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.