Solution of two-dimensional convolution integral in geoid determination by parallel computing

Despite the increasing power of computers; some algorithms, tasks, or problems still require excessive computation time to run on a personal computer. In recent years, the appeal of parallel computing methods in engineering calculations has grown, and researchers have been striving to execute well-known methods and algorithms in parallel. The primary reasons for the shift to parallel methods are the rapid growth in data size and the accelerating advancements in hardware. The geoid, which serves as the reference surface for heights in Earth sciences, is a closed surface representing the Earth's real shape. In the literature, various methods have been proposed for geoid determination; among them, the gravimetric approach, which relies on gravity data, is one of the most commonly used. The major challenge of the gravimetric method lies in solving the two-dimensional integral involved in the formulation, which is a computationally time-consuming process. In this study, the computational steps, strengths, and weaknesses of parallel computation of two-dimensional integral involved in gravimetric geoid determination using threads are discussed. The speed-up graphs are plotted based on the integration cap size, the grid interval, and the number of threads. Numerical results demonstrate that parallel computing significantly contributes to geoid determination processes. For illustration, parallel computing provides time gain up to 8 times and 10 times from the point of view of the cap size and data density, respectively.