Transform methods—what can they contribute to (computational) dynamics?
Review articleOpen access
Abstract:

AbstractIn comparison to FEM or to time step procedures integral transform methods (ITM) have a very restricted domain for application. Under the condition however, that they can be used at all, they lead to a deeper understanding of the physical nature of the problem, they may allow to ameliorate existing computational techniques and they can be used to develop new approaches “on their own right”.The paper shows examples for illustration. After a short introduction of different well known transform techniques and respective operations in the original and the transformed domains, it deals with signal processing: In a first example different possibilities for the interpretation of time dependent signals in the original domain, in a Fourier or in a wavelet transformed domain are compared. After that the usefulness of ITM is illustrated in regard of reliability questions. It is shown that typical characteristics known for time depending signals exist in a comparable, however more general, manner also in regard of spatial relations for problems of half space dynamics. ITM does not only allow interpretations but –– e.g. for the half space dynamics –– it leads also to very efficient solution techniques, particularly for moving loads. It can be used also for the development of auxiliary techniques for FEM or BEM approaches. Finally also in stochastic dynamics it is applicable with great advantages.

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