260003 VO Computational Physics I: Basics (2018W)

In one of the major paradigm shifts in physics in the past half century, Computational Physics, the application of purely computer-based methods to the solution of physical problems, has established itself as an independent "third methodology", in addition to the conventional approaches, Experimental and Theoretical Physics. Like its sister disciplines, Computational Physics is a method, rather than a specific subfield of physics, and thus is not limited to any particular area: Applications range from tests of approximate theoretical methods (by providing numerically exact results for well-chosen model systems) to replacement/extension of laboratory experiments to extreme space and time scales or physical conditions. Thanks to the continuous increase in computer power, more and more sophisticated physical models may be simulated in detail and their properties investigated at will.
The first part of this two-semester course, which aims at depth rather than breadth, offers an introduction to the following topics:
(Fast) Fourier Transform
Finite Difference Equations
Partial Differential Equations
Solution of Large Systems of Equations
Finite Elements
Monte Carlo Methods.
Part two, to be held in the spring term, is devoted to simulation techniques. Since the emphasis of the course is on providing practical knowledge, all algorithms are explained in detail and illustrated by sample programs, so that students may readily extend them or write their own code if they wish to. For the same reason, the accompanying problem class is considered an integral part of the course.
Computational Physics I and II are suggested as a basis for the Computational Physics Laboratory.
Prerequisites: Scientific Computing or equivalent, introductory calculus and linear algebra, good programming skills.