Math 679-002: Wavelets, Fast Algorithms and PDEs

Course Announcement



 
TR 11:10-12:25pm

Wavelets, Fast Algorithms
and PDEs
Math 679-002
214 Ayres Hall




INSTRUCTOR:

PHONE, E-MAIL:

COURSE WEB PAGE:
TEXTBOOK:
Dr. Petr Plechac, 313 Ayres Hall  & JICS-ORNL
Dr. George Fann, Oak Ridge National Laboratory
974-4329, plechac@math.utk.edu,
gif@ornl.gov
http://www.math.utk.edu/~plechac/M679
TBA


For further details please contact the course instructors by e-mail.

Description:
This course introduces and applies fast multiscale and multiresolution methods (e.g., fast multipole methods, wavelets, local Fourier basis, etc) to solve problems which are common in science and engineering. These techniques are a part of real analysis based algorithms. Fast methods have made significant impact on recent developments in scientific computing, signal and image processing as well as mathematical analysis. Examples include the JPEG2000 standard, quantum chemistry and physics, electromagnetic scattering and magnetic resonance imaging.

We will emphasize practical applications and algorithms with a connection between the continuum and discrete approximation a nd compression of functions, operators and data. Application of fast algorithms for data analysis, solution of partial differential equations, and efficient approximation of functions and operators will be explained. The PDE aspects of the course will be explained and demonstrated with multiresolution multi-scale methods for numerical solution of Poisson equation, scattering problems (Helmholtz equation) and Schroedinger equation. Although mathematics and algorithms are central in this course, the emphasis will be on how to construct, derive and use mathematical tools rather than on the details of proofs and derivations. By design this course is accessible to students in engineering, chemistry and physics.

Prerequisites:
Some familiarity with graduate level Fourier analysis, partial differential equations, numerical analysis or signal analysis is required or with instructor's consent. Working knowledge of one of the programming languages (C, C++, FORTRAN, and Python) is required.