Optimized Algorithms for Solving Structural Inverse Gravimetry and Magnetometry Problems on GPUs

In this article, we construct new variants of iteratively regularized linearized gradient-type methods for solving structural inverse gravimetry and magnetometry problems, namely the regularized conjugate gradient method, the modified regularized conjugate gradient method, and the hybrid regularized conjugate gradient method. The main idea of the modification is to calculate the Jacobian matrix of the integral operator at a fixed point, without updating it during the entire iteration process. We also developed memory-optimized and time-efficient parallel algorithms and programs on the basis of the constructed modified methods. The memory optimization uses the block-Toeplitz structure of the Jacobian matrix. The algorithms were implemented on GPUs using the NVIDIA CUDA technology. We performed an efficiency and speedup analysis, and solved a model problem with synthetic disturbed data.