Algorithms for solving inverse geophysical problems on parallel computing systems
For solving inverse gravimetry problems, efficient stable parallel algorithms based on iterative gradient methods are proposed. For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, a parallel matrix sweep algorithm, a square root method, and a conjugate gradient method with preconditioner are proposed. The algorithms are implemented numerically on a parallel computing system of the Institute of Mathematics and Mechanics (PCS-IMM), NVIDIA graphics processors, and an Intel multi-core CPU with some new computing technologies. The parallel algorithms are incorporated into a system of remote computations entitled “Specialized Web-Portal for Solving Geophysical Problems on Multiprocessor Computers.” Some problems with “quasi-model” and real data are solved.
Keywordsinverse gravimetry problems parallel algorithms direct and iterative methods parallel computing systems
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- 1.Martyshko, P.S. and Koksharov, D.E., Determination of Density in a LayeredMedium by Gravitational Data, Geofiz. Zh., 2005, vol. 27, no. 4, pp. 678–684.Google Scholar
- 2.Numerov, B.V., Interpretation of Gravitational Observations in the Case of One Contact Surface, Dokl. Akad. Nauk SSSR, 1930, no. 21, pp. 569–574.Google Scholar
- 3.Vasin, V.V. and Eremin, I.I., Operatory i iteratsionnye protsessy feierovskogo tipa. Teoriya i prilozheniya (Operators and Iterative Processes of Fejer Type: Theory and Applications), Yekaterinburg: UrB RAS, 2005.Google Scholar
- 4.Dashevskii, Yu.A., Surodina, I.V., and Epov, M.I., Quasi-Three-Dimensional Mathematical Simulation of Diagrams of Nonaxisymmetric Direct Current Sondes in AnisotropicMedia, Sib. Zh. Ind.Mat., 2002, vol. 5, no. 3 (11), pp. 76–91.Google Scholar
- 5.Martyshko, P.S. and Prutkin, I.L., Technology of Separation of Gravitational Field Sources in Depth, Geofiz. Zh., 2003, vol. 25, no. 3, pp. 159–168.Google Scholar
- 8.Akimova, E.N. and Belousov, D.V., Parallelization of Algorithms for Solving the Linear Inverse Problem of Gravimetry on PCS-1000 and Graphic Processors, Vestnik NNGU, pt. 1, 2010, no. 5, pp. 193–200.Google Scholar
- 10.Faddeev, V.K. and Faddeeva, V.N., Vychislitel’nye metody lineinoi algebry (Computational Methods of Linear Algebra), Moscow: Gostekhizdat, 1963.Google Scholar
- 12.Samarskii, A.A. and Nikolaev, E.S., Metody resheniya setochnykh uravnenii (Methods for Solving Grid Equations), Moscow: Nauka, 1978.Google Scholar
- 13.Akimova, E.N. and Gemaidinov, D.V., Parallel Algorithms for Solving the Inverse Gravimetry Problem and Organization of Remote Communication between PCS-1000 and the User, Vych. Met. Progr., 2008, vol. 9, no. 1, pp. 133–144.Google Scholar
- 14.Martyshko, P.S., Vasin, V.V., Akimova, E.N., and P’yankov, V.A., Complex Interpretation of Gravitational and Magneto-Variational Data (Using Pre-Ural Bashkiria as an Example), Geofiz., 2011, no. 4, pp. 30–36.Google Scholar
- 15.Metodika razrabotki mnogopotochnykh prilozhenii: printsipy i prakticheskaya realizatsiya (Methods of Developing Multithread Applications: Principles and Practical Implementation), URL: http://www.rsdn.ru/article/baseserv/RUThreadingMethodology.xml (download date: 06.02.2012).