Computational Performance Analysis of Full Vectorization and Nested Loop in Last–Kubik Gravity Forward Modeling

Abstract

Gravity forward modeling based on the Last–Kubik kernel requires intensive computation as the number of model blocks and observation points increases. This study analyzes the computational performance of Full Vectorization (FV) compared with Nested Loop (NL) without modifying the mathematical formulation of the Last–Kubik kernel. Experiments were conducted using synthetic models with 20 configurations ranging from 20,000 to 168,200 blocks. Algorithm performance was evaluated based on gravity-response consistency, computational time, and memory usage. Computational time was assessed using Total Execution Time (TET) and Mean Core Computational Time (MCCT) from 30 repetitions, while memory usage was evaluated using Kernel Workspace Memory Increase (KWMI). The results show that the FV and NL implementations produce numerically identical gravity responses, with a maximum absolute difference of 0 for the tested configurations. FV provides an MCCT speedup of approximately 6–7 times for small to medium-sized models, but the speedup decreases to 1.56 times at 168,200 blocks. In contrast, FV requires approximately 18 times more memory than NL. Regression analysis shows a very strong linear relationship between KWMI and the number of observation–block pairs. The results demonstrate that FV effectively accelerates gravity forward modeling but has scalability limitations due to its substantially higher memory requirements