Stable parallel algorithms for solving the inverse gravimetry and magnetometry problems / Akimova E.N., Vasin V.V. // International Journal for Engineering Modelling. - 2004. - V. 17, l. 1-2. - P. 13-19.

ISSN:

13301365

Type:

Article

Abstract:

The three-dimensional inverse problems of gravimetry and magnetometry for finding the interfaces between mediums from the gravitational and magnetic data are investigated. We assume that a model of the lower half-space consists of three mediums with constant densities which are separated by the surfaces S1, and S2 to be determined. The inverse pr oblems are reduced to nonlinear integral equations of the first kind, hence these problems are ill-posed. After discretization of the integral equation we obtain a system of nonlinear equations of large dimension. To solve this system, we use the iteratively regularized Gauss-Newton method. To realize one step of this method, we have to solve a system of linear algebraic equations with full matrix. For this aim, parallel variants of the Gauss, Gauss-Jordan and the conjugate gradient method are applied. Their realization has been implemented on the Massively Parallel Computing System MVS-1000. The analysis of the efficiency of parallelization of the iterative algorithms with different numbers of processors is carried out. Parallelization of the algorithms decreases significantly the time of solving the problems. The interfaces S1 and S2 obtained by the Gauss-Newton method correspond to the real geological perceptions about the Ural region under investigation.

Author keywords:

Gravimetry; Magnetometry; Parallel algorithms; Parallelization

Index keywords:

Gravimetric analysis; Integral equations; Interfaces (materials); Mathematical models; Nonlinear equations; Parallel algorithms; Parallel processing systems; Magnetometry; Nonlinear integral equations

DOI:

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-27744524410&partnerID=40&md5=1d9f122f199e811e990d11ba4f571381

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Другие поля

Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-27744524410&partnerID=40&md5=1d9f122f199e811e990d11ba4f571381
Affiliations	Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str. 16, Ekaterinburg 620219, Russian Federation
Author Keywords	Gravimetry; Magnetometry; Parallel algorithms; Parallelization
References	Vasin, V.V., Perestoronina, G.Ya., Prutkin, I.L., Timerkhanova, L.Yu., Reconstruction of the relief of geological boundaries in the three-layered medium using the gravitational and magnetic data (2001) Proc. of the Conference on Geophysics and Mathematics, pp. 35-41. , Institute of Mines, UrB RAS, Perm; Bakushinsky, A.B., A regularizing algorithm on the basis of the Newton- Kantorovich method for the solution of variational inequalities (1976) Zh. Vychisl. Mat. Mat. Fiz., 16 (6), pp. 1397-1404; Streng, G., (1980) Linear Agebra and Its Applications, , Mir, Moskva; Bakhvalov, N.S., Zhidkov, N.P., Kobelkov, G.M., (1987) Numerical Methods, , Nauka, Moskva; Vasin, V.V., Ageev, A.L., (1993) Ill-posed Problems With a Priori Information, , Nauka, Ekaterinburg; Akimova, E.N., Parallelization of an algorithm for solving the gravity inverse problem (2003) Journal of Computational and Applied Mechanics, 4 (1), pp. 5-12. , Miskolc University Press; Baranov, A.V., Latsis, A.O., Sazhin, C.V., Khramtsov, M.Yu., The MVS-1000 System User's Guide, , http://parallel.ru/mvs/user.html; Kwiatkowski, J., Evaluation of parallel programs by measurement of its granularity (2001) Proc. of the Conference on Parallel Processing and Applied Mathematics, 2328, pp. 145-153. , Lecture Notes in Computer Science
Correspondence Address	Akimova, E.N.; Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, S. Kovalevskaya str. 16, Ekaterinburg 620219, Russian Federation; email: aen@imm.uran.ru
CODEN	IEMOE
Language of Original Document	English
Abbreviated Source Title	Int. J. Eng. Model.
Source	Scopus