explicit), Crank-Nicolson and Newmark schemes.

Source files

Definition at line 66 of file sixDoFRigidBodyMotion.H.

Constructor & Destructor Documentation

◆ sixDoFRigidBodyMotion() [1/3]

sixDoFRigidBodyMotion ( )

Construct null.

Definition at line 73 of file sixDoFRigidBodyMotion.C.

◆ sixDoFRigidBodyMotion() [2/3]

sixDoFRigidBodyMotion	(	const dictionary &	dict,
		const dictionary &	stateDict
	)

Construct from constant and state dictionaries.

Definition at line 94 of file sixDoFRigidBodyMotion.C.

References Foam::diag(), dict, dictionary::found(), Foam::I, Foam::magSqr(), R, and Foam::sqr().

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◆ sixDoFRigidBodyMotion() [3/3]

sixDoFRigidBodyMotion ( const sixDoFRigidBodyMotion & sDoFRBM )

Construct as copy.

Definition at line 156 of file sixDoFRigidBodyMotion.C.

◆ ~sixDoFRigidBodyMotion()

~sixDoFRigidBodyMotion ( )

Destructor.

Definition at line 179 of file sixDoFRigidBodyMotion.C.

Member Function Documentation

◆ rotationTensorX()

Foam::tensor rotationTensorX ( scalar deltaT ) const

inlineprivate

Calculate the rotation tensor around the body reference.

frame x-axis by the given angle

Definition at line 29 of file sixDoFRigidBodyMotionI.H.

References Foam::cos(), phi, and Foam::sin().

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◆ rotationTensorY()

Foam::tensor rotationTensorY ( scalar deltaT ) const

inlineprivate

Calculate the rotation tensor around the body reference.

frame y-axis by the given angle

Definition at line 43 of file sixDoFRigidBodyMotionI.H.

References Foam::cos(), phi, and Foam::sin().

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◆ rotationTensorZ()

Foam::tensor rotationTensorZ ( scalar deltaT ) const

inlineprivate

Calculate the rotation tensor around the body reference.

frame z-axis by the given angle

Definition at line 57 of file sixDoFRigidBodyMotionI.H.

References Foam::cos(), phi, and Foam::sin().

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◆ rotate()

Foam::Tuple2< Foam::tensor, Foam::vector > rotate	(	const tensor &	Q0,
		const vector &	pi,
		const scalar	deltaT
	)		const

inlineprivate

Apply rotation tensors to Q0 for the given torque (pi) and deltaT.

and return the rotated Q and pi as a tuple

Definition at line 72 of file sixDoFRigidBodyMotionI.H.

References Tuple2::first(), Foam::constant::mathematical::pi(), R, and Tuple2::second().

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◆ applyRestraints()

void applyRestraints ( )

private

Apply the restraints to the object.

Definition at line 32 of file sixDoFRigidBodyMotion.C.

References sixDoFRigidBodyMotion::a(), sixDoFRigidBodyMotion::centreOfRotation(), forAll, Foam::Info, sixDoFRigidBodyMotion::mass_, UPstream::master(), sixDoFRigidBodyMotion::Q(), sixDoFRigidBodyMotion::report_, sixDoFRigidBodyMotion::restraints_, Tensor::T(), sixDoFRigidBodyMotion::tau(), and Vector< scalar >::zero.

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◆ updateAcceleration()

void updateAcceleration	(	const vector &	fGlobal,
		const vector &	tauGlobal
	)

private

Update and relax accelerations from the force and torque.

Definition at line 270 of file sixDoFRigidBodyMotion.C.

◆ restraints()

const Foam::PtrList< Foam::sixDoFRigidBodyMotionRestraint > & restraints ( ) const

inlineprivate

Return the restraints.

Definition at line 107 of file sixDoFRigidBodyMotionI.H.

References sixDoFRigidBodyMotion::restraints_.

◆ constraints()

const Foam::PtrList< Foam::sixDoFRigidBodyMotionConstraint > & constraints ( ) const

inlineprivate

Return the constraints.

Definition at line 114 of file sixDoFRigidBodyMotionI.H.

◆ initialCentreOfRotation() [1/2]

Foam::point & initialCentreOfRotation ( ) const

inlineprivate

Return the initial centre of rotation.

Definition at line 121 of file sixDoFRigidBodyMotionI.H.

◆ initialQ() [1/2]

Foam::tensor & initialQ ( ) const

inlineprivate

Return the initial orientation.

Definition at line 128 of file sixDoFRigidBodyMotionI.H.

◆ Q() [1/2]

Foam::tensor & Q ( ) const

inlineprivate

Return the orientation.

Definition at line 134 of file sixDoFRigidBodyMotionI.H.

