NewmarkNLSIM Class Reference

Newmark-based solution driver for dynamic isogeometric FEM simulators. More...

#include <NewmarkNLSIM.h>

Inheritance diagram for NewmarkNLSIM:

Collaboration diagram for NewmarkNLSIM:

Public Member Functions
	NewmarkNLSIM (SIMbase &sim)
	The constructor initializes default solution parameters.
virtual	~NewmarkNLSIM ()
	The destructor deletes the Finert system vector.
virtual bool	parse (const tinyxml2::XMLElement *elem)
	Parses a data section from an XML document.
virtual void	printProblem (bool stopInputTimer=false) const
	Prints out problem-specific data to the log stream. More...
virtual void	initPrm ()
	Initializes time integration parameters for the integrand.
virtual void	initSol (size_t nSol, size_t nDof=0)
	Initializes the primary solution vectors.
virtual void	setSolution (const RealArray &newSol, int idx)
	Modifies the current solution vector (used by sub-iterations only).
virtual bool	isLinear () const
	Returns whether this solution driver is linear or not.
virtual bool	serialize (SerializeMap &data) const
	Serialize solution vectors for restarting purposes. More...
virtual bool	deSerialize (const SerializeMap &data)
	Set solution vectors from a serialized state. More...
virtual bool	parse (const tinyxml2::XMLElement *elem)
	Parses a data section from an XML document.
Public Member Functions inherited from NewmarkSIM
	NewmarkSIM (SIMbase &sim)
	The constructor initializes default solution parameters.
bool	initAcc (double zero_tolerance=1.0e-8, std::streamsize outPrec=0)
	Calculates initial accelerations.
virtual bool	advanceStep (TimeStep &param, bool updateTime=true)
	Advances the time step one step forward.
virtual SIM::ConvStatus	solveStep (TimeStep &param, SIM::SolutionMode=SIM::STATIC, double zero_tolerance=1.0e-8, std::streamsize outPrec=0)
	Solves the dynamic equations by a predictor/multi-corrector method. More...
SIM::ConvStatus	solveIteration (TimeStep &param)
	Solves the linearized system of current iteration. More...
int	getMaxit () const
	Returns the maximum number of iterations.
virtual bool	isDynamic () const
	Returns whether this is a dynamic solution driver or not.
const Vector &	getVelocity () const
	Returns a const reference to current velocity vector.
const Vector &	getAcceleration () const
	Returns a const reference to current velocity vector.
bool	saveStep (int iStep, TimeStep &param)
	Saves the converged solution to VTF file for a given time step. More...
virtual void	dumpResults (double time, utl::LogStream &os, std::streamsize precision=3, bool formatted=true) const
	Dumps solution variables at user-defined points. More...
virtual bool	parse (const tinyxml2::XMLElement *elem)
	Parses a data section from an XML document. More...
virtual bool	parse (char *keyWord, std::istream &is)
	Parses a data section from an input stream.
virtual bool	parse (const tinyxml2::XMLElement *elem)
	Parses a data section from an XML document.
bool	saveStep (int iStep, double time, const char *vecName=nullptr)
	Saves the converged solution to VTF file of a given time/load step. More...
bool	saveStep (int iStep, int &rBlock, double time, const char *vecName=nullptr)
	Saves the converged solution to VTF file of a given time/load step. More...
bool	saveStep (int iStep, int &rBlock, const char *vecName)
	Saves the converged solution to VTF file of a given time/load step. More...
Public Member Functions inherited from MultiStepSIM
virtual const char **	getPrioritizedTags () const
	Returns a list of prioritized XML-tags.
bool	initEqSystem (bool withRF=true, size_t nScl=0)
	Allocates the FE system matrices. More...
virtual bool	preprocess (const std::vector< int > &ignored, bool fixDup)
	Performs some pre-processing tasks on the FE model. More...
void	setStartGeo (int gID)
	Initializes the geometry block counter.
bool	saveModel (const char *fileName)
	Opens a new VTF-file and writes the model geometry to it. More...
bool	saveModel (int &gBlock, int &rBlock, const char *fileName=nullptr, bool clearG=true)
	Opens a new VTF-file and writes the model geometry to it. More...
bool	saveModel (int &gBlock, int &rBlock, double time)
	Writes the model geometry and BCs to an already opened VTF-file. More...
bool	saveStep (int iStep, double time, const char *vecName=nullptr)
	Saves the converged solution to VTF file of a given time/load step. More...
bool	saveStep (int iStep, int &rBlock, double time, const char *vecName=nullptr)
	Saves the converged solution to VTF file of a given time/load step. More...
bool	saveStep (int iStep, int &rBlock, const char *vecName)
	Saves the converged solution to VTF file of a given time/load step. More...
bool	checkForRestart ()
	Restores the solution from a serialized state in case of restart.
void	dumpStep (int iStep, double time, utl::LogStream &os, bool withID=true) const
	Dumps the primary solution for inspection. More...
bool	hasPointResultFile () const
	Returns whether a points result file has been defined or not.
bool	savePoints (double time, int step) const
	Saves point-wise solution to file for a given time/load step. More...
const SIMoutput &	getModel () const
	Returns a const reference to the FE model.
void	setSubIteration (SubIt flag)
	Updates the sub-iteration flag.
SubIt	getSubIteration () const
	Returns the sub-iteration flag.
virtual size_t	numSolution () const
	Returns the number of solution vectors.
virtual const Vector &	realSolution (int i=0) const
	Returns a const reference to the current real solution vector. More...
virtual const Vectors &	realSolutions (bool=false)
	Returns a const reference to the current real solution vectors. More...
double *	theRefNorm ()
	Returns a pointer to the reference norm variable.
const double *	getRefNorm () const
	Returns a const pointer to the reference norm variable.
virtual bool	parse (char *keyWord, std::istream &is)
	Parses a data section from an input stream.
virtual bool	parse (const tinyxml2::XMLElement *elem)
	Parses a data section from an XML document.
Public Member Functions inherited from SIMsolution
virtual const Vectors &	getSolutions () const
	Returns a const reference to the solution vectors.
virtual Vectors &	theSolutions ()
	Returns a reference to the solution vectors (for assignment).
virtual const Vector &	getSolution (int ix=0) const
	Returns a const reference to current solution vector.
Public Member Functions inherited from SIMadmin
virtual	~SIMadmin ()
	Empty destructor.
virtual bool	read (const char *fileName)
	Reads model data from the specified input file *fileName.
virtual bool	parse (char *keyWord, std::istream &is)
	Parses a data section from an input stream.
virtual bool	preprocessC (const IntVec &, bool, double=0.0)
	Performs some pre-processing tasks on the FE model.
const ProcessAdm &	getProcessAdm () const
	Returns the parallel process administrator.
int	getGlobalProcessID () const
	Returns the global process ID. More...
const std::string &	getHeading () const
	Returns the simulator heading.
void	setHeading (const std::string &heading)
	Defines the simulator heading.
void	printHeading (int &supStep) const
	Prints the heading of this simulator, if any, to IFEM::cout.
Public Member Functions inherited from XMLInputBase
bool	readXML (const char *fileName, bool verbose=true)
	Reads an XML input file. More...
bool	loadXML (const char *xml)
	Loads data from an XML-formatted text string. More...

