Geometrically defined discrete Hodge operator for polyhedral cell complexes

26 maggio 2016
Versione stampabile

Luogo:  Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
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. Physical variables are defined as fluxes or circulations on oriented geometric elements of a pair of dual interlocked cell complexes, while physical laws are expressed in a metric-free fashion with incidence matrices. The metric and the material information are encoded in the discrete counterpart of the constitutive laws of materials, also referred to as material matrices or discrete Hodge operators. The stability and consistency of the method is guaranteed by precise properties (symmetry, positive definiteness, geometric consistency) that material matrices have to fulfill. The main advantage of this approach is that material matrices, even for arbitrary star-shaped polyhedral elements, can be geometrically defined, by simple closed-form expressions, in terms of the geometric elements of the primal and dual grids.
This is the third and last seminar of a short series on "Computational Homology and  Applications in Electromagnetism" that Prof. Ruben Specogna is holding during his research stay at the Department of Mathematics of the University of Trento.

Referenti: Ana Maria Alonso Rodriguez and Riccardo Ghiloni