We present a parallel algorithm for solution of the three-dimensional Helmholtz equation in the frequency domain using volume-integral equations. The algorithm is applied to seismic forward modeling. The method of integral equations reduces the size of the problem by dividing the geologic model into the anomalous and background parts, but leads to a dense system matrix. Tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the equation system solver, and also for parallelizing across multiple sources. Practical examples and efficiency tests are presented.
- Integral equations