Courses:

Introduction to Modeling and Simulation >> Content Detail



Syllabus



Syllabus

This page includes a calendar of lecture topics.



Course Overview




Why Modeling and Simulation (Mod/Sim)?


Modeling is a fundamental and quantitative way to understand complex systems and phenomena. Simulation is complementary to the traditional approaches of theory and experiment. Together, they (Mod/Sim) make up an approach that can deal with a wide range of physical problems, and at the same time exploit the power of large-scale computing. This paradigm is becoming increasingly widespread in a number of disciplines in science and technology, giving rise to active fields of studies such as computational physics, chemistry, mechanics, and biology, to name just a few. Through modeling and simulation one can readily cross over from one discipline to another, which is to say that the basic concepts and techniques one learns are applicable to problems seemingly very different at the surface.



Why Teach Mod/Sim at the Undergraduate Level?


Mod/Sim studies are mostly being carried out at the graduate and postgraduate levels. But there is no reason why the undergraduates cannot participate in a meaningful way and benefit from the physical insights and technical know-how that these activities can provide. We believe that engaging the undergrads broadly across the Institute through a team of multidisciplinary faculty, as instructors and mentors, can succeed at MIT. The students would gain a broader academic exposure than what they would normally encounter within their own departments. Because this is a new way of teaching and networking among the faculty, everyone who participates can contribute to the success of this experiment, and in turn learn a great deal about studying across traditional boundaries. Intro Mod Sim is receiving considerable support from the Dean of Engineering and has the blessings of the department heads of all the participating units. In many ways, a subject like this is an experiment in educational innovation. We hope the students will get into the spirit and work with us to make it a worthwhile experience for all concerned.



What are the aims of Mod/Sim?


We expect the students will gain a significant appreciation of the broad use of modeling in several fields of science and engineering, acquire hands-on experience with simulation, ranging from basic use of computers to advanced techniques, and develop communication skills by working with practicing professionals. Additional benefits could come from further interactions with the faculty afterwards, such as mentoring, UROPs, thesis supervision, etc.



Prerequisites


18.03



Textbook


There is no required textbook for the course. Class lectures and tutorial discussions will be supported by various readings that will be assigned from various books and journals.



Grading



activitiespercentages
Problem Sets40%
Quiz 120%
Quiz 220%
Term Project20%



Course Structure


Lectures are grouped into 3 parts: Continuum Methods (CM), Particle Methods (PM), and Quantum Methods (QM).

CM Faculty: Beers, Powell, Radovitzky, Ulm
PM Faculty: Bazant, Buehler, Hadjiconstantinou, Mirny
QM Faculty: Yip



Calendar



lec #topicsinstructorskey dates
Introduction
1Overview - Aspirations of Modeling and Simulation, LogisticsYip
2Diffusion at the Particle LevelYip
3From Random Walks to Continuum DiffusionBazant
Part 1: Continuum Methods (CM)
4Conservation LawsRosales
5Constitutive RelationsRosales
6Discrete/Continuum IssuesRosales
7Finite Difference MethodsPowell
8Weighted Residual Finite Element MethodsPowell
9Heat ConductionPowell
10Materials Processing ApplicationsPowellProblem set 1 due
11Variational Finite Element MethodsUlm
12Elasticity Concepts and ProblemsUlm
13Applications in Structural MechanicsUlmProblem set 2 due
14Equations of Fluids DynamicsBeers
15Problems in Incompressible FlowBeers
16Fluid-Structure InteractionsRadovitzky
17Multiscale Problems involving Continuum MechanicsRadovitzky
18CM ReviewProblem set 3 due
19Quiz 1
Part 2: Particle Methods (PM)
20Monte Carlo Methods I: PercolationBazant
21Monte Carlo Methods II: Fractal PatternsBazant
22Monte Carlo Methods III: Random PackingsBazant
23Basic Monte CarloMirny
24Monte Carlo Modeling of Physical SystemsMirnyProblem set 4 due
25Optimization by MC and Genetic ProgrammingMirny
26Stochastic Simulations in BiologyMirny
27Basic Classical Molecular DynamicsBuehler
28Introduction to Interatomic PotentialsBuehlerProblem set 5 due
29Modeling of MetalsBuehler
30Reactive PotentialsBuehler
31MD Simulation of FluidsHadjiconstantinou
32Dilute Gases and Direct Simulation Monte Carlo (DSMC) IHadjiconstantinou
33Dilute Gases and DSMC IIHadjiconstantinouProblem set 6 due
34PM Review
35Quiz 2
Part 3: Quantum Methods (QM)
36Quantum Calculations in Modeling and SimulationYip
37Introduction - Hartree-Fock and Density Function Theory MethodsYip
Final Project PresentationsFinal paper due two days after the final project presentations

 








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