GPU Acceleration of Partial Differential Equation Solvers

Differential equations are often directly solvable by analytical means only in their 1-D version. Partial differential equations are generally not solvable by analytical means in 2-D and 3-D, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular such methods is the finite element method. Our main areas of focus are the Poisson heat equation and the plate bending equation. The purpose of the current paper is to provide a quick walk through of the various approaches we followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.