Weak-form BCGS-FFT algorithm for volume integral equationsin stratified medium

Key words:  volume integral equations  weak-form BCGS-FFT algorithm  dyadic Green's function  stratified medium electric well-logging

Abstract:

The volume integral equations in stratified medium were accurately calculated by weak-form stabilized biconjugate-gradient fast Fourier transform ( BCGS-FFT) algorithm. The dyadic Greens functions in stratified medium were calculated by recursive matrix method，which can be easily combined with the volume integral equations. The rooftop functions were chosen as basis function and testing function to get the weak-form discretization of the volume integral equations，thus the singularity can be circumvented. The discrete form of the volume integral equations was solved via the stabilized biconjugate-gradient iteration method，so that the distribution of the electric field within the inhomogeneous objects can be obtained. It is assumed that the inhomogeneous objects are only in one layer of the stratified medium, so that the product between the dyadic Green1 s function and the contrast source within the volume integral equations can be expressed in the form of convolution or correlation, which can be accelerated by adopting the fast Fourier transform in xfy and z directions during each iteration of BCGS. Numerical examples show the accuracy and efficiency of the algorithm.