Unstructured Finite Element Computations on Configurable Computers

Abstract

Scientific solutions to physical problems are computationally intensive. With the increasing emphasis in the area of Custom Computing Machines, many physical problems are being solved using configurable computers. The Finite Element Method (FEM) is an efficient way of solving physical problems such as heat equations, stress analysis and two- and three-dimensional Poisson's equations. This thesis presents the solution to physical problems using the FEM on a configurable platform. The core computational unit in an iterative solution to the FEM, the matrix-by-vector multiplication, is developed in this thesis along with the framework necessary for implementing the FEM solution. The solutions for 2-D and 3-D Poisson's equations are implemented with the use of an adaptive mesh refinement method. The dominant computation in the method is matrix-by-vector multiplication and is performed on the Wildforce board, a configurable platform. The matrix-by-vector multiplication units developed in this thesis are basic mathematical units implemented on a configurable platform and can be used to accelerate any mathematical solution that involves such an operation.