Referenced by sixDoFRigidBodyMotion::applyRestraints().

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◆ a() [1/2]

Foam::vector & a ( ) const

inlineprivate

Return the current acceleration.

Definition at line 146 of file sixDoFRigidBodyMotionI.H.

Referenced by sixDoFRigidBodyMotion::applyRestraints().

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◆ pi() [1/2]

Foam::vector & pi ( ) const

inlineprivate

Return the current angular momentum.

Definition at line 152 of file sixDoFRigidBodyMotionI.H.

◆ tau() [1/2]

Foam::vector & tau ( ) const

inlineprivate

Return the current torque.

Definition at line 158 of file sixDoFRigidBodyMotionI.H.

Referenced by sixDoFRigidBodyMotion::applyRestraints().

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◆ initialCentreOfRotation() [2/2]

point& initialCentreOfRotation ( )

inlineprivate

Return the centre of rotation.

◆ initialQ() [2/2]

tensor& initialQ ( )

inlineprivate

Return initial orientation.

◆ Q() [2/2]

tensor& Q ( )

inlineprivate

Return non-const access to the orientation.

◆ v() [1/2]

Foam::vector & v ( )

inlineprivate

Return non-const access to vector.

Definition at line 140 of file sixDoFRigidBodyMotionI.H.

Referenced by linearDamper::restrain().

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◆ a() [2/2]

vector& a ( )

inlineprivate

Return non-const access to acceleration.

◆ pi() [2/2]

vector& pi ( )

inlineprivate

Return non-const access to angular momentum.

◆ tau() [2/2]

vector& tau ( )

inlineprivate

Return non-const access to torque.

◆ mass()

Foam::scalar mass ( ) const

inline

Return the mass.

Definition at line 208 of file sixDoFRigidBodyMotionI.H.

Referenced by uncoupledSixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs(), and sixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs().

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◆ momentOfInertia()

const Foam::diagTensor & momentOfInertia ( ) const

inline

Return the inertia tensor.

Definition at line 215 of file sixDoFRigidBodyMotionI.H.

◆ state()

const Foam::sixDoFRigidBodyMotionState & state ( ) const

inline

Return the motion state.

Definition at line 222 of file sixDoFRigidBodyMotionI.H.

◆ centreOfRotation() [1/2]

Foam::point & centreOfRotation ( ) const

inline

Return the current centre of rotation.

Definition at line 228 of file sixDoFRigidBodyMotionI.H.

Referenced by sixDoFRigidBodyMotion::applyRestraints(), sphericalAngularSpring::restrain(), linearAxialAngularSpring::restrain(), tabulatedAxialAngularSpring::restrain(), and sixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs().

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◆ initialCentreOfMass()

const Foam::point & initialCentreOfMass ( ) const

inline

Return the initial centre of mass.

Definition at line 235 of file sixDoFRigidBodyMotionI.H.

◆ centreOfMass()

Foam::point centreOfMass ( ) const

inline

Return the current centre of mass.

Definition at line 241 of file sixDoFRigidBodyMotionI.H.

References Foam::transform().

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◆ orientation()

const Foam::tensor & orientation ( ) const

inline

Return the orientation tensor, Q.

globalVector = Q & bodyLocalVector bodyLocalVector = Q.T() & globalVector

Definition at line 254 of file sixDoFRigidBodyMotionI.H.

Referenced by sphericalAngularSpring::restrain(), linearAxialAngularSpring::restrain(), and tabulatedAxialAngularSpring::restrain().

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◆ omega()

Foam::vector omega ( ) const

inline

Return the angular velocity in the global frame.

Definition at line 260 of file sixDoFRigidBodyMotionI.H.

References Foam::inv(), and Foam::constant::mathematical::pi().

Referenced by sphericalAngularDamper::restrain(), sphericalAngularSpring::restrain(), linearAxialAngularSpring::restrain(), and tabulatedAxialAngularSpring::restrain().

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◆ v() [2/2]

const vector& v ( ) const

inline

Return the current velocity.

◆ momentArm()

Foam::vector momentArm ( ) const

inline

Definition at line 247 of file sixDoFRigidBodyMotionI.H.

Referenced by sixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs().

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◆ report()

bool report ( ) const

inline

Return the report Switch.

Definition at line 266 of file sixDoFRigidBodyMotionI.H.

Referenced by sphericalAngularDamper::restrain(), linearDamper::restrain(), sphericalAngularSpring::restrain(), linearAxialAngularSpring::restrain(), linearSpring::restrain(), and tabulatedAxialAngularSpring::restrain().

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◆ newTime()

void newTime ( )

inline

Store the motion state at the beginning of the time-step.

Definition at line 272 of file sixDoFRigidBodyMotionI.H.

Referenced by uncoupledSixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs(), and sixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs().

