Research and Coursework

I'm afraid we need to use ... MATH. - Professor Farnsworth (Futurama)

Presentations/Talks

• DOE Grad Student/ Post Doc Blitz (9/25/2012): Norm-Preserving Discretization and Divergence-Form Elliptic Differential Equations

Coursework

• Final Project for Numerical Optimization (CSCI-GA.2945-002) taught by Margaret Wright.
  • Title: Inverse Scattering and Bound-Constrained Nonlinear Optimization
  • Abstract: We describe an investigation into the inverse scattering problem for the Helmholtz equation in 1-d. For a fixed frequency, we attempt to find the optimal scatterer for minimizing the total transmission response given an incidental wave on the left with coefficient 1. We pose this problem as a bound-constrained optimization problem whose objective function is the norm squared of the coefficient of the transmitted wave. We briefly describe our implementation of a bound-constrained Quasi-Newton method for solving this problem in Section 3. Evaluating the objective function and its gradient requires solving the 1-d Helmholtz equation. We describe an efficient method for doing so in Section 4. The results of some numerical experiments are given in Section 5. The optimal scatterers found resemble Bragg gratings from optical fibre design.
  • Paper
  • Project Code
• Final Project for High Performance Computing (MATH-GA.2011.001) taught by Andreas Kloeckner and Marsha Berger.
  • Title: An Investigation into Parallel SVD
  • Abstract: We discuss an investigation into parallelizing the computation of a singular value decomposition (SVD). We break the process into three steps: bidiagonalization, computation of the singular values, and computation of the singular vectors. We discuss the algorithms, parallelism, implementation, and performance of each of these three steps. The original goal was to accom- plish all three tasks using a graphics processing unit (GPU) but the final implementation uses a combination of GPU computing and multicore central processing unit (CPU) computing. The two parallelization standards used were OpenCL and OpenMP. Our SVD implementation and its components are available freely online.
  • Note: This was a group project with Michael "Boston Mike" Lewis and Steven Delong. My primary contribution to the project was writing the GPU based bidiagonalization code.
  • Paper
  • Project Code

Back Home

Updated: 1/14/2013