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### Renumbering the nodes to decrease the profile

The profile of a matrix is obtained by marking in each column the uppermost nonzero entry. This way one gets a kind of skyscraper picture. Reducing the profile as much as possible by renumbering the nodes usually speeds up the solution of the equation system. This is done using an algorithm published by Sloan ([60]) in subroutine renumber.f. It not only takes the topology of the elements into account, it can also take care of additional equations introduced by *EQUATION or *MPC statements. Although it is primarily effective when using a profile solver [68], it seems to have a beneficial effect on the solver time of SPOOLES as well. Therefore, it is always activated.