1. 1. 6 Algebraic Methods

In order to solve algebraic problems, for instance a linear algebraic equation system or an eigenvalue problem, special algebraic methods have to be used. For the solution of discrete problems, a large variety of such solution methods are available. One such software package is Trilinos [4], which covers many different methods and offers high flexibility of solution mechanisms as long as Trilinos internal methods are used. Perhaps the most annoying fact related to these environments is that all algebraic environments use different software interfaces and a large effort has to be spent on making the single environments compatible with each other.

For this reason it is impossible to separate the discrete algebraic problem from the algebraic methods used. As some simulation environments even combine discretization schemes with algebraic methods, it is nearly impossible to separate the discretization, the data storage of the discrete problem, and the algebraic methods.

In the layered model the origin of the mathematical problem does not have any impact on the method used. Instead, only the discrete problem has to be taken into account.