Computational Engineering       (IV terms)

1^st Term courses – compulsory              hours               ECTS         exam

C1       Continuum Mechanics                   30                          3                   90

C2       The Finite Element Method          30+30                    6                 120

C3       Fracture Mechanics                        30                          3                  90

C4      Programming in Engineering        30+30                    6

C5       Numerical Methods                         30                          3

C6       Theory of Plasticity                         30                           3                 90

C7       Dynamics of Structure                    30+30                     6               120

                                                                       300                        30

C5     Numerical Methods

Lecturer: Đ. Đorđević

Course Contents

Introduction to numerical methods used for analyzing mechanical systems.

General principles of numerical calculations, machine numbers, error estimation, numerical stability.

Linear algebra: Cholesky-decomposition, Gaussian elimination, LU-decomposition, QR-decomposition, iterative methods, least squares problems. Iterative solution of large systems of linear equations (conjugate gradients, the multigrid idea).

Standard methods for ordinary differential equations (single-step and multistep methods, explicit and implicit methods, stiffness);

Basic discretization schemes for partial differential equations (finite differences vs. finite elements);

Grid generation (structured grids, unstructured grids, varying geometries). 

Eigenvalue problem, computation of eigenvectors.

Programming numerical methods in Fortran/Mathematica (MatLab)/Pascal/C++/Java (Free choice of language).

The lecture is supplemented by computer exercises