SIAM Journal on Scientific and Statistical Computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Variants of BICGSTAB for matrices with complex spectrum
SIAM Journal on Scientific Computing
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
SIAM Journal on Scientific Computing
Separation-of-variables as a preconditioner for an iterative Helmholtz solver
Applied Numerical Mathematics
Journal of Computational Physics
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
SIAM Journal on Scientific Computing
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Journal of Computational Physics
| Hi-index | 31.45 |
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 ONlogN, 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 ON. 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.