Protected Member Functions
virtual bool	predictStep (TimeStep &param)
	Calculates predicted velocities and accelerations.
virtual bool	correctStep (TimeStep &param, bool converged)
	Updates configuration variables (solution vector) in an iteration.
virtual void	finalizeRHSvector (bool)
	Finalizes the right-hand-side vector on the system level.
Protected Member Functions inherited from NewmarkSIM
virtual bool	solutionNorms (const TimeDomain &, double zero_tolerance=1.0e-8, std::streamsize outPrec=0)
	Computes and prints some solution norm quantities. More...
virtual SIM::ConvStatus	checkConvergence (TimeStep &param)
	Checks whether the corrector iterations have converged or diverged.
Protected Member Functions inherited from MultiStepSIM
	MultiStepSIM (SIMbase &sim)
	The constructor initializes the FE model reference. More...
void	printStep (const TimeStep &param) const
	Prints out time/load step identification. More...
int	getLastSavedStep () const
	Returns the last step that was saved to VTF.
Protected Member Functions inherited from SIMsolution
	SIMsolution ()=default
	The default constructor is protected to allow sub-classes only.
virtual	~SIMsolution ()=default
	Empty default destructor.
void	initSolution (size_t ndof, size_t nsol=1)
	Initializes the solution vectors. More...
void	pushSolution (unsigned short int nVecState=1)
	Pushes the solution vector stack. More...
bool	saveSolution (SerializeMap &data, const std::string &name) const
	Writes current solution to a serialization container. More...
bool	restoreSolution (const SerializeMap &data, const std::string &name)
	Restores the solution from a serialization container. More...
Protected Member Functions inherited from SIMadmin
	SIMadmin (const char *heading=nullptr)
	The default constructor initializes the process administrator.
	SIMadmin (SIMadmin &anotherSIM)
	Copy constructor.
Protected Member Functions inherited from XMLInputBase
const tinyxml2::XMLElement *	loadFile (tinyxml2::XMLDocument &doc, const char *fileName, bool verbose=false)
	Loads an XML input file into a tinyxml2::XMLDocument object. More...

