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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 426902, 12 pages
Research Article

A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem

1Electrical Geodesics, Inc., Eugene, OR 97403, USA
2Department of Computer and Information Science, 1202 University of Oregon, Eugene, OR 97403, USA
3Department of Mathematics and Mechanics, Belarusian State University, 220050 Minsk, Belarus

Received 28 September 2013; Revised 25 November 2013; Accepted 26 November 2013; Published 12 January 2014

Academic Editor: Jianlong Qiu

Copyright © 2014 Sergei Turovets et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.