Krylov and rational Krylov methods of numerical solution of some problems of computational geophysics
https://doi.org/10.18303/2619-1563-2024-1-29
Abstract
The solutions of many spatially discretized problems, related with computational geophysics, are presented as 𝑢 = 𝑓(𝐴)𝜑, where 𝐴 ∈ 𝑹𝑁×𝑁, 𝜑 ∈ 𝑹𝑁, 𝑓 is a function. We consider approximations to 𝑢 on the basis of Galerkin approach for polynomial and rational Krylov subspaces. We describe the corresponding computational methods – the ones of Lanczos and rational Arnoldi, and also their application to solving some problems of computational geophysics (in the area of electrologging, thermal logging, electrical prospecting). The aim of this review paper is to instruct the reader to apply the methods described here to his applied problems.
Supporting agencies: The study was supported by Moscow Center of Fundamental and Applied Mathematics at Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences (Agreement No. 075-15-2022-286 with the Ministry of Science and Higher Education of the Russian Federation).
About the Author
L. A. Knizhnerman
Marchuk Institute of Numerical Mathematics RAS
Russian Federation
Russian Federation
8, Gubkin Str., Moscow, 119333.
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Review
For citations:
Knizhnerman L.A. Krylov and rational Krylov methods of numerical solution of some problems of computational geophysics. Russian Journal of Geophysical Technologies. 2024;(1):29-46. (In Russ.) https://doi.org/10.18303/2619-1563-2024-1-29
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