Private Attributes
Vector	incDis
	Incremental displacement vector.
Vector	predVel
	Predicted velocity vector.
Vector	predAcc
	Predicted acceleration vector.
SystemVector *	Finert
	Actual inertia forces in last converged time step.

Additional Inherited Members
Public Types inherited from MultiStepSIM
enum	SubIt { ITER = 0 , FIRST = 1 , LAST = 2 , NONE = 3 }
	Enum describing sub-iteration status.
Public Attributes inherited from SIMadmin
SIMoptions &	opt
	Simulation control parameters.
Static Public Attributes inherited from NewmarkSIM
static const char *	inputContext = "newmarksolver"
	Input file context for solver parameters.
Static Public Attributes inherited from SIMadmin
static int	msgLevel = 2
	Controls the console output amount during solving.
Protected Types inherited from MultiStepSIM
enum	NormOp { MAX , ALL }
	Enum describing reference norm options.
Protected Types inherited from SIMsolution
using	SerializeMap = std::map< std::string, std::string >
	Convenience type.
Protected Types inherited from SIMadmin
using	IntVec = std::vector< int >
	Convenience alias.
Static Protected Member Functions inherited from SIMsolution
static std::string	serialize (const double *v, size_t n)
	Helper method for serializing a double array into a text string. More...
static void	deSerialize (const std::string &data, double *v, size_t n)
	Helper method for deserializing a double array from a text string. More...
Protected Attributes inherited from NewmarkSIM
double	alpha1
	Mass-proportional damping parameter.
double	alpha2
	Stiffness-proportional damping parameter.
double	beta
	Newmark time integration parameter.
double	gamma
	Newmark time integration parameter.
bool	solveDisp
	If true, use incremental displacements as unknowns.
char	predictor
	Predictor type flag.
int	maxit
	Maximum number of iterations in a time step.
int	maxIncr
	Maximum number of iterations with increasing norm.
int	nupdat
	Number of iterations with updated tangent.
int	saveIts
	Time step for which iteration result should be saved.
char	saveVelAc
	Flag the saving of velocity and acceleration to VTF.
double	rTol
	Relative convergence tolerance.
double	aTol
	Absolute convergence tolerance.
double	divgLim
	Relative divergence limit.
unsigned short int	cNorm
	Option for which convergence norm to use.
std::string	factor_file
	File for storage of factorized Newton matrix.
bool	write_factor
	If true, write new factorized Newton matrix.
bool	read_factor
	If true, read factorized Newton matrix.
LinAlg::StorageFormat	fmt
	Factorized Newton matrix storage format.
Protected Attributes inherited from MultiStepSIM
SIMoutput &	model
	The isogeometric FE model.
Vector	loadVec
	System load vector (for output to VTF)
Vector	residual
	Residual force vector.
Vector	linsol
	Linear solution vector.
NormOp	refNopt
	Reference norm option.
double	refNorm
	Reference norm value used in convergence checks.
double	rCond
	Reciprocal condition number of the linear equation system.
SubIt	subiter
	Sub-iteration flag.
size_t	nRHSvec
	Number of right-hand-side vectors to assemble.
char	rotUpd
	Option for how to update of nodal rotations.
int	geoBlk
	Running VTF geometry block counter.
int	nBlock
	Running VTF result block counter.
Protected Attributes inherited from SIMsolution
Vectors	solution
	Stack of solution vectors.
Protected Attributes inherited from SIMadmin
ProcessAdm	adm
	Parallel administrator.
int	myPid
	Processor ID in parallel simulations.
int	nProc
	Number of processors in parallel simulations.
std::string	myHeading
	Heading written before reading the input file.

Detailed Description

Newmark-based solution driver for dynamic isogeometric FEM simulators.

