This subject provides an introduction to modeling and simulation. Scientists and engineers have long used models to better understand the system they study, for analysis and quantification, performance prediction and design. This subject will provide you with the relevant theoretical and numerical tools that are necessary to build models of complex physical phenomena and to simulate their behavior using computers. The physical system can be a collection of electrons and nuclei/core shells, atoms, molecules, structural elements, grains, or a continuum medium. The lectures will provide an exposure to areas of application, based on the scientific exploitation of the power of computation.


The subject will be taught by three instructors, each covering approximately one third of the subject. Each lecturer will teach a consecutive set of 7 or 8 lectures (part I, Lec #2-9, Raúl Radovitzky, continuum methods; part II, Lec #10-18, Markus Buehler, atomistic and molecular methods; part III, Lec #19-27, Timo Thonhauser, quantum mechanics). The three parts are not independent. Instead, they will base on one another and are integrated.


Detailed lecture notes will be distributed for each lecture, usually covering "theoretical" aspects (derivations, concepts etc.) in more detail or in a different manner than done during class. The subject content is defined by the material presented in lectures, recitations and reading assignments, so regular attendance is advisable.


There will be one recitation each week on Monday. Recitations will illustrate and/or expand concepts presented in lectures by working through numerical example problems, or by showing how to use the simulation code. Material covered in recitations is often related to the problem sets and is considered part of the subject content, so regular attendance is advisable.

Lecture Notes

Each instructor will distribute his own lecture notes and details about the format will be announced at the beginning of each part.


We will assign a total of 6-8 problem sets. Each problem set is designed to build upon the material covered in the preceding lectures and recitations. Some of the homework assignments will be prepared by teams consisting of three students. In this case, each team will hand in one solution, with the names of team members who contributed as indicated on the coverpage. The problem sets worked out by a team of students typically cover more complex problem that require numerical simulation.

Due dates for problem sets are firm and homework assignments will be corrected and handed back (with solutions) no later than two lectures after the due date. You may use any material to complete the solution. However, it is important that you properly reference the material used (e.g. books, Web site, journal articles).


There will be two in-class 1.5 hour exams. There will also be a 1.5 hour scheduled final exam. All exams are open-book, but bear in mind to develop an appropriate exam strategy. The exams typically cover theoretical material and important concepts.

Grading Scheme

The final grade will be based on:

Homework 40%
In-class exams 40%
Final exam 20%