Friday, 25 November 2016, 3.30 p.m. (sharp), Prof. Franco Brezzi, (IMATI CNR Pavia), at the conference room "Luisella
Sironi U4-08", Piazza della Scienza, Università degli Studi di Milano-Bicocca, will give the opening lecture of the PhD in Mathematics (Pavia - Milano Bicocca - INdAM):
RECENT DEVELOPMENTS IN SCIENTIFIC COMPUTING.
After a short presentation of Scientific Computing, of its problems
and its typical results, we recall some fundamental equations ruling
the mathematical representation of most “real-life” problems. Going
more into details, we consider their “Variational Formulation”, and
the Ritz-Galerkin approach for the computation of an approximate
solution. Further into details, we present the approximations based on
a decomposition of the computational domain into “elements” (that is,
tiny pieces of the domain: more and smaller pieces for a more accurate
result). Among them we concentrate on the approximations based on
decompositions made of elements of more complicated geometries,
instead of the commonly used simplices and boxes (in two dimensions:
triangles and quadrilaterals). We discuss pros and cons of these
choices, the theoretical and practical difficulties, and the
expectations that made the subject so popular in the very last years.
At the final level of detail, we present the Virtual Element Method,
introduced by the Pavia-Milano team and now quickly spreading around
the world (to our great satisfaction!).