| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
|
| Initial Amendment Date: | August 20, 2004 |
| Latest Amendment Date: | August 20, 2004 |
| Award Number: | 0411448 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Leland Jameson
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2004 |
| End Date: | August 31, 2008 (Estimated) |
| Total Intended Award Amount: | $115,231.00 |
| Total Awarded Amount to Date: | $115,231.00 |
| Funds Obligated to Date: |
|
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
201 ANDY HOLT TOWER KNOXVILLE TN US 37996-0001 (865)974-3466 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
201 ANDY HOLT TOWER KNOXVILLE TN US 37996-0001 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | COMPUTATIONAL MATHEMATICS |
| Primary Program Source: |
|
| Program Reference Code(s): |
|
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
In its broader outlines, this research program aims at the development,
analysis and computer implementation of numerical methods designed to
approximate the solutions of some partial differential equations that have
important applications in the fields of engineering and physics. Indeed,
elliptic equations, the Navier-Stokes equations and nonlinear wave
equations despite having been cultivated for decades, still offer fertile
ground for further exploration, for there are still a plethora of
unanswered questions and a pressing need for more efficient and faster
algorithms. The discontinuous Galerkin method will constitute the core methodology of
this effort. While going back to 1973, major interest did not focus on it
until the nineties. Today it constitutes one of the most active areas
within finite elements if not the whole range of methods for the numerical
treatment of partial differential equations. It has not been as
extensively explored as the standard Galerkin version, yet what is known
so far offers a tantalizing glimpse of its potential. The project will
involve various areas at the cutting edge of numerical analysis and
scientific computing, in particular, the development of convergent and
efficient adaptive methods designed to reduce the run time of the
algorithms by finding optimal or quasi-optimal meshes. These adaptive
methods will require continuing the work on the development of sharp
a-posteriori error estimators designed to identify regions where the
solution is varying rapidly. Major efforts will be directed towards
pursuing a recently identified strategy for reducing the number of
iterations that current adaptive algorithms require in achieving a
prescribed level of accuracy.
Scientific computing is recognized as crucial to the advancement of
science. As such, the development of state of the art algorithms and codes
is important for the progress of technology. Specifically, improved
adaptive codes resulting from this project will have impact on a wide
range of problems and applications involving fluid flow phenomena, the
elucidation of extremely fast chemical reactions by femtosecond lasers,
and numerical simulations of supernova explosions.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
Please report errors in award information by writing to: awardsearch@nsf.gov.
