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This paper presents a general method to associate the operator splitting for the Peaceman-Rachford procedure with a decomposition of the domain in problems arising from finite element discretization of partial differential equations. The algorithm is provably convergent without any symmetry requirement. Moreover, this method possesses the significant advantage of making the linear systems of the Peaceman-Rachford iteration block diagonal and therefore perfectly appropriate for parallel processing. Not only is sparsity not affected but a reduction of the bandwidth occurs. In fact, for appropriate choices of nonconforming finite element spaces, this method makes directly possible elementwise processing. This option remains available in general for higher-dimensional problems by applying the splitting algorithm recursively. Practical implementation requires nothing more than the standard finite element assembly procedure and some bookkeeping to relate a few different orderings of the nodes. In addition to all these attractive features, the method is rapidly convergent and remains highly competitive even when used on a serial machine. [ABSTRACT FROM AUTHOR]

In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of these algorithms with those presented by Bova and Carey (1992). Although both of the meshes are very similar, the current algorithms automatically build and manage sequences of nested irregular discretizations of the domain. The author illustrates here how the application of IFS families is equivalent to the use of an adaptive strategy that combines the refinement procedure with the derefinement one. [ABSTRACT FROM AUTHOR]

A 2D electrical impedance tomography (EIT) system has been developed at Duke University as an experimental system to test the forward and inverse algorithms for EIT application. The forward model is based on the 2nd-order finite element method (FEM), while the image reconstruction is based on the distorted Born iterative method (DBIM). The major contributions of this work are the application of the higher-order FEM as a forward solver, and the DBIM as an inverse solver to the integrated EIT system. The forward model has been validated with the measured data to within 0.5% accuracy. Excellent images have been reconstructed with these collected EIT data sets. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2989–2998, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22938 [ABSTRACT FROM AUTHOR]