The Topological Derivative Method and Artificial Neural Networks for Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of a observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions

Monitoring and Visualization of Crystallization Processes Using Electrical Resistance Tomography: CaCO3 and Sucrose Crystallization Case Studies

In the current research work, electrical resistance tomography (ERT) was employed for monitoring and visualization of crystallization processes. A first-of-its-kind MATLAB-based interactive GUI application "ERT-Vis" is presented. Two case studies involving varied crystallization methods were undertaken. The experiments were designed and performed involving calcium carbonate reactive (precipitative) crystallization for the high conductivity solution-solute media, and the cooling crystallization of sucrose representing the lower conductivity solution-solute combination. The software successfully provided key insights regarding the process in both crystallization systems. It could detect and separate the solid concentration distributions in the low as well as high conductivity solutions using the visual analytics tools provided. The performance and utility of the software were studied using a software evaluation case study involving domain experts. Participant feedback indicated that ERT-Vis software helps by reconstructing images instantaneously, interactively visualizing, and evaluating the output of the crystallization process monitoring data

The topological derivative method and artificial neural networks for numerical solution of shape inverse problems

Theme 4 - Simulation et optimisation de systemes complexes - Projet NumathSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1999 n.3739 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc