LinearSOE

#include \(<\tilde{ }\)/system_of_eqn/linearSOE/LinearSOE.h\(>\)

class LinearSOE: public SystmOfEqn

MovableObject
SystemOfEqn

LinearSOE is an abstract class. A LinearSOE object provides an abstraction of a system of linear equations. A linear system of equation of order \(n\):

\[\begin{array}{ccccccccc} a_{0,0}x_0 & + & a_{0,1}x_1 & + & ... & + & a_{0,n-1}x_{n-1} & = & b_0 \\ a_{1,0}x_0 & + & a_{1,1}x_1 & + & ... & + & a_{1,n-1}x_{n-1} & = & b_1 \\ ... & & ... & & & & ... & & ... \\ a_{n-1,0}x_0 & + & a_{n-1,1}x_1 & + & ... & + & a_{n-1,n-1}x_{n-1} & = & b_{n-1} \\ \end{array}\]

can be expressed by the matrix equation \(Ax=b\), where \(A\) is a matrix of order \(n\) X \(n\) and \(b\) and \(x\) are vectors or order \(n\). A LinearSOE object is responsible for storing these equations and for providing methods at the interface to set up and obtain the equations. Each LinearSOE object will be associated with a LinearSOESolver object. It is the LinearSOESolver objects that is responsible for solving the linear system of equations.

The integer classTag is passed to the constructor for the SystemOfEqn. The constructor sets sets the pointer for the currently associated LinearSOESolver object to point to theSolver.

Does nothing.

Causes the SystemOfEqn object to invoke solve() on the currently associated LinearSOESolver object. Returns a \(0\) if successful, negative number if not; the actual value depending on the LinearSOESolver. To solve a linear system of equations means to find \(x\) such that the equation \(Ax=b\) is satisfied.

A method which returns the number of equations in the system, i.e. the number of unknowns.

Invoked to allow the LinearSOE object to determine the size and sparsity of the matrix \(A\) and vectors \(x\) and \(b\). This information can be deduced from the number of vertices and the connectivity between the vertices in the Graph object G. To return \(0\) if successful, a negative number if not.

The LinearSOE object assembles fact times the Matrix M into the matrix \(A\). The Matrix is assembled into \(A\) at the locations given by the ID object loc, i.e. \(a_{loc(i),loc(j)} += M(i,j)\). Numbering in \(A\) starts at \((0,0)\), i.e. C style. If a location specified is outside the range, i.e. \((-1,-1)\) the corresponding entry in M is not added to \(A\). To return \(0\) if successful, a negative number if not. virtual int addB(const Vector & theVector, const ID & loc, double fact = 1.0) =0;
The LinearSOE object assembles fact times the Vector V into the vector \(b\). The Vector is assembled into \(b\) at the locations given by the ID object loc, i.e. \(b_{loc(i)} += V(i)\). If a location specified is outside the range, e.g. \(-1\), the corresponding entry in V is not added to \(b\). To return \(0\) if successful, a negative number if not.

virtual int setB(const Vector & theVector, double fact = 1.0) =0;

The LinearSOE object sets the vector b to be fact times the Vector V. To return \(0\) if successful, a negative number if not.

virtual void zeroA(void) =0;

To zero the matrix \(A\), i.e. set all the components of \(A\) to \(0\).

virtual void zeroB(void) =0;

To zero the vector \(b\), i.e. set all the components of \(b\) to \(0\).

virtual const Vector &getX(void) = 0;

To return, as a Vector object, the vector \(x\). A const reference is returned, meaning the Vector that is returned cannot be modified, i.e. no non-const method can be invoked on the Vector.

virtual const Vector &getB(void) = 0;

To return as a Vector object the vector \(b\). A const reference is returned, meaning the Vector that is returned cannot be modified, i.e. no non-const method can be invoked on the Vector.

virtual double normRHS(void) =0;

To return the 2-norm of the vector \(x\).

virtual void setX(int loc, double value) =0;

The LinearSOE object is responsible for setting \(x(loc) = value\). This is needed in domain decomposition methods and could be useful in iterative solution strategies when an initial approximation is known.

This is invoked to set the currently associated LinearSOESolver object to be newSolver. Each subclass will provide it’s own variation of setSolver() method (needed so subclasses can verify type of Solver object passed). the subclasses in their variation of the setSolver() method (unless they wish to implement their own solve() method) invoke this method. Returns \(0\).

Returns a pointer to the associated LinearSOESolver object.