Inglese

English

An introduction to numerical methods which are used in solving problems in physics, including solutions of differential equations, matrix operations and eigenvalue problems, interpolation and numerical integration, modeling of data and Monte Carlo methods.

General reference books:
Computational Physics - Problem Solving with Computers
R. H. Landau, M. J. Páez, and C. C. Bordeianu
WILEY

Computational Physics
P.O.J. Scherer
Springer

Computational Physics – Lecture Notes Fall 2015
M. Hjorth-Jensen
University of Oslo

The student will develop a familiarity with some of the most used algorithms in Physics. Several examples of problems in physics will be used in order to demonstrate various numerical methods. The examples span over several fields.
The course is project based and through the various projects, normally five, the participants will be exposed to fundamental research problems in these fields. The students will learn to develop and structure codes for studying these systems, develop a critical understanding of the capabilities and limits of the various numerical methods, get acquainted with supercomputing facilities and parallel computing and learn to handle scientific projects.

The basic knowledge of one of the following computing languages: C/C++, Python, Fortran

The course is offered for one semester and comprises 40 hours of lectures, in addition to 36 hours of laboratory exercises aided by the use of a computer. The course will also include five projects that students will receive feedback on.
Attendance is not compulsory but strongly recommended.

Specific knowledge will be verified in the oral exams with questions starting from the projects realized and presented by the students.

1) Errors and Uncertainties in Computations
2) Numerical differentiation and interpolation .
3) Non-linear Equations
4) Numerical Integration
5) Linear algebra and eigenvalue problems
• Gaussian elimination and LU decomposition
• How to solve linear equations
• How to obtain the inverse and the determinant of a real symmetric matrix
• Iterative solvers
• Cubic spline
• Tridiagonal matrix decomposition
• Householder’s tridiagonalization technique and finding eigenvalues basedon this
• Jacobi’s method for finding eigenvalues
6) Ordinary differential equations
• Euler’s method and improved Euler’s method, truncation errors
• Runge Kutta methods, 2nd and 4th order, truncation errors
• Verlet algoritm
7) Partial differential equations
• Diffusion equation
• Laplace’s and Poisson’s Equations
• Wave Equation in two Dimensions
8) Monte Carlo methods in physics
• Random walks and Markov chains
• Metropolis algorithm
• Applications to statistical physics systems
• Monte Carlo sampling