Three-dimensional visco-acoustic modeling using a renormalized integral equation iterative solver

We present a frequency-domain renormalized integral equation formulation for solving a three-dimensional visco-acoustic medium using an iterative solver. Upon applying this special renormalization, the resulting integral equation operator can be proven to have a contraction property. Hence, solving the linear-system of equations using a Krylov optimization method, will result in a good convergence rate. Furthermore since the matrix–vector multiplication can be done using a Fast-Fourier transform (FFT) technique, its operation is of the order of O N log N , where N is the size of the discretization grid. This technique also allows us to use matrix-free implementation. Hence, the memory usage is about O N . Numerical tests show that the computational time and memory usage of this renormalized integral equation approach can be quite competitive with the frequency-domain finite difference iterative solver. Further, the numerical examples demonstrate that it is possible to solve a problem with over 100 million unknowns using an integral equation approach.