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◆ centreOfRotation() [2/2]

point& centreOfRotation ( )

inline

Return non-const access to the centre of rotation.

◆ addRestraints()

void addRestraints ( const dictionary & dict )

Add restraints to the motion, public to allow external.

addition of restraints after construction

Definition at line 186 of file sixDoFRigidBodyMotion.C.

References dict, forAllConstIter(), dictionary::found(), sixDoFRigidBodyMotionRestraint::New(), and dictionary::subDict().

Referenced by sixDoFRigidBodyMotion::read().

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◆ addConstraints()

void addConstraints ( const dictionary & dict )

Add restraints to the motion, public to allow external.

addition of restraints after construction

Definition at line 220 of file sixDoFRigidBodyMotion.C.

References pointConstraint::constraintTransformation(), dict, Foam::endl(), forAllConstIter(), dictionary::found(), Foam::Info, sixDoFRigidBodyMotionConstraint::New(), Foam::nl, and dictionary::subDict().

Referenced by sixDoFRigidBodyMotion::read().

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◆ update()

void update	(	bool	firstIter,
		const vector &	fGlobal,
		const vector &	tauGlobal,
		scalar	deltaT,
		scalar	deltaT0
	)

Symplectic integration of velocities, orientation and position.

Changes to Crank-Nicolson integration for subsequent iterations.

Definition at line 298 of file sixDoFRigidBodyMotion.C.

References UPstream::master(), and Pstream::scatter().

Referenced by uncoupledSixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs(), and sixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs().

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◆ status()

void status ( ) const

Report the status of the motion.

Definition at line 320 of file sixDoFRigidBodyMotion.C.

References Foam::endl(), Foam::Info, and Foam::nl.

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◆ velocity()

Foam::point velocity ( const point & pt ) const

inline

Return the velocity of a position.

Definition at line 285 of file sixDoFRigidBodyMotionI.H.

Referenced by linearSpring::restrain().

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◆ transform() [1/3]

Foam::point transform ( const point & initialPoints ) const

inline

Transform the given initial state point by the current motion.

state

Definition at line 294 of file sixDoFRigidBodyMotionI.H.

Referenced by linearSpring::restrain(), uncoupledSixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs(), and sixDoFRigidBodyDisplacementPointPatchVectorField::updateCoeffs().

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◆ transform() [2/3]

Foam::tmp< Foam::pointField > transform ( const pointField & initialPoints ) const

Transform the given initial state pointField by the current.

motion state

Definition at line 333 of file sixDoFRigidBodyMotion.C.

◆ transform() [3/3]

Foam::tmp< Foam::pointField > transform	(	const pointField &	initialPoints,
		const scalarField &	scale
	)		const

Transform the given initial state pointField by the current.

motion state scaled by the given scale

Definition at line 346 of file sixDoFRigidBodyMotion.C.

References forAll, septernion::I, points, s(), Foam::slerp(), Foam::T(), Foam::transform(), and septernion::transform().

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◆ write()

void write ( Ostream & os ) const

Write.

Definition at line 49 of file sixDoFRigidBodyMotionIO.C.

References token::BEGIN_BLOCK, Foam::decrIndent(), token::END_BLOCK, token::END_STATEMENT, Foam::endl(), forAll, Foam::incrIndent(), Foam::indent(), IOstream::name(), Foam::nl, and Ostream::writeKeyword().

Referenced by sixDoFRigidBodyDisplacementPointPatchVectorField::write().

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◆ read()

bool read ( const dictionary & dict )

Read coefficients dictionary and update system parameters,.

constraints and restraints but not the current state

Definition at line 31 of file sixDoFRigidBodyMotionIO.C.

References sixDoFRigidBodyMotion::aDamp_, sixDoFRigidBodyMotion::addConstraints(), sixDoFRigidBodyMotion::addRestraints(), sixDoFRigidBodyMotion::aRelax_, sixDoFRigidBodyMotion::constraints_, dict, sixDoFRigidBodyMotion::mass_, sixDoFRigidBodyMotion::momentOfInertia_, sixDoFRigidBodyMotion::report_, and sixDoFRigidBodyMotion::restraints_.

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Friends And Related Function Documentation

◆ sixDoFSolver

friend class sixDoFSolver

friend

Definition at line 68 of file sixDoFRigidBodyMotion.H.

Field Documentation

◆ motionState_

sixDoFRigidBodyMotionState motionState_

private

Motion state data object.

Definition at line 73 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFSolver::centreOfRotation().

◆ motionState0_

sixDoFRigidBodyMotionState motionState0_

private

Motion state data object for previous time-step.

Definition at line 76 of file sixDoFRigidBodyMotion.H.

