High-order approximation compact schemes for forward subsurface scattering problems

Yury A. Gryazin

doi:10.1117/12.2050189

29 May 2014 High-order approximation compact schemes for forward subsurface scattering problems

Yury A. Gryazin

Proceedings Volume 9077, Radar Sensor Technology XVIII; 90770G (2014) https://doi.org/10.1117/12.2050189
Event: SPIE Defense + Security, 2014, Baltimore, MD, United States

Abstract

We develop an efficient iterative approach to the solution of the discrete three-dimensional Helmholtz equation with variable coefficients and PML boundary conditions based on compact fourth and sixth order approximation schemes. The coefficient matrices of the resulting systems are not Hermitian and possess positive as well as negative eigenvalues so represent a significant challenge for constructing an efficient iterative solver. In our approach these systems are solved by a combination of a Krylov subspace-type method with a matching high order approximation preconditioner with coefficients depending only on one spatial variable. In the algorithms considered, the direct solution of high order preconditioning system is based on a combination of the separation of variables technique and Fast Fourier Transform (FFT) type methods. The resulting numerical methods allow for efficient implementation on parallel computers. Numerical results confirm the high efficiency of the proposed iterative algorithms.

Citation Download Citation

Yury A. Gryazin "High-order approximation compact schemes for forward subsurface scattering problems", Proc. SPIE 9077, Radar Sensor Technology XVIII, 90770G (29 May 2014); https://doi.org/10.1117/12.2050189

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