This class implements the Hilber-Hughes-Taylor (HHT) time integration algorithm, with a constant displacement predictor step. The algorithm relies on the following three algorithm parameters:

α_H = parameter defining the amount of numerical damping
α₁ = mass-proportional damping factor
α₂ = stiffness-proportional damping factor

For a given time discretization, t₀ = 0 and t_n = t_n-1 + Δt_n for n=1...n_step, the HHT time integration algorithm goes like this:

Initialisation of time step loop:

\[ \beta \;=\; \frac{1}{4}(1.0-\alpha_H)^2,\; \gamma \;=\; \frac{1}{2}-\alpha_H \]

\[ \begin{array}{lcll} t &=& 0 & \mbox{(initial time)} \\ {\bf u}_0 &=& {\bf 0} & \mbox{(initial displacements)} \\ \dot{\bf u}_0 &=& {\bf 0} & \mbox{(initial velocity)} \\ \ddot{\bf u}_0 &=& {\bf 0} & \mbox{(initial acceleration)} \\ \tilde{\bf R}_0 &=& {\bf 0} & \mbox{(initial actual inertia force)} \\ \end{array} \]

FOR n = 1 TO n_step DO

1. Initialisation of iteration loop:

   \begin{eqnarray*} i &=& 0 \quad\mbox{(iteration counter)}\\ t &=& t + \Delta t_n \\ {\bf u}_n^0 &=& {\bf u}_{n-1} \\ \Delta{\bf u}_n &=& {\bf 0} \quad\mbox{(displacement increment)} \end{eqnarray*}

2. Predict new velocity and acceleration:

   \begin{eqnarray*} {\bf v}_n &=& (\frac{\gamma}{\beta}-1)\dot{\bf u}_{n-1} + \Delta t_n(\frac{\gamma}{2\beta}-1)\ddot{\bf u}_{n-1} \\ {\bf a}_n &=& (\frac{1}{2\beta}-1)\ddot{\bf u}_{n-1} + \frac{1}{\Delta t_n\beta}\dot{\bf u}_{n-1} \end{eqnarray*}

   \[ \begin{array}{lcll} \dot{\bf u}_n^0 &=& {\bf v}_n & \mbox{(predicted velocity)} \\ \ddot{\bf u}_n^0 &=& {\bf a}_n & \mbox{(predicted acceleration)} \end{array} \]

3. Assemble FE matrices and right-hand-side force vectors:

   \[ \begin{array}{lcll} {\bf K}_n^0 &=& {\bf K}({\bf u}_n^0,t) & \mbox{(tangential stiffness matrix)} \\ {\bf C}_n^0 &=& {\bf C}({\bf u}_n^0,t) & \mbox{(damping matrix)} \\ {\bf M}_n^0 &=& {\bf M}({\bf u}_n^0,t) & \mbox{(mass matrix)} \\ {\bf F}_n^{S,0} &=& {\bf F}^S({\bf u}_n^0,t) & \mbox{(internal stiffness forces)} \\ {\bf F}_n^{I,0} &=& {\bf F}^I({\bf u}_n^0,\ddot{\bf u}_n^0,t) & \mbox{(internal inertia forces)} \\ {\bf F}_n^{E,0} &=& {\bf F}^E({\bf u}_n^0,t) & \mbox{(external forces)} \end{array} \]

4. Compute Newton matrix and associated incremental load vector:

   \begin{eqnarray*} {\bf N}_n^0 &=& a_n{\bf M}_n^0 + b_n{\bf C}_n^0 + c_n{\bf K}_n^0 \\ {\bf R}_n^0 &=& (1+\alpha_H)\left[{\bf F}_n^{E,0} - {\bf F}_n^{S,0} + (\alpha_1{\bf M}_n^0 + \alpha_2{\bf K}_n^0 + {\bf C}_n^0){\bf v}_n\right] + {\bf F}_n^{I,0} - \alpha_H\tilde{\bf R}_{n-1} \end{eqnarray*}

   where

   \begin{eqnarray*} a_n &=& \frac{1}{\Delta t_n^2\beta} + (1+\alpha_H)\frac{\alpha_1\gamma}{\Delta t_n\beta} \\ b_n &=& (1+\alpha_H)\frac{\gamma}{\Delta t_n\beta} \\ c_n &=& (1+\alpha_H)\left(1+\frac{\alpha_2\gamma}{\Delta t_n\beta}\right) \end{eqnarray*}

   and

   \[ \tilde{\bf R}_n \;=\; {\bf F}_n^E - {\bf F}_n^S - (\alpha_1{\bf M}_n+\alpha_2{\bf K}_n)\dot{\bf u}_n \quad\mbox{(actual inertia force in time step $n > 0$)} \]

5. Solve for the incremental displacement:

   \[ {\bf N}_n^0 \Delta{\bf u}_n^0 \;=\; {\bf R}_n^0 \quad\Longrightarrow\; \Delta{\bf u}_n^0 \]

