A concept of separated numerical formulations for the solution and evaluation of complex field problems

Abstract

Nowadays, a variety of numerical methods and numerical formulations exits to solve complex or coupled field problems in three dimensions. Most of them are generally applicable to nearly arbitrary kind of field problems. On the other hand, some highly optimized methods are available, which are predestined for the solution of a specific kind of problem. Especially in the case of weakly coupled multiphysics problems, a mixture of several numerical methods is very advantages to benefit from different properties of numerical methods for diverse physical sub-problems. A very promising approach for a flexible coordination of the related solution process is the application of software agents. Then, the results of one sub-problem are converted into boundary values or volume source distributions for another sub-problem and software agents choose solution methods independently for each subproblem. Furthermore, two main aspects have to be considered in applications of numerical methods. First, the solution of a boundary value problem should be computed efficiently and second, the solution is evaluated for visualization and interpretation of obtained results. In practice, it is difficult to choose a single appropriate method, which is well suited both for the solution of a problem and its evaluation, since the demands differ in both cases. Here, a concept is presented to apply various numerical methods successfully to the solution and evaluation of complex field problems. Attention is mainly turned on the integration of boundary element methods into the concept of mixed numerical formulations.