Using general-purpose computing on graphics processing units (GPGPU) to accelerate the ordinary kriging algorithm

Abstract

Spatial interpolation methods have been applied to many disciplines, the ordinary kriging interpolation being one of the methods most frequently used. However, kriging comprises a computational cost that scales as the cube of the number of data points. Therefore, one most pressing problems in geostatistical simulations is that of developing methods that can reduce the computational time. Weights calculation and then the estimate for each unknown point is the most time-consuming step in ordinary kriging. This work investigates the potential reduction in execution time by selecting the suitable operations involved in this step to be parallelized by using general-purpose computing on graphics processing units (GPGPU) and Compute Unified Device Architecture (CUDA). This study has been performed by taking into account comparative studies between graphic and central processing units on two different machines, a personal computer (GPU, GeForce 9500, and CPU, AMD Athlon X2 4600) and a server (GPU, Tesla C1060, and CPU, Xeon 5600). In addition, two data types (float and double) have been considered in the executions. The experimental results indicate that parallel implementation of matrix inverse by using GPGPU and CUDA will be enough to reduce the execution time of weights calculation and estimation for each unknown point and, as a result, the global performance time of ordinary kriging. In addition, suitable array dimensions for using the available parallelized code have been determined for each case. Thus, it is possible to obtain relevant saved times compared to those resulting from considering wider parallelized extension. This fact demonstrates the convenience of carrying out this kind of study in other interpolation calculation methodologies using matrices.