Faculty Advisor or Committee Member

Sarah Olson, Advisor

Identifier

etd-042915-170530

Abstract

There is an increasing amount of evidence in scientific research and industrial engineering indicating that the graphic processing unit (GPU) has a higher efficiency and a stronger ability over CPUs to process certain computations. The heat equation is one of the most well-known partial differential equations with well-developed theories, and application in engineering. Thus, we chose in this report to use the heat equation to numerically solve for the heat distributions at different time points using both GPU and CPU programs. The heat equation with three different boundary conditions (Dirichlet, Neumann and Periodic) were calculated on the given domain and discretized by finite difference approximations. The programs solving the linear system from the heat equation with different boundary conditions were implemented on GPU and CPU. A convergence analysis and stability analysis for the finite difference method was performed to guarantee the success of the program. Iterative methods and direct methods to solve the linear system are also discussed for the GPU. The results show that the GPU has a huge advantage in terms of time spent compared with CPU in large size problems.

Publisher

Worcester Polytechnic Institute

Degree Name

MS

Department

Mathematical Sciences

Project Type

Thesis

Date Accepted

2015-04-29

Accessibility

Unrestricted

Subjects

Heat equation, GPU, linear systems., CPU

Share

COinS