Full text loading...
-
An Iterative Method to Solve 3D Helmholtz Equation with Use of HPC Clusters
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 6th EAGE Saint Petersburg International Conference and Exhibition, Apr 2014, Volume 2014, p.1 - 5
Abstract
We propose a preconditioned iterative method for solving the Helmholtz equation in heterogeneous media. Our method is based on Krylov type linear solvers, similarly to several other iterative solver approaches. The distinctive feature of our method is the use of multilevel preconditioner. Firstly, as a preconditioner we suggest to use complex damped Helmholtz operator for vertically-inhomogeneous media. We represent the initial problem as a perturbation of a preconditioner. As a result, a matrix-by-vector multiplication of the preconditioned system may be evaluated via 2D FFT in x and y directions followed by solution of a number of small banded systems of linear equations in z directions. A second level preconditioner based on Neumann series decomposition provides fast convergence in complex situation. After decomposition of the computational domain along one lateral direction we parallelize our algorithm to be used on high performance computer systems with hybrid architecture (MPI+OpenMP).