TALK 1 : MIMETIC DIVERGENCE, GRADIENT, CURL, AND BOUNDARY OPERATORS OVER NON-UNIFORM, TWO-DIMENSIONAL MESHES TALK 2 : SIMULATING THE NONLINEAR SCHRÖDINGER EQUATION USING THE COMPUTATIONAL CAPABILITY OF NVIDIA GRAPHICS CARDS
TITLE:
TALK 1 : MIMETIC DIVERGENCE, GRADIENT, CURL, AND BOUNDARY OPERATORS OVER NON-UNIFORM, TWO-DIMENSIONAL MESHES
TALK 2 : SIMULATING THE NONLINEAR SCHRÖDINGER EQUATION USING THE COMPUTATIONAL CAPABILITY OF NVIDIA GRAPHICS CARDS
DATE:
Friday, May 7th, 2010
TIME:
3:30 PM
LOCATION:
GMCS 214
SPEAKER:
Speaker 1 : David Batista, PhD Student, CSRC
Speaker 2 : Ron Caplan, PhD Student, CSRC
ABSTRACT:
Abstract 1:
Mimetic operators are approximations that satisfy discrete versions of continuum conservation laws and are used for finding numerical solutions of partial differential equations (PDE’s). A technique for constructing mimetic schemes over non-uniform, structured, two-dimensional meshes is proposed. We construct divergence, gradient, curl, and boundary operators based on the application of local transformations and show how to use them for solving PDE’s with general boundary conditions. Finally, a numerical convergence analysis is presented by solving a boundary layer like problem over different kind of meshes.
Abstract 2:
Much research in systems governed by the nonlinear Schrödinger equation (NLSE) continues to this day. Most work is performed using numerical simulations, but in order to make the research more efficient (and in some cases, even, plausible), it is desirable to have new numerical methods and technology which speed up the computation time of the simulations. A recent development in parallel computation is the use of video graphics cards for scientific numerical problems.
We describe our efforts to use NVIDIA graphics cards to speed up computations of the one-dimensional NLSE. This is done by modifying our original code using a C-language extension API called CUDA. We also describe our numerical methods which include a two-step high-order compact finite difference scheme as well as a simple to implement constant modulus-squared background boundary condition. We find that by using a single inexpensive graphics card, our simulations can run up to 70 times faster. We hope to extend the results to two and three dimensions, where such speedup will have the most benefit.
HOST:
Jose Castillo and Ricardo Carretero
DOWNLOAD: