Effects of OpenCL-Based Parallelization Methods on Explicit Numerical Methods to Solve the Heat Equation

Abstract

In recent years, the need for high-performance computing solutions has increased due to the growing complexity of computational tasks. The use of parallel processing techniques has become essential to address this demand. In this study, an Open Computing Language (OpenCL)-based parallelization algorithm is implemented for the Constant Neighbors (CNe) and CNe with Predictor–Corrector (CpC) numerical methods, which are recently developed explicit and stable numerical algorithms to solve the heat conduction equation. The CPU time and error rate performance of these two methods are compared with the sequential implementation and Euler’s explicit method. The results demonstrate that the parallel version’s CPU time remains nearly constant under the examined circumstances, regardless of the number of spatial mesh points. This leads to a remarkable speed advantage over the sequential version for larger data point counts. Furthermore, the impact of the number of timesteps on the crossover point where the parallel version becomes faster than the sequential one is investigated.