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