Math 627 - Introduction to Parallel Computing

Fall 2014 - Matthias K. Gobbert

Presentations of the Class Projects

Friday, December 12, 2014, 01:00 p.m.

01:05-01:20
Investigating the Use of pMatlab to Solve the Poisson Equation on the Cluster maya
Sarah Swatski, Department of Mathematics and Statistics
Many physical phenomena can be described by partial differential equations which can be discretized to form systems of linear equations. We apply the finite difference method to the Poisson equation with homogeneous Dirichlet boundary conditions, which yields a system of linear equations with a large sparse system matrix. We implement pMatlab code which utilizes the conjugate gradient method to solve this system. We do not recommend the use of pMatlab at this time as we find that it is very limited, its implementation is highly complex and the results are inconsistent.
01:25-01:40
Performance of Linear Time-Dependent Partial Differential Equation on a Hybrid CPU/GPU Node
Jonathan Graf, Department of Mathematics and Statistics
A linear, time-dependent PDE is used to test the performance of code implemented for Graphics Processing Units (GPUs). A program in C with MPI has demonstrated good performance so I now use an implementation of the programming model with CUDA and MPI that utilizes GPUs and observe the effect on timings. I report initial results that demonstrate limited speedup using a hybrid node's GPUs over CPU only results.
01:45-02:00
Approximation of Fisher Information Matrix of Poisson Mixture Model
Qing Ji, Department of Mathematics and Statistics
An approximation of the Fisher information matrix for mixture model was proposed by Raim, Neerchal, and Morel (2014). For a mixture of two Poisson distributions, a program in C with MPI is designed to test the performance of this approximation under different parameter values. The result shows that this approximation method is great when the two parameters of these two Poisson distributions are far apart.
02:05-02:20
Parallel Performance Studies for an Elliptic Test Problem on the Cluster maya 2013: Using 1-D and 2-D Domain Subdivisions
Kourosh Kalayeh, Department of Mechanical Engineering
One of the most important aspects of parallel computing is the communication between processes, since it has tremendous impact on overall performance of this method of computing. Consequently, it is important to implement the parallel code in a way that communications between processes are taking place in a most efficient way. In this study, we investigate the effect of domain subdivision, 1-D or 2-D, on performance of parallel computing. The Poisson equation is solved as a test problem using finite difference method with both 1-D and 2-D domain subdivisions. Both methods show good speedup. Although in most cases the grid-structured communication show slightly better performance, the overall performance of 2-D domain subdivision does not indicate the superiority of this method.
02:25-02:40
A comparison of Drift-Diffusion Equation using ode15s and Newton's Method in Matlab in the Cluster maya
Yue Hu, Department of Computer Science and Electrical Engineering
In this report, we solve drift-diffusion model in a simple p-i-n photodetector in 1D. Finite difference method is used to discretize the drift-diffusion equations. We solve the drift-diffusion equations with Newton's method and ode15s in Matlab. We found that ode15s performs much better than Newton's method, especially when the mesh node increases.