Math 116: Boundary methods and wave asymptotics

Alex Barnett, Winter 2006, Tu and Th 2-3:50pm (2A), Bradley 103

2D wave scattering from an obstacle

My goal is for you to learn the theory and practice of boundary-based numerical methods for partial differential equations. I expect to focus on Helmholtz's equation, which describes linear waves (acoustics, electromagnetics, optics, etc) in the frequency domain, and is incredibly useful in engineering/physics. Boundary methods are easier to code than Finite Elements, and are very efficient especially at short wavelengths. The course will split roughly into wave scattering (first part) and eigenmodes of the Laplacian (second part). You will use tools you build to explore some wave asymptotics such as WKB, ray methods, and quantum chaos, or spectral geometry.

Jump to... Schedule, Resources, or Flyer, tentative Syllabus, Class Homework/Projects

SCHEDULE, READINGS and HOMEWORKS

Office hours: M 3-4pm, W 3-5pm

Lecture outline .............. download in PDF: Lectures 2-10, Lectures 12-18 (note there's no Lec. 11)

Optional topics/projects:see list.

Assessment: (Note you may work in groups of 2-3)

RESOURCES

PDEs / Analysis

Quantum chaos / semiclassical analysis

Numerical methods

MATLAB

Web authoring for homework submission

CLASS HOMEWORK and PROJECTS