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APPLICATION OF SPECTRAL LANCZOS DECOMPOSITION METHOD TO LARGE
SCALE PROBLEMS ARISING GEOPHYSICS

T. Tamarchenko
Western Atlas Logging Services
10201 Westheimer
Houston, TX 77042, USA
E-mail: tanya.tamarchenko@waii.com
This paper presents an application of Spectral Lanczos Decomposition Method (SLDM)
to numerical modeling of electromagnetic diffusion and elastic waves propagation in
inhomogeneous media. SLDM approximates an action of a matrix function as a linear
combination of basis vectors in Krylov subspace.
I applied the method to model electromagnetic fields in three-dimensions a
nd elastic waves in two dimensions. The finite-difference approximation of the spatial part
of differential operator reduces the initial boundary-value problem to a system of
ordinary differential equations with respect to time. The solution to this system requires
calculating exponential and sine/cosine functions of the stiffness matrices.
Large scale numerical examples are in a good agreement with the theoretical
error bounds and stability estimates given by Druskin, Knizhnerman, 1987.