SPARSE MATRIX METHODS FOR USE IN ELECTRICAL IMPEDANCE TOMOGRAPHY

The objective of electrical impedance tomography is to reconstruct images representing the electrical impedance properties within a region from measurements on its surface. The region of interest is usually Þrst discretized into Þnite elements and its impedance distribution updated using an iterative process. This iterative process comprises two problems: the forward problem and the inverse problem. The inverse problem is the term given to the procedure to Þnd the internal impedance distribution from a set of boundary measurements, and the forward problem is the determination of the internal voltages given the impedance distribution and boundary conditions. In this paper several Þnite element labelling algorithms, implemented by the authors in C, are investigated and their impact on the forward problem solver e¦ciency analysed. The algorithms investigated are: Nested Dissection (ND), Minimum Degree (MDG), Minimum DeÞciency (MDF) and Simulated Annealing for Fill-in (SAFR) Reduction during Cholesky Factorization. These renumbering strategies were applied to a collection of representative two-dimensional meshes used in electrical impedance tomography and a number of sparse symmetric matrices from the HarwellÐBoeing sparse matrix collection for comparison purposes