APPLICATION OF SPECTRAL LANCZOS DECOMPOSITION METHOD TO LARGE
SCALE PROBLEMS ARISING GEOPHYSICS
Western Atlas Logging Services
Houston, TX 77042, USA
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.