Meotdi Numerici

Meotdi Numerici INTERNATIONAL MASTER COURSE

IN CIVIL ENGINEERING

I Semester, Credits: 12 (6+6)

Instructors: Prof. Fiorella Sgallari, Dr. Alessandro Lanza

Prof. Fabiana Zama

Introduction:

The course is designed to introduce the principles of numerical techniques to civil engineering students.

This course will consist of two parts. During the first part of the course, numerical analysis topics considered are:

accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.

Included are numerical methods for solving engineering problems that entail roots of functions, curve-fitting,

interpolation, numerical differentiation and integration, and numerical linear algebra.

During the second part, the course will offers an advanced introduction on numerical methods for solving differential equations.

Topics include the application of finite difference techniques and finite elements to parabolic, hyperbolic and elliptic partial differential equations (PDEs); convergence and error analysis, development and application of computer programs to case studies derived from civil engineering practices.

In addition to discussing established solution techniques, open problems will also be presented.

Students should still come to appreciate many state-of-the-art techniques and recognize when to consider applying them.

Course Outline:

Numerical Mehtods I

Key Idea: accuracy, precision, truncation and round-off errors, condition numbers,

operation counts, convergence and stability.

Numerical Linear Algebra: direct and iterative methods for linear systems.
Solution to single equations and multiple non-linear equations.
Interpolation and approximation: interpolating polynomials, cubic splines, least-square fitting.
Numerical differentiation and integration: Newton-Cotes quadrature formulas, Gaussian quadrature.
Classification of PDEs: elliptic, parabolic and hyperbolic equations.
Finite difference methods. Stability, consistency, and convergence theory.

Numerical Mehtods II

Finite Elements Methods
(formulation of the finite element method in 1-D and 2-D continuum, basic 1-D and 2-D finite elements,
modeling and programming aspects of the finite element method).