The basic idea for efficient parallizing finite element codes is a data structure that avoids additional communication costs for performing the four main steps of a f.e. computation: pre processing - gererate/assembly - solve - post processing. We show that the typical DD-data-splitting follows from the analytical definition of the method (by bilinear functionals) and guarantees an efficient f.e. run on parallel computers even without use of the typical DD-techniques. Based on the DD-data-splitting we prove that all steps of a f.e. run behave optimal with respect to communication and arithmetic if for the preconditioner used within the CG-solver the folowing 3 facts hold:

• 1. optimal condition number of the preconditioned matrix, so #IT = O(1).
• 2. optimal artihmetical effort (O(N)).
• 3. efficient parallel run (1 data exchange per call)

This is true for all the modern hierarchical techniques if they are combined with DD-ideas.

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