Simon Fraser University
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Course Outlines

Fall 2021 - APMA 922 G100

Numerical Solution of Partial Differential Equations (4)

Class Number: 1937

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 8 – Dec 7, 2021: Wed, 10:30 a.m.–12:20 p.m.
    Burnaby

    Sep 8 – Dec 7, 2021: Fri, 10:30 a.m.–12:20 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Analysis and application of numerical methods for solving partial differential equations. Potential topics include finite difference methods, spectral methods, finite element methods, and multi-level/multi-grid methods.

COURSE DETAILS:

This is an introductory graduate-level overview of the numerical analysis of ordinary and partial differential equations. We will begin the term with a review of Runge-Kutta and multi-step methods for IVP. We then study 3 important discretization schemes in the context of elliptic problems: finite difference, finite element and spectral methods. We finally study some methods for time-dependent parabolic and hyperbolic PDE.  Both theoretical and computational aspects will be discussed.

Additional workshops on 'software carpentry',  technical writing, research methods and ethics may be provided.

Grading

  • Four homework sets (equally weighted) 50%
  • Term project (Grade will be based on a 'midway' presentation (1/5) and final report) 30%
  • Final (combination of take-home and final) 20%

REQUIREMENTS:

Prerequisite: A prior course in undergraduate numerical analysis and PDE is strongly recommended, as is some familiarity with programming in Matlab, Python, C++ or Fortran.

Materials

RECOMMENDED READING:

Material will also be drawn from other books, several of which will be available in the library reserves.  In particular, significant parts of the course will largely be based on chapters from the following texts:

- Lloyd N. Trefethen, “Spectral Methods in MATLAB”, SIAM

- Arieh Iserles, “A First Course in the Numerical Analysis of Differential Equations” (2nd ed.), Cambridge University Press

- Randall J. LeVeque, “Finite Difference Methods for Ordinary and Partial Differential Equations”, SIAM   (we will cover most of this book)

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

TEACHING AT SFU IN FALL 2021

Teaching at SFU in fall 2021 will involve primarily in-person instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place.  Whether your course will be in-person or through remote methods will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the fall 2021 term.