"Gradient methods for solving inverse gravimetry and magnetometry problems on the Uran supercomputer"
Akimova E.N., Misilov V.E., Skurydina A.F., and Tret'yakov A.I.

A modified linearized steepest descent method with variable weight factors is proposed to solve three-dimensional structural inverse gravimetry and magnetometry problems of finding the interfaces between constant density or magnetization layers in a multilayer medium. A linearized conjugate gradient method and its modified version with weight factors for solving the gravimetry and magnetometry problems in a multilayer medium is constructed. On the basis of the modified gradient-type methods, a number of efficient parallel algorithms are numerically implemented on an Intel multi-core processor and NVIDIA GPUs. The developed parallel iterative algorithms are compared for a model problem in terms of the relative error, the number of iterations, and the execution time.

Keywords: inverse gravimetry and magnetometry problems, parallel algorithms, gradient-type methods, multi-core and graphics processors.

  • Akimova E.N. – Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Sof ’i Kovalevskoi 16, Ekaterinburg, 620990, Russia; Leading Scientist, Doctor of Phys. and Math. Sci., e-mail: aen15@yandex.ru
  • Misilov V.E. – Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Sof ’i Kovalevskoi 16, Ekaterinburg, 620990, Russia; Graduate Student, e-mail: out.mrscreg@gmail.com
  • Skurydina A.F. – Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Sof ’i Kovalevskoi 16, Ekaterinburg, 620990, Russia; Leading Mathematician, e-mail: afinapal@gmail.com
  • Tret'yakov A.I. – Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Sof ’i Kovalevskoi 16, Ekaterinburg, 620990, Russia; Programmer, e-mail: fr1z2rt@gmail.com