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Dettaglio Insegnamento Contesto Anno Accademico 2021/2022 Corso di Studi Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering Anno di Corso 1 Scheda Insegnamento Codice Identificativo 056325 Denominazione Insegnamento HIGH-ORDER DISCRETIZATION METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS Tipo Insegnamento MONODISCIPLINARE Crediti Formativi Universitari (CFU) 5.0 Programma sintetico The course aims at presenting advanced high order Galerkin methods for the approximation of Partial Differential Equations (PDEs), by focusing in particular on high-‐order polygonal Discontinuous Galerkin (PolyDG) methods and Isogeometric Analysis, and discussing their applications to Computational Mechanics problems. Part I. High-‐order PolyDG methods. a) Challenges of extending the Finite Element paradigm to computational grids made of arbitrarily shaped polygonal/polyhedral grids. b) The theoretical setting: trace/inverse estimates and hp-‐polynomial approximation bounds on polytopic elements. c) The PolyDG method: introduction, features and theoretical analysis. d) Computational challenges: construction of the discrete space, numerical evaluation of integrals, and development of efficient solvers. e) Hints on other families of high-‐order finite element methods on polygonal and polyhedral grids: Virtual Elements. f) Application to acoustic and elastic wave propagation problems. Part II. Isogeometric Analysis. a) Geometric representations by NURBS and NURBS function spaces. b) The isogeometric concept and NURBS-‐based IGA in the framework of the Galerkin method. c) Approximation properties and algebraic aspects. d) Numerical solution of PDEs at the calculator using MATLAB. e) IGA for nonlinear and time dependent problems; solution of high order and surface PDEs. f) Application to fluid dynamics problems and phase field models. Part III. Machine and Deep Learning for Computational Mechanics. a) Machine and Deep learning for physics-‐driven simulation. b) Improving numerical solvers by Machine and Deep learning algorithms. Settori Scientifico Disciplinari (SSD) -- Dettaglio Scaglione Docente Programma dettagliato Da (compreso) A (escluso) A ZZZZ Antonietti Paola Francesca, Dede' Luca

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12/08/2022