GPU acceleration of average gradient method for solving partial differential equations

Abstract

Previously presented method of calculating local average gradients for solvingpartial differential equations (PDEs) is enhanced by accelerating it with graphics processingunits (GPUs) and combining a previous technique of interpolating between grid points in thecalculation of the gradients instead of using interpolation to create a denser grid.For accelerating the calculation with GPUs, we have ported the original naive Matlabimplementation to C++ and CUDA, and after optimizing the code we observe a speedupfactors more than two thousand, which is largely due to the original code not being optimized.