BandSPDLinSOE

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

class BandSPDLinSOE: public LinearSOE

MovableObject
SystemOfEqn
LinearSOE

BandSPDLinSOE is class which is used to store a banded symmetric system with ku superdiagonals. The \(A\) matrix is stored in a 1d double array with (ku+1)*n elements, where n is the size of the system. \(A_{i,j}\) is stored at location \((ku+1+i-j) + j*(ku+1)\), where \(i\) and \(j\) range from \(0\) to\(n-1\), i.e. C notation. For example when \(n=5\), \(ku = 2\):

\[\left[ \begin{array}{ccccc} a_{0,0} & a_{0,1} & a_{0,1} & 0 & 0 \\ a_{1,0} & a_{1,1} & a_{1,2} & a_{1,3} & 0 \\ a_{2,0} & a_{2,1} & a_{2,2} & a_{2,3} & a_{2,4} \\ 0 & a_{3,1} & a_{3,2} & a_{3,3} & a_{3,4} \\ 0 & 0 & a_{4,2} & a_{4,3} & a_{4,4} \\ \end{array} \right]\]

is stored in:

\[\left[ \begin{array}{cccccccccccccccccccc} * & * & a_{0,0} & * & a_{0,1} & a_{1,1} & a_{0,2} & a_{1,2} & a_{2,2} & a_{1,3} & a_{2,3} & a_{3,3} & a_{2,4} & a_{3,4} & a_{4,4}\\ \end{array} \right]\]

The \(X\) and \(B\) vectors are stored in 1d double arrays of length \(N\).

The solver and a unique class tag (defined in \(<\)classTags.h\(>\)) are passed to the LinearSOE constructor. The system size is set to \(0\) and the matrix \(A\) is marked as not having been factored. Invokes setLinearSOE(*this) on the solver. No memory is allocated for the 3 1d arrays.

BandSPDLinSOE(int N, int ku, BandSPDLinSolver &theSolver);

The solver and a unique class tag (defined in \(<\)classTags.h\(>\)) are passed to the LinearSOE constructor. Sets the size of the system to \(N\), the number of superdiagonals to ku. Allocates memory for the arrays; if not enough memory is available a warning message is printed and the system size is set to \(0\). Sets the solver to be called when solving the equations to theSolver. Invokes setLinearSOE(\*this) and setSize() on the theSolver, printing a warning message if setSize() returns a negative number. Also creates Vector objects for \(x\) and \(b\) using the (double *,int) Vector constructor.

Calls delete on any arrays created.

Invokes setLinearSOE(\*this) on newSolver. If the system size is not equal to \(0\), it also invokes setSize() on newSolver, printing a warning and returning the returned value if this method returns a number less than \(0\). Finally it returns the result of invoking the LinearSOE classes setSolver() method.

A method which returns the current size of the system.

The size of the system is determined by looking at the adjacency ID of each Vertex in the Graph object G. This is done by first setting ku equal to \(0\) and then checking for each Vertex in G, whether any of the vertex tags in the Vertices adjacency ID results in ku being increased. Knowing ku and the size of the system (the number of Vertices in G, a check to see if the previously allocated 1d arrays for \(A\), \(x\) and \(b\) are large enough. If the memory portions allocated for the 1d arrays are not big enough, the old space is returned to the heap and new space is allocated from the heap. Prints a warning message if not enough memory is available on the heap for the 1d arrays and returns a \(-1\). If memory is available, the components of the arrays are zeroed and \(A\) is marked as being unfactored. If the system size has increased, new Vector objects for \(x\) and \(b\) using the (double *,int) Vector constructor are created. Finally, the result of invoking setSize() on the associated Solver object is returned.

First tests that loc and M are of compatible sizes; if not a warning message is printed and a \(-1\) is returned. The LinearSOE object then 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. \(a_{loc(i),loc(j)} += fact * M(i,j)\). If the location specified is outside the range, i.e. \((-1,-1)\) the corresponding entry in M is not added to \(A\). If fact is equal to \(0.0\) or \(1.0\), more efficient steps are performed. Returns \(0\).

int addB(const Vector & V, const ID & loc, double fact = 1.0) =0;

First tests that loc and V are of compatible sizes; if not a warning message is printed and a \(-1\) is returned. The LinearSOE object then 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. \(b_{loc(i)} += fact * V(i)\). If a location specified is outside the range, e.g. \(-1\), the corresponding entry in V is not added to \(b\). If fact is equal to \(0.0\), \(1.0\) or \(-1.0\), more efficient steps are performed. Returns \(0\).

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

First tests that V and the size of the system are of compatible sizes; if not a warning message is printed and a \(-1\) is returned. The LinearSOE object then sets the vector b to be fact times the Vector V. If fact is equal to \(0.0\), \(1.0\) or \(-1.0\), more efficient steps are performed. Returns \(0\).

void zeroA(void) =0;

Zeros the entries in the 1d array for \(A\) and marks the system as not having been factored.

void zeroB(void) =0;

Zeros the entries in the 1d array for \(b\).

const Vector &getX(void) = 0;

Returns the Vector object created for \(x\).

const Vector &getB(void) = 0;

Returns the Vector object created for \(b\).

double normRHS(void) =0;

Returns the 2-norm of the vector \(x\).

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

If loc is within the range of \(x\), sets \(x(loc) = value\).

Returns \(0\). The object does not send any data or connectivity information as this is not needed in the finite element design.

Returns \(0\). The object does not receive any data or connectivity information as this is not needed in the finite element design.