high performance computing on graphics processing units: hgpu.org

In this project, boundary value problems of the electric field governed by the Laplace equation were formulated using different numerical methods such as FEM and BEM. The resulting systems of linear equations were then solved using different solving algorithms. The accuracy and complexity of FEM and BEM were compared. The space and time complexity of different solving algorithms were also evaluated. One of the solving algorithms was implemented on a parallel computation device, an nVIDIA GPU, the solving time of which is then compared with its serial counterpart. Both FEM and BEM were able to solve the problem smoothly. The accuracy of the two methods was found to be comparable given the same mesh density. Two classes of solving algorithms, namely direct and iterative, were evaluated in this project. Despite some alleged convergence issue, iterative algorithms triumphed direct algorithms in terms of time complexity as far as problems in this report are concerned. In addition, the parallel computation device was able to significantly speed up one iterative algorithm, and is expected to give a similar amount of speedup to other iterative methods.