Physics-preserving schemes on polyhedral meshes for elliptic problems

Luogo:  Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula 7
Ore 14.30

Relatore:

• Ruben Specogna (Università di Udine, Dip. Politecnico di Ingegneria ed Architettura)

Abstract:
In the recent years, reformulating the mathematical description of physical laws in an algebraic form using tools from algebraic topology gained popularity in computational physics and numerical analysis. Physical variables are modeled as cochains with real or complex coefficients while physical laws are exactly expressed in a metric-free fashion with the coboundary operator. The metric and the material information are encoded in the discrete counterpart of the constitutive material laws, that may be interpreted as discrete Hodge star operators. The discrete Hodge star operators, called also material matrices, can be explicitly constructed thanks to dualities arising when two dual interlocked cell complexes are introduced. Moreover, such construction is purely geometric. Similarities and differences with respect to Finite Elements will be emphasized.

This is the second one of a short series of seminars on "Computational Homology and  Applications in Electromagnetism" that Prof. Ruben Specogna will hold during his research stay at the Department of Mathematics of the University of Trento.

Referente: Ana Maria Alonso Rodriguez and Riccardo Ghiloni