◆ restraints_

PtrList<sixDoFRigidBodyMotionRestraint> restraints_

private

Motion restraints.

Definition at line 79 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFRigidBodyMotion::applyRestraints(), sixDoFRigidBodyMotion::read(), and sixDoFRigidBodyMotion::restraints().

◆ constraints_

PtrList<sixDoFRigidBodyMotionConstraint> constraints_

private

Motion constaints.

Definition at line 82 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFRigidBodyMotion::read().

◆ tConstraints_

tensor tConstraints_

private

Translational constraint tensor.

Definition at line 85 of file sixDoFRigidBodyMotion.H.

◆ rConstraints_

tensor rConstraints_

private

Rotational constraint tensor.

Definition at line 88 of file sixDoFRigidBodyMotion.H.

◆ initialCentreOfMass_

point initialCentreOfMass_

private

Centre of mass of initial state.

Definition at line 91 of file sixDoFRigidBodyMotion.H.

◆ initialCentreOfRotation_

point initialCentreOfRotation_

private

Centre of rotation of initial state.

Definition at line 94 of file sixDoFRigidBodyMotion.H.

◆ initialQ_

tensor initialQ_

private

Orientation of initial state.

Definition at line 97 of file sixDoFRigidBodyMotion.H.

◆ mass_

scalar mass_

private

Mass of the body.

Definition at line 100 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFRigidBodyMotion::applyRestraints(), and sixDoFRigidBodyMotion::read().

◆ momentOfInertia_

diagTensor momentOfInertia_

private

Moment of inertia of the body in reference configuration.

(Q = I)

Definition at line 104 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFRigidBodyMotion::read().

◆ aRelax_

scalar aRelax_

private

Acceleration relaxation coefficient.

Definition at line 107 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFRigidBodyMotion::read().

◆ aDamp_

scalar aDamp_

private

Acceleration damping coefficient (for steady-state simulations)

Definition at line 110 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFRigidBodyMotion::read().

◆ report_

Switch report_

private

Switch to turn reporting of motion data on and off.

Definition at line 113 of file sixDoFRigidBodyMotion.H.

Referenced by sixDoFRigidBodyMotion::applyRestraints(), and sixDoFRigidBodyMotion::read().

◆ solver_

autoPtr<sixDoFSolver> solver_

private

Motion solver.

Definition at line 116 of file sixDoFRigidBodyMotion.H.

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

src/sixDoFRigidBodyMotion/sixDoFRigidBodyMotion/sixDoFRigidBodyMotion.H
src/sixDoFRigidBodyMotion/sixDoFRigidBodyMotion/sixDoFRigidBodyMotion.C
src/sixDoFRigidBodyMotion/sixDoFRigidBodyMotion/sixDoFRigidBodyMotionI.H
src/sixDoFRigidBodyMotion/sixDoFRigidBodyMotion/sixDoFRigidBodyMotionIO.C

Public Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ sixDoFRigidBodyMotion() [1/3]

◆ sixDoFRigidBodyMotion() [2/3]

◆ sixDoFRigidBodyMotion() [3/3]

◆ ~sixDoFRigidBodyMotion()

Member Function Documentation

◆ rotationTensorX()

◆ rotationTensorY()

◆ rotationTensorZ()

◆ rotate()

◆ applyRestraints()

◆ updateAcceleration()

◆ restraints()

◆ constraints()

◆ initialCentreOfRotation() [1/2]

◆ initialQ() [1/2]

◆ Q() [1/2]

◆ a() [1/2]

◆ pi() [1/2]

◆ tau() [1/2]

◆ initialCentreOfRotation() [2/2]

◆ initialQ() [2/2]

◆ Q() [2/2]

◆ v() [1/2]

◆ a() [2/2]

◆ pi() [2/2]

◆ tau() [2/2]

◆ mass()

◆ momentOfInertia()

◆ state()

◆ centreOfRotation() [1/2]

◆ initialCentreOfMass()

◆ centreOfMass()

◆ orientation()

◆ omega()

◆ v() [2/2]

◆ momentArm()

◆ report()

◆ newTime()

◆ centreOfRotation() [2/2]

◆ addRestraints()

◆ addConstraints()

◆ update()

◆ status()

◆ velocity()

◆ transform() [1/3]

◆ transform() [2/3]

◆ transform() [3/3]

◆ write()

◆ read()

Friends And Related Function Documentation

◆ sixDoFSolver

Field Documentation

◆ motionState_

◆ motionState0_

◆ restraints_

◆ constraints_

◆ tConstraints_

◆ rConstraints_

◆ initialCentreOfMass_

◆ initialCentreOfRotation_

◆ initialQ_

◆ mass_

◆ momentOfInertia_

◆ aRelax_

◆ aDamp_

◆ report_

◆ solver_