Recent developments in scientific computing. Lezione inaugurale del XXXII ciclo di dottorato in Matematica, Pavia-Milano Bicocca-INdAM.
Prof. Franco Brezzi, IMATI Pavia
Aula Luisella Sironi U4-08, Piazza della Scienza, Università degli Studi di Milano-Bicocca - Friday, November 25, 2016 h.15:30
Abstract. 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!).
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