Abstract
The formulation of different physical laws, in terms of algebraic operators, was presented in the previous chapters. From an analysis of the Tonti diagrams, it emerges that they are not related to a specific physical phenomenon, but they can be considered as a common framework for several theories, that is, a scaffolding into which the variables that arise from different physics are rigorously placed. From this general consideration, it is natural to think it would be possible to exploit the underlying structure provided by the Tonti diagrams and apply this to develop a multiphysics environment for numerical techniques.
The aim of this chapter is to show that the Tonti diagrams are a natural underlying structure that can be used to develop multiphysics numerical formulations. When the same discretization is shared by different problems, topological operators can only be built once and used to assemble the stiffness matrices that correspond to different problems and the coupling terms [1]
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Alotto, P., Freschi, F., Repetto, M., Rosso, C. (2013). Multiphysics Problems. In: The Cell Method for Electrical Engineering and Multiphysics Problems. Lecture Notes in Electrical Engineering, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36101-2_5
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DOI: https://doi.org/10.1007/978-3-642-36101-2_5
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