Linear

# Linear

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

class Linear: public EquiSolnAlg;

MovableObject
SolutionAlgorithm
EquiSolnAlgo

The Linear class is an algorithmic class which uses the linear solution algorithm to solve the equations. This is based on a Taylor expansion of the linear system \(\R(\U) = \zero\) about an approximate solution \(\U_{a}\).

\[\R(\U) = \R(\U_{a}) + \left[ {\frac{\partial \R}{\partial \U} \vert}_{\U_{a}}\right] \left( \U - \U_{a} \right)\] which can be expressed as: \[\ \K_{a} \Delta \U = \R(\U_{a})\] which is solved for \(\Delta \U\) to give the approximation \(\U = \U_{a} + \Delta \U\). To start the iteration \(\U_a = \U_{trial}\), i.e. the current trial response quantities are chosen as approximate solution quantities.

// Constructor

// Destructor

// Public Methods

// Public Methods for Output

The integer EquiALGORITHM_TAGS_Linear (defined in \(<\)classTags.h\(>\)) is passed to the EquiSolnAlgo classes constructor.

This method performs the linear solution algorithm:

while ̄ whilewhilewhilewhilewhilewhilewhilewhilewhile ̄ theIntegrator-\(>\)formTangent() // form \(\K_{a}\)
theIntegrator-\(>\)formUnbalance() // form \(\R(\U_{a})\)
theSOE-\(>\)solveX() // solve for \(\Delta \U\)
theIntegrator-\(>\)update(theSOE-\(>\)getX()) // set \(\U = \U_{a} + \Delta \U\)

The method returns a 0 if successful, otherwise warning message is printed and a negative number is returned; a \(-1\) if error during formTangent(), a \(-2\) if error during formUnbalance(), a \(-3\) if error during solve(), 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.

int sendSelf(int commitTag, Channel &theChannel);

Does nothing. Returns 0. int recvSelf(int commitTag, Channel &theChannel, FEM_ObjectBroker &theBroker);
Does nothing. Returns 0.

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

Sends the string ‘Linear Algorithm’ to the stream.