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.
KeywordsNonlinear gradient-type methods Parallel algorithms Gravimetry and magnetometry problems Toeplitz matrix GPU
- 2.Akimova, E.N., Martyshko, P.S., Misilov, V.E.: Parallel algorithms for solving structural inverse magnetometry problem on multucore and graphics processors. In: Proceedings of 14th International multidisciplinary scientific GeoConference SGEM 2014, vol. 1(2), pp. 713–720 (2014)Google Scholar
- 3.Akimova, E.N., Martyshko, P.S., Misilov, V.E.: A fast parallel gradient algorithm for solving structural inverse gravity problem. In: AIP Conference Proceedings, vol. 1648, 850063 (2015). doi: 10.1063/1.4913118
- 4.Akimova, E.N., Misilov, V.E.: A fast componentwise gradient method for solving structural inverse gravity problem. In: Proceedings of 15th International Multidisciplinary Scientific GeoConference SGEM 2015, vol. 3(1), pp. 775–782 (2015)Google Scholar
- 6.Malkin, N.R.: On solution of inverse magnetic problem for one contact surface (the case of layered masses). DAN SSSR, Ser. A, vol. 9, pp. 232–235 (1931)Google Scholar
- 9.Martyshko, P.S., Prutkin, I.L.: Technology of depth distribution of gravity field sources. Geophys. J. 25(3), 159–168 (2003)Google Scholar
- 10.Numerov, B.V.: Interpretation of gravitational observations in the case of one contact surface. Doklady Akad. Nauk SSSR, pp. 569–574 (1930)Google Scholar