6. WHILE i < MaxIt AND \(\|\Delta{\bf u}_n^i\|>\epsilon_{\rm tol}\) DO

   1. Update configuration:

      \begin{eqnarray*} i &=& i + 1 \\ \Delta{\bf u}_n &=& \Delta{\bf u}_n + \Delta{\bf u}_n^{i-1} \\ {\bf u}_n^i &=& {\bf u}_{n-1} \oplus \Delta{\bf u}_n \\ \dot{\bf u}_n^i &=& \frac{\gamma}{\Delta t_n\beta}\Delta{\bf u}_n - {\bf v}_n \\ \ddot{\bf u}_n^i &=& \frac{1}{\Delta t_n^2\beta}\Delta{\bf u}_n - {\bf a}_n \end{eqnarray*}

   2. Assemble FE matrices and right-hand-side force vectors:

      \[ \begin{array}{lll} {\bf K}_n^i \;=\; {\bf K}({\bf u}_n^i,t)\;, & {\bf C}_n^i \;=\; {\bf C}({\bf u}_n^i,t)\;, & {\bf M}_n^i \;=\; {\bf M}({\bf u}_n^i,t) \\[1mm] {\bf F}_n^{S,i} =\; {\bf F}^S({\bf u}_n^i,t)\;, & {\bf F}_n^{I,i} \;=\; {\bf F}^I({\bf u}_n^i,\ddot{\bf u}_n^i,t)\;, & {\bf F}_n^{E,i} \;=\; {\bf F}^E({\bf u}_n^i,t) \end{array} \]

   3. Compute Newton matrix and associated incremental load vector:

      \begin{eqnarray*} {\bf N}_n^i &=& a_n{\bf M}_n^i + b_n{\bf C}_n^i + c_n{\bf K}_n^i \\ {\bf R}_n^i &=& (1+\alpha_H)\left[{\bf F}_n^{E,i} - {\bf F}_n^{S,i} - (\alpha_1{\bf M}_n^i + \alpha_2{\bf K}_n^i + {\bf C}_n^i)\dot{\bf u}_n^i\right] - {\bf F}_n^{I,i} - \alpha_H\tilde{\bf R}_{n-1} \end{eqnarray*}

   4. Solve for the iterative displacement:

      \[ {\bf N}_n^i \Delta{\bf u}_n^i \;=\; {\bf R}_n^i \quad\Longrightarrow\; \Delta{\bf u}_n^i \]

   END DO

7. Update converged configuration:

   \begin{eqnarray*} \Delta{\bf u}_n &=& \Delta{\bf u}_n + \Delta{\bf u}_n^i \\ {\bf u}_n &=& {\bf u}_{n-1} \oplus \Delta{\bf u}_n \\ \dot{\bf u}_n&=&\frac{\gamma}{\Delta t_n\beta}\Delta{\bf u}_n-{\bf v}_n \\ \ddot{\bf u}_n&=&\frac{1}{\Delta t_n^2\beta}\Delta{\bf u}_n - {\bf a}_n \end{eqnarray*}

END DO

Member Function Documentation

deSerialize()

bool NewmarkNLSIM::deSerialize ( const SerializeMap &  data )

virtual

Set solution vectors from a serialized state.

Parameters

[in]

data

Container for serialized data

Reimplemented from MultiStepSIM.

References SIMsolution::deSerialize(), SystemVector::dim(), Finert, SIMbase::getName(), SIMbase::getNoEquations(), SystemVector::getPtr(), MultiStepSIM::model, and SIMsolution::restoreSolution().

printProblem()

void NewmarkNLSIM::printProblem ( bool  stopInputTimer = false ) const

virtual

Prints out problem-specific data to the log stream.

Parameters

[in]

stopInputTimer

If true, stop file input timer before print

Reimplemented from NewmarkSIM.

References NewmarkSIM::alpha2, IFEM::cout, MultiStepSIM::nRHSvec, and NewmarkSIM::printProblem().

serialize()

bool NewmarkNLSIM::serialize ( SerializeMap &  data ) const

virtual

Serialize solution vectors for restarting purposes.

Parameters

data	Container for serialized data

Reimplemented from MultiStepSIM.

References SystemVector::dim(), Finert, SIMbase::getName(), SystemVector::getPtr(), MultiStepSIM::model, SIMsolution::saveSolution(), and SIMsolution::serialize().

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

• src/SIM/NewmarkNLSIM.h
• src/SIM/NewmarkNLSIM.C