Course title:

Monte Carlo Methods

Primary programme:

Fizikus mérnök BSc

ECTS credits:

4

Course type:

elective

Number of lectures per week:

2

Number of practices per week:

1

Number of laboratory exercises per week:

0

Further knowledge transfer methods:

Grading:

Examination

Special grading methods:

homeworks, programming

Semester:

5

Prerequisites:

Probability Theory

Responsible lecturer:

Dr. Dávid Légrády, associate professor, PhD

Lecturers and instructors:

Course description:

Random number generation. Experimental and algorithmic methods. Generation of uniformly distributed pseudorandom numbers on computers. Multiplicative, congruential and other algoriths. Statistical tests of random number series. Randomness, indeoendency. Chi-square test. One- and two-dimensional frequency tests, digit test, gap test, poker test, run test, test of subseries. Sampling discrete random variables by Monte Carlo method. Techniques for acceleration of sampling. Sampling continuous random variables. Methods for sampling one-dimensional density functions. Inverse cumulative function method, acceptance-rejection algorithm, composition method, table look-up techniques. Application of Monte Carlo methods for particle transport simulation. Methods for choosing uniformly a random point from the surface of a sphere. Sphere slicing, in-cube out-of-sphere rejection and Marsaglia’s algorithm. Free flight sampling in homogeneous, regionally homogeneous and inhomogeneous media. Woodcock’s method. Analog and non-analog simulation of particle transport. Variance reduction techniques. Statistical weight, implicit capture, spatial importance, biasing, splitting, Russian roulette. Monte Carlo integration. Interpolation of multivariate functions using Monte Carlo method.

Reading materials:

Alireza Haghighat: Monte Carlo Methods for Particle Transport; CRC Press, 2014, ISBN 9781466592537
Stephen A. Dupree and Stanley K. Fraley: A Monte Carlo Primer - A Practical Approach to Radiation Transport; Kluwer Academic/Plenum Publishers, New York, 2002
I. Lux, L. Koblinger: Monte Carlo Particle Transport Methods: Neutron and Photon CalculationsCRC Press, Boca Raton (1991);

List of competences:

Please find the detailed list, as quoted from the Hungarian training and outcome requirements of the Physicist Engineer program, in the Hungarian version of the course description.