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Proceedings Paper

High-order approximation compact schemes for forward subsurface scattering problems
Author(s): Yury A. Gryazin
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Paper 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.

Paper Details

Date Published: 29 May 2014
PDF: 9 pages
Proc. SPIE 9077, Radar Sensor Technology XVIII, 90770G (29 May 2014); doi: 10.1117/12.2050189
Show Author Affiliations
Yury A. Gryazin, Idaho State Univ. (United States)


Published in SPIE Proceedings Vol. 9077:
Radar Sensor Technology XVIII
Kenneth I. Ranney; Armin Doerry, Editor(s)

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