Geodesic
Gradient methods for solving inverse gravimetry and magnetometry problems on the Uran supercomputer
Numerical methods and programming, Tome 16 (2015) no. 1, pp. 155-164

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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. 
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     author = {E. N. Akimova and V. E. Misilov and A. F. Skurydina and A. I. Tret'yakov},
     title = {Gradient methods for solving inverse gravimetry and magnetometry problems on the {Uran} supercomputer},
     journal = {Numerical methods and programming},
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     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2015_16_1_a15/}
}
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E. N. Akimova; V. E. Misilov; A. F. Skurydina; A. I. Tret'yakov. Gradient methods for solving inverse gravimetry and magnetometry problems on the Uran supercomputer. Numerical methods and programming, Tome 16 (2015) no. 1, pp. 155-164. http://geodesic.mathdoc.fr/item/VMP_2015_16_1_a15/