Before solving the linear system we can eliminate equations which degrade
the condition of our equation system. Such equations might result from
boundary or material interface conditions. Therefore, we split the system
matrix into the following structure
where denotes the so-called boundary matrix,
the row
transformation matrix and
gives the interior (segment) matrix. The
row transformation matrix is used to specify whether solution variables are
eliminated from the system or modified during transformation by the segment
matrix
and added to the global system matrix
. We apply the
same transformation to the right-hand-side and get
To assemble the whole system matrix, the following steps have to be done:
For efficient memory management of the system matrix we use the modified compressed sparse row (MCSR) matrix format [Saa90]. Two arrays are used for the storage of large matrices. One array contains the data and the other the pointers to the beginning and ending elements of the matrix rows.