4.2 Operations with sparse matrices

A lot of engineering applications are solved by means of FEM, FDM or FVM. These methods combine local approximations of the pde to one huge system of equations. The matrix of that system of equations is sparse (local effects), i.e., each row of the matrix stores only a few non-zero elements - most of the elements are 0. If one thinks of the matrix as a table and fills all places of non-zero elements then we get the pattern of the matrix. Depending on the properties of that pattern we call a matrix structured or unstructured. The length of the interval from the diagonal element to the last non-zero element of a row/column is called band/profile.
In the following, sparse matrices are always thought as unstructured, i.e., we will not take advantage of special structured sparse matrices.