File decompression software, such as Winzip® or StuffIt®, is required to open the .zip files in this section. MATLAB® software is required to run the .m files in this section.
Project Overview
18.086 has two main parts, Initial Value Problems and Solving Large Linear Systems. The lectures will present the underlying theory and many of the key algorithms for these important problems.
A project on Part 1 is due the day after spring break. A project on Part 2 is due before the end of the semester, with a brief oral report to the class. The scope of the projects will be discussed in class (see also the sample project below).
Project 1 compares numerical methods with analytical methods for the numerical solution of initial value problems governed by partial differential equations. This is the lecture topic in the first half of the course. The key questions are stability, accuracy, and computational speed.
Project 2 will study one or more algorithms for the solution of large linear systems. The week-by-week reading list indicates many of the important algorithms: elimination with reordering, iterations with preconditioning, multigrid methods, and Krylov methods. The goal is to share the experience of applying these algorithms and evaluating their performance.
Our whole purpose is that the projects, and the oral reports on that work, provide an ideal opportunity to try different methods and to present the results in a report and to a relaxed and supportive class.
Sample Project
This sample project is courtesy of Joseph Kovac, a student in the class, and is used with permission. The project implements a 2D multigrid solver for Laplace's and Poisson's equation.
Overview of Multi-grid Project (PDF)
Project File: The Fundamentals and Advantages of Multigrid Techniques (PDF)
Matlab_Files_for_Project (ZIP) (The ZIP file contains: 10 .m files.)