Parallel algorithm for 3D modeling of monochromatic acoustic field by the method of integral equations

Mikhail S. Malovichko; Nikolay E. Khokhlov; Nikolay B. Yavich; Michael S. Zhdanov

doi:10.14529/jsfi160406

Authors

Mikhail S. Malovichko Moscow Institute of Physics and Technology, Moscow
Nikolay E. Khokhlov Moscow Institute of Physics and Technology, Moscow
Nikolay B. Yavich Moscow Institute of Physics and Technology, Moscow
Michael S. Zhdanov The University of Utah, Salt Lake City

DOI:

https://doi.org/10.14529/jsfi160406

Abstract

We present a parallel algorithm for solution of the three-dimensional Helmholtz equation in the frequency domain by the method of 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.
A 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.

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