ModifiedNewton

#include <analysis/algorithm/equiSolnAlgo/ModifiedNewton.h>

class ModifiedNewton: public EquiSolnAlg;

MovableObject
SolutionAlgorithm
EquiSolnAlgo

The ModifiedNewton class is an algorithmic class which obtains a solution to a non-linear system using the modified Newton-Raphson iteration scheme. The Newton-Rapson iteration scheme is based on a Taylor expansion of the non-linear system of equations \(\R(\U) = \zero\) about an approximate solution \(\U{(i)}\): \[\R(\U) = \R(\U^{(i)}) + \left[ {\frac{\partial \R}{\partial \U} \vert}_{\U^{(i)}}\right] \left( \U - \U^{(i)} \right)\]

which can be expressed as: \[\ \K^{(i)} \Delta \U{(i)} = \R(\U^{(i)})\] which is solved for \(\Delta \U^{(i)}\) to give approximation for \(\U^{(i+1)} = \U^{(i)} + \Delta \U^{(i)}\). To start the iteration \(\U^{(1)} = \U_{trial}\), i.e. the current trial response quantities are chosen as initial response quantities. in the modified version the tangent is formed only once, i.e \[\ \K^{(1)} \Delta \U^{(i)} = \R(\U^{(i)})\]

To stop the iteration, a test must be performed to see if convergence has been achieved at each iteration. Each NewtonRaphson object is associated with a ConvergenceTest object. It is this object which determines if convergence has been achieved.

// Constructors

// Destructor

// Public Member Functions

// Public Methods for Output

The constructor takes as an argument the ConvregenceTest object theTest, the object which is used at the end of each iteration to determine if convergence has been obtained. The integer EquiALGORITHM_TAGS_ModifiedNewton (defined in \(<\)classTags.h\(>\)) is passed to the EquiSolnAlgo classes constructor.

Provided for FEM_ObjectBroker to instantiate a blank object with a class tag of EquiALGORITHM_TAGS_ModofiedNewton. recvSelf() must be invoked on this object.

Does nothing.

When invoked the object first sets itself as the EquiSolnAlgo object that the ConvergenceTest is testing and then it performs the modified Newton-Raphson iteration algorithm:

while ̄ while ̄ theTest-\(>\)start();
theIntegrator-\(>\)formTangent();
do {
theIntegrator-\(>\)formUnbalance();
theSOE-\(>\)solveX();
theIntegrator-\(>\)update(theSOE-\(>\)getX());
} while (theTest-\(>\)test() \(==\) false)

The method returns a 0 if successful, otherwise a negative number is returned; a \(-1\) if error during formTangent(), a \(-2\) if error during formUnbalance(), a \(-3\) if error during solve(), and a \(-4\) if error during update(). If an error occurs in any of the above operations the method stops at that routine, none of the subsequent operations are invoked. A \(-5\) is returned if any one of the links has not been setup.

void setTest(ConvergenceTest &theTest);

A method to set the tolerance criteria of the algorithm to be equal to the value theTol.

int sendSelf(int commitTag, Channel &theChannel);

Creates an ID object, puts the values of the theTest objects class and database tags into this ID. It then invokes sendVector() on the Channel object theChannel to send the data to the remote object. It then invokes sendSelf() on theTest. Returns \(0\) if successful, the channel error if not. int recvSelf(int commitTag, Channel &theChannel, FEM_ObjectBroker &theBroker);
Creates an ID object, invokes recvVector() on the Channel object. Uses the data in the ID to create a ConvergenceTest object of appropriate type and sets its dbTag. It then invokes recvSelf() on this test object.

int Print(OPS_Stream &s, int flag =0);

Sends the string ‘ModifiedNewton’ to the stream if flag equals \(0\).