Finite elements and anisotropic EIT reconstruction

Anisotropic Reenement Algorithms for Finite Elements

Error estimates for anisotropic finite elements and applications

The finite element method is one of the most frequently used techniques to approximate the solution of partial differential equations. It consists in approximating the unknown solution by functions which are polynomials on each element of a given partition of the domain, made of triangles or quadrilaterals (or their generalizations to higher dimensions). A fundamental problem is to estimate the...

Developments in EIT Reconstruction Algorithms

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or “inverse crimes” to avoid.

Anisotropic finite elements for the transient transport equation

Grating Profile Reconstruction Based on Finite Elements and Optimization Techniques

We consider the inverse diffraction problem to recover a two-dimensional periodic structure from scattered waves measured above and beneath the structure. The task is reformulated in form of an optimization problem including special regularization terms. The solvability and the dependence on the parameter of regularization is analyzed. Numerical results for synthetic data demonstrate the practi...