CAAM 652 · Topics in numerical PDEs

Spring 2018 · Rice University

LECTURE: Duncan Hall 3076, 10-11am Wednesdays
INSTRUCTOR: Jesse Chan (
Duncan Hall 3023, (713) 348-6113
OFFICE HOURS: Wednesdays 11-12am or by appointment.
PREREQUISITE: Background in numerical analysis, linear algebra, and MATLAB programming.
GRADING: Projects and presentations.
TEXTS: Nodal Discontinuous Galerkin Methods: Theory and Application by Jan Hesthaven and Tim Warburton.
RECOMMENDED TEXTS Implementing spectral methods for partial differential equations: Algorithms for scientists and engineers by David Kopriva
Mathematical aspects of discontinuous Galerkin methods by Daniele Di Pietro and Alexandre Ern
Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation by Beatrice Riviere.
MATLAB Guide by Desmond J. Higham and Nicholas J. Higham, 2nd ed., SIAM, 2005
Lecture schedule: Lecture 13 (4/18): Final project presentations.
Lecture 12 (4/11): variable coefficient advection problems, curved meshes.
Lecture 11 (4/4): curvilinear meshes, stability of the skew-symmetric matrix formulation. Code for curved meshes curved meshes.
Lecture 10 (3/28): curvilinear meshes, cont.
Lecture 9 (3/14): curvilinear meshes. Wave code for heterogeneous media.
Lecture 8 (3/7): Cancelled (instructor out of town).
Lecture 7 (2/28): Two-dimensional acoustics, boundary conditions, second order formulations. Variable coefficients.
Lecture 6 (2/21): Two-dimensional acoustic wave equation. wave2d_demo.m
Lecture 5 (2/14): Two-dimensional problems. 2D DG codes
Lecture 4 (2/7): Convergence, symmetric hyperbolic systems, the acoustic wave equation. Advection convergence code and acoustic wave equation demo.
Lecture 3 (1/31): Energy stability, upwind/dissipative/penalty numerical fluxes, periodic boundary conditions. Modified advection code: advec1D_periodic.m
Lecture 2 (1/24): Nodal bases, 1D advection code (for download here). To run code, unzip and "cd" into directory and run advec1D.m.
Lecture cancelled (1/17): bad weather.
Lecture 1 (1/10): Lecture 1: class overview, time-dependent hyperbolic PDEs, high order DG methods for 1D advection.
Homeworks: Homework 1 (due Feb 21).
Homework 2 (TBA).

Any student with a disability requiring accommodation in this course is encouraged
to contact the instructor during the first week of class, and also to contact
Disability Support Services in the Ley Student Center.