GPU COMPUTING FOR 2D WAVE EQUATION BASED ON IMPLICIT FINITE DIFFERENCE SCHEMES

Abstract

In this paper we will consider the numerical implementation of the 2d wave equation which is a fundamental equation in many engineering problems. An approximate solution of a function is calculated from discrete points in spatial grid based on discrete time steps. The initial values are given by the initial value condition. First we will interpret how to transform a differential equation into an implicit finitedifference equation, respectively, a set of finite-difference equations that can be used to calculate an approximate solution. Then we will change this algorithm to parallelize this task on GPU. Special focus is on improving the performance of the parallel algorithm. In addition, we will run the implemented parallel code on the GPU and serial code the central processor, calculate the acceleration based on the execution time. We present that the parallel code that runs on a GPU gives the expected results by comparing our results to those obtained by running serial code of the same simulation on the CPU. In fact, in some cases, simulations on the GPU are found to run 22 times faster than on a CPU