Numerical Analysis RIT
- Focus of the RIT in Fall 2004
-
The main focus of the RIT in Numerical Analysis is the theory and the numerical approximation
of stochastic differential equations. In order to understand the material, the main effort
in Fall 2003 and in Spring 2004 is to read the lecture notes on
stochastic differential equation by
L. C. Evans. The lecture notes are available on L. C. Evans' web page
or along with other useful lecture notes on the web.
A useful review article on
numerical methods has been written by D. J. Higham (SIAM Rev. 43 (2001), no. 3,
525-546).
- Meeting schedule in Fall 2004 : The RIT meets on Mondays from 3:00-4:00 in MATH 2300.
- August 30: Discussion on the article "Galerkin Finite Element Approximations of Stochastic Elliptic
Partial Differential Equations", by I. Babuska, R. Tempone, G. E. Zouraris, SIAM J. Numer. Anal.
Vol 42, no.2, pp 800-825 (Kyoung-Sook Moon)
- September 6: Labor day
- September 13: Discussion on the article "Galerkin Finite Element Approximations of Stochastic Elliptic
Partial Differential Equations", by I. Babuska, R. Tempone, G. E. Zouraris (Kyoung-Sook Moon)
- September 20: Discussion on the article "Efficient Iterative Algorithms for the
Stochastic Finite Element Method with Application to Acoustic Scattering", by
Howard C. Elman, Oliver G. Ernst, Dianne P. O'Leary and Michael Stewart,
UMCP-CSD:CS-TR-4423, 2002,(Howard C. Elman)
- September 27: Stochastic partial differential equations I (Raul Tempone)
- September 30: Stochastic partial differential equations II (Raul Tempone)
NOTE that the time is 3:30-4:30pm on Thursday and room 1308 !!!
- October 4: Solving SPDEs using
the polynomial chaos expansion method based on the paper "Modeling uncertainty in steady state diffusion problems via generalized
polynomial chaos", Comput. Methods Appl. Mech. Engrg., 191:4927-4948, 2002. (Darran Furnival)
- October 11 and 18: Random fields based on the note "Random Fields and Their Geometry"
by Robert Adler and Jonathan E. Taylor.
[Link] (Jeffery Cooper)
- October 25 and November 1: Karhunen-Loeve expansions of random fields
(Khamron Mekchay).
- Participants in Spring 2004
- Faculty:
Jeffery Cooper (Mathematics),
Georg Dolzmann (Mathematics),
Howard Elman (Computer Science),
Ricardo Nochetto (Mathematics),
Dianne P. O'Leary (Computer Science),
John Osborn (Mathematics),
Tobias von Petersdorff (Mathematics),
Konstantina Trivisa (Mathematics)
Postdocs:
Sören Bartels (Mathematics, DAAD fellow),
Kyoung-Sook Moon (Mathematics),
Marco Verani (Visitor from Politecnico di Milano).
Graduate students:
Gunay Dogan (Mathematics),
Khamron Mekchay (Mathematics),
Shawn Walker(Aerospace Engineering),
Chensong Zhang (Mathematics)
Darran Furnival (Computer Science)
- Graduate prerequisites
- Introductory PDEs (MATH 462) and numerical computation (AMSC 460 or 466).
- Undergraduate prerequisites
- Several variable calculus (MATH 241) and differential equations (MATH 246).
Concurrent enrollment in scientific computing (AMSC 460) or numerical analysis (AMSC/MATH 466).
- What we did in past terms
- Spring 2004
- Fall 2003
- Academic year 2002-03
(Daniel Kessler's web page, currently not maintained)
Kyoung-Sook Moon
Last modified: Mon Sep 20